College of Arts and Sciences

# Archived BC Mathematics Seminars

## department of mathematics

### 2012-2013 Seminars and Colloquia

#### BC-MIT Number Theory Seminar

 October 16, 2012 at BC 9 Lake Street, room 100 Directions Jeff Hoffstein (Brown University) Title: Multiple Dirichlet series and shifted convolutions, with applications to number theory Sujatha Ramdorai (University of British Columbia) Title: Congruences and Noncommutative Iwasawa theory November 13, 2012 at MIT, room 4-163 Jim Cogdell (Ohio State University) Title: The local Langlands correspondence for GL(n) and the symmetric and exterior square epsilon–factors Yuri Tschinkel (New York University) Title: Igusa integrals December 4, 2012 at BC, McGuinn 521 Richard Taylor (Institute for Advanced Study) Title: Galois representations for regular algebraic cuspidal automorphic forms 3:00 - 4:00 p.m., McGuinn 521 Max Lieblich (University of Washington) Title: Recent results on supersingular K3 surfaces 4:30 - 5:30 p.m., McGuinn 521 February 5, 2013 at MIT, room 10-250 Abhinav Kumar (MIT) Title: Real multiplication abelian surfaces with everywhere good reduction Felipe Voloch (University of Texas) Title: Local-global principles in the moduli space of abelian varieties and Galois representations March 19, 2013 at BC, Fulton 220 Andrew Granville (Universite' de Montre'al) Title: A different way to use Perron's formula Michael Zieve (University of Michigan) Title: Polynomial mappings of number fields April 9, 2013 at MIT, room 32-144 Frank Calegari (Northwestern) Title: The cohomology of congruence subgroups of SL_N(Z) for large N and algebraic K-theory Rachel Pries (Colorado State University) Title: The geometry of the p-rank stratification of the moduli space of curves

#### BC Distinguished Lecturer in Mathematics series

Distinguished Lecturer: Dr. Bernd Sturmfels,
Professor of Mathematics, Statistics and Computer Science
University of California, Berkeley

##### Lecture 1: April 23, 2013

7:00 p.m. in Merkert 127

Title: Tropical Mathematics

Abstract: In tropical arithmetic, the sum of two numbers is their maximum and the product of two numbers is their usual sum. Many results familiar from algebra and geometry, including the Quadratic Formula and the Fundamental Theorem of Algebra, continue to hold in the tropical world. In this lecture we learn how to draw tropical curves and why evolutionary biologists might care about this.

##### Lecture 2: April 24, 2013

4:30 p.m. in Fulton 115

Title: The Convex Hull of a Space Curve

Abstract: The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We express the degree of this surface in terms of the degree, genus and singularities of the curve. We present methods for computing their  defining polynomials, and we exhibit a wide range of examples. Most of these are innocent-looking trigonometic curves such as (cos(t),sin(2t),cos(3t)). This is joint work with Kristian Ranestad.

##### Lecture 3: April 25, 2013

4:30 p.m. in Fulton 145

Title: Non-negative Polynomials versus Sums of Squares

Abstract: We discuss the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be Noether-Lefschetz loci of K3 surfaces. The projective duals of these hypersurfaces are defined by rank constraints on Hankel matrices. We compute their degrees using numerical algebraic geometry, thereby verifying results due to Maulik and Pandharipande. The non-SOS extreme rays of the two cones of non-negative forms are parametrized respectively by the Severi variety of plane rational sextics and by the variety of quartic symmetroids. This lecture is based on work of Greg Blekherman, and a joint paper with Jonathan Hauenstein, John Christian Ottem and Kristian Ranestad.

#### BC Math Society/Mathematics Department Undergraduate Lectures

BCMS Careers in Mathematics Series
"Careers in Mathematics: A Panel Discussion
Tuesday, November 13, 5:30 p.m.
Location: 9 Lake Street, Room 100

January 30, 2013
Information Session on Summer REUs
Carney 309, 4:00 p.m.

March 14, 2013
Pi Day
Special Events, 12:00 noon, Carney 309

BCMS Careers in Mathematics Series
April 3, 2013, 5:006:00 pm., Stokes S117
Mike Brown (US Navy)
"Careers in Mathematics:  Cybersecurity"

#### BC Geometry/Topology Seminar

Schedule for the BC Geometry/Topology Seminar

Organizers: Ian Biringer, Eli Grigsby, Joshua Greene

#### BC Number Theory/Algebraic Geometry Seminar

Schedule for the BC Number Theory/Algebraic Geometry Seminar

Organizers: Avner Ash, Dawei Chen, Marksym Fedorchuk, Sol Friedberg, Ben Howard, Dubi Kelmer

#### BC Colloquium Series

To be determined.

The Mathematical Gazette is published weekly by the Worcester Polytechnic Institute Mathematical Sciences Department. It provides a list of mathematical seminars and colloquia in the Massachusetts area.

### 2012-2013 Seminar Schedule

Seminars will meet roughly monthly on Thursdays from 2:00 p.m. to 3:30 p.m.

##### Thursday, October 4, 2012, 2:00 p.m.
 Place: Campion 139 Speaker: Prof. Hung-Hsi Wu (U. of California - Berkeley) Title: The School Mathematics Curriculum: 1975-2012 Abstract: This talk will discuss the ups and downs of the school math curriculum roughly between 1975 (beginning of Back to Basics) and 2010 (release of Common Core Standards), and what lies ahead beginning with 2010. Although the period 1975-2010 includes the Math Wars, it is not generally recognized that there is a common thread that runs through the curriculum of this period, namely, inattention to mathematical integrity. The talk will look at key examples of this curriculum of 1975-2010, and explain why it is basically not learnable. But can the Common Core live up to its promise

##### Thursday, November 29, 2012, 2:00 p.m.
 Place: Campion 139 Speaker: Al Cuoco (Director, Center for Mathematics Education, EDC) Title: Mathematics for Teaching: Suggestions for the Mathematical Preparation and Professional Development of Secondary Teachers. Abstract: Based on work with secondary teachers, on my own high school teaching experience, and on the new CBMS report "The Mathematical Preparation of Teachers,'' I'll give some examples from undergraduate mathematics that have useful applications to middle and high school teaching. Some of these applications help connect topics in the pre-college curriculum with major themes in mathematics, while others are useful tools for teachers as they plan lessons, design problems, or develop ideas. Part of the talk will describe my joint work with Joseph Rotman (University of Illinois at Urbana-Champaign) to develop an abstract algebra course that addresses some needs of prospective high school teachers.

##### Thursday, March 14, 2013, 2:00 p.m.
 Place: Campion 139 Speaker: Prof. Patricio Herbst (University of Michigan) Title: Conceptualizing and Measuring Teachers' Recognition of the Diagrammatic Register Abstract The presentation of proof problems in American high school geometry is semiotically different than what it used to be in the 1870s when proof problems started to appear in geometry textbooks and also different than the problems that might be assigned in geometry-for-teachers classes at the university. In earlier work we've described the presentation of those problems as relying on a diagrammatic register and proposed that it is a norm of the instructional situation of "doing proofs" for the teacher to present those problems using the diagrammatic register. Important consequences of the existence of such norm include (1) that a range of geometric properties (collinearity, concurrence, separation) are alienated from the proof problems that students do, and (2) that students' interactions with diagrams remains distal (hence they are unlikely to incorporate into a proof objects that were not provided with the problem). One might think that just coming up with a more diverse set of proof problems would help improve students' mathematical experience but if the proposition that the diagrammatic register is normative were true there might be a resistance to other proof problems—perhaps the norm is in place to prevent instructional problems that might arise otherwise?The problem space described above is one that the GRIP research group has been involved in in the context of a larger project where we investigate how to study empirically the norms of mathematics instruction using multimedia and the internet. What does the proposition that the diagrammatic register is normative mean and how can it be studied empirically? What is the likelihood that practitioners would appraise positively a departure from the norm and how might they justify it? In the talk I describe efforts to develop measures of teachers' recognition of this instructional norm both using traditional survey like instruments and multimedia questionnaires. I show how this instrument development process helped improved our conceptualization of the notion of a "diagrammatic register." The presentation illustrates how representations of instructional practice can be involved in the design of research instruments that preserve attention to the mathematics of classroom interaction and the complexities of teaching practice.

##### Thursday, March 21, 2013, 2:00 p.m.
 Place: Campion 139 Speaker: Prof. Jacqueline Leonard (University of Denver) Title: Learning to Enact Social Justice Pedagogy in Early Childhood and Elementary Mathematics Classrooms Abstract: Some mathematics educators (e.g., Bartell (2012); Frankenstein (2012); Gonzalez (2009); Gutstein (2006); Stinson (2004)) assert that P-12 students respond better to mathematics when it is taught for culturally relevance and social justice. Providing teachers with examples of how to use culturally relevant pedagogy (CRP) and social justice pedagogy (SJP) is critical to enacting these strategies in mathematics classrooms. The results of this teacher-research study reveal that teacher candidates (TCs) had greater understanding about how to teach for social justice after taking a mathematics education course that used literature circles to learn and understand SJP. We also found that mathematics lesson plans aligned well with principles of teaching for social justice and that target TCs’ beliefs about teaching for social justice were malleable. However, additional studies are warranted to determine if activities like the ones described in this study actually lead to changes in classroom practice.

##### Friday, April 12, 2013, 2:00 p.m.
 Place: Campion 139 Speaker: Prof. Roger Howe (Yale) Title: Problematics of Functions Abstract: Calls for an emphasis on functions as a basic theme in K-12 mathematics have come from many quarters, and curricula, even elementary curricula, have been developed that give functions a prominent role. They also feature in the Common Core State Standards for Mathematics. However, the concept of function is not a simple one, and many, perhaps most, of the treatments of functions at the K-12 level have significant flaws. This talk will discuss some observed errors in dealing with functions, some of the questions that arise in dealing with them, and will make some tentative proposals about their role in K-12 mathematics.

### 2011-2012 Seminar Schedule

##### Mathematics Education Seminar

October 27, 2011
Location: Campion 139
Title: Mostly Geometry with Some Algebra
Abstract
: Geometry is the part of school mathematics which is most in need of help. We will start with rectangles and triangles in late elementary school and show how some of the ideas used there can be used again in high school. The algebra part will involve setting up an algebraic version of a geometry problem, solving it and getting a surprising result, and then doing the same with another problem and also getting a surprising result. In both cases, factoring turns out to be very useful.

December 7, 2011
Dan Chazan (University of Maryland)
Location: Campion 139
Special time: 12:00 p.m. to 1:30 p.m.
Title: New Technologies and Challenges in Depicting and Discussing Teaching
Abstract: Teaching can be conceptualized as the ephemeral, time-bound activity that happens in classrooms among teachers, students, and the subject matter that is taught. A key challenge in discussing teaching is how to transcend the particular in order to have practitioners talk across differences of context (e.g., school, students, curricula, …). In this presentation, I’ll use analogies to representations of mathematics used in the high school algebra and geometry curriculum to consider how non-fictional videotapes of actual classroom interaction and fictional animations depicting scenes from classrooms can support talk about teaching. Examples will come from both research, the NSF-funded Thought Experiments in Mathematics Teaching (ThEMaT) project, and from professional development initiatives, the National Council of Teachers of Mathematics (NCTM)’s nascent Digital Library of Practice.

March 22, 2012
Natasha Speer (University of Maine)
Location: Campion 139
Title: Definitions of mathematical knowledge for teaching: Using these constructs in research on secondary and college mathematics teachers.
Abstract: The construct  “mathematical knowledge for teaching” (MKT) has received considerable attention in the mathematics education community over the past decade. Much effort has been put towards the delineation and definition of particular types of knowledge used and needed by mathematics teachers, including Common Content Knowledge (CCK) and Specialized Content Knowledge (SCK). The various lines of research have yielded important and useful findings.

These efforts have been pursued almost exclusively in the context of elementary mathematics teaching. But what happens when researchers look instead at secondary or post-secondary teachers? Do these descriptions of various types of knowledge fit as well with data from non-elementary contexts given differences in background and content knowledge typically possessed by these populations of teachers?

I will present some theoretical questions that arose when using definitions of CCK and SCK in investigations into the nature of MKT at secondary and undergraduate levels. These questions will be illustrated with data from two mathematics instructional settings.

April 19, 2012
William McCallum (University of Arizona)
Location
: Campion 139
Title:
Illustrative Mathematics: Building a discerning community of mathematics educators.
Abstract:
Illustrative Mathematics (illustrativemathematics.org) provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards. Equally important, it is building a discerning community that can discuss, critique, and revise tasks. I will discuss the project and engage the audience in examples of the work the community is carrying out.

##### BC-MIT Number Theory Seminar

Organizers: Sol Friedberg and Ben Howard at BC, and Ben Brubaker and Bjorn Poonen at MIT.

 September 20, 2011 at BC - 9 Lake Street, Room 035 Directions 3:00–4:00 p.m. Marie-France Vigneras (Jussieu) Title: From $p$-adic Galois representations to $G$-equivariant sheaves on the flag variety $G/P$ 4:30–5:30 p.m. Kristin Lauter (Microsoft Research) Title: Arithmetic Intersection Theory on the Siegel Moduli Space October 18, 2011 at MIT, Room 2-132 3:00–4:00 p.m. Fernando Rodriguez Villegas (University of Texas at Austin) Title: Hypergeometric motives: the case of Artin L-functions 4:00–4:30 p.m. Xinyi Yuan (Princeton University) Title: On the height of the Gross-Schoen cycle November 15, 2011 at BC, McGuinn 521 Brian Conrey (AIM) Title: A reciprocity formula for a cotangent sum Steven D. Miller (Rutgers) Title: Fourier Coefficients of Automorphic Forms on Exceptional Groups February 14, 2012 at MIT, Room 3-333 Dihua Jiang (Minnesota) Title: Constructions of Cuspidal Automorphic Forms for Classical Groups Wenzhi Luo (Ohio State) Title: Asymptotic Variance for the Linnik Distribution March 20, 2012 at BC, McGuinn 521 3:00 - 4:00 p.m. Kannan Soundararajan (Stanford) Title: Moments and the distribution of values of L-functions 4:30 - 5:30 p.m. Samit Dasgupta (UC Santa Cruz) Title: On the p-adic L-functions of totally real fields. April 3, 2012 at MIT, Room 3-333 Wen-Ching Winnie Li (Penn State) Title: Recent progress on noncongruence modular forms Alex Kontorovich (Yale) Title: On Zaremba's Conjecture

##### BC Distinguished Lecturer in Mathematics series
 April 18, 2012 3:00–4:00 p.m. McGuinn 121 Robert Grist, University of Pennsylvania Talk 1 (general audience) Title: The Mathematics of Holes Abstract: Mathematics merely begins with the study of numbers; it advances to motions and machines; computations and colorings; the strings and arrows of life. A singular expression of the beauty and power of Mathematics is revealed in its ability to quantify and qualify that which is not there—the holes. This talk introduces `topology'—the mathematical study of holes—and uses a century's worth of its innovations to explain why your cell phone drops calls, how to survive without GPS, and why you can't find good, cheap, healthy fast-food. April 19, 2012 4:00–5:00 p.m. Cushing 209 Talk 2 (colloquial) Title: Euler Calculus Abstract: This colloquium surveys a surprisingly beautiful integral calculus based on Euler characteristic, with a focus on computations and applications to problems of network data aggregation. April 20, 2012 4:00–5:00 p.m. Fulton 145 Talk 3 (specialized) Title: Sheaves and Data Abstract: Algebraic topology invented sheaves as a tool for integrating local data into a global structure. This talk will give an introduction to constructible sheaves; their (co)homology; and, most importantly, their recent applications to problems in optimization, networks, and sensing.

##### BC Math Society/Mathematics Department Undergraduate Lectures
 September 26 4:00–5:00 p.m. Carney 102 Dr. Paul Garvey, Chief Scientist, MITRE Corporation Title: "Evaluating Risky Prospects, with a little Calculus" October 12 Noon Carney 309 Math for America Info Session November 17 4:30–5:30 p.m. Carney 102 Frank Sullivan (Boston College Alumnus) Title: "On the role of mathematics in my career" February 16 4:30 p.m. Devlin 227 Speaker: Puneet Batra Title: "The Science Behind Big Data" Abstract: Thousands of organizations now have the means to collect extreme amounts of data per year, from petabyes to exabytes. This explosion of 'Big Data' has led to a number of new insights, from Facebook's 'People You May Know' to algorithms that optimize drug choice for new cancer patients. The Big Data revolution has been driven by analyses on consumer behavior, web traffic, machine logs, cell-phone traffic and healthcare data. In this talk, I'll discuss some of the mathematical and statistical tools that data scientists use to derive meaningful results from 'Big Data' using some concrete examples from services that we've all used, including netflix and facebook. March 29 5:45 p.m.  McGuinn 521 Speaker: Steven J. Miller Title: "Pythagoras at the Bat: An Introduction to Statistics and Modeling" Abstract: Let RS (resp., RA) denote the average number of runs scored (resp., allowed) in a baseball game by a team. It was numerically observed years ago that a good predictor of a team's won-loss percentage is RS^2 / (RS^2 + RA^2), though no one knew WHY the formula worked. We review elementary concepts of probability and statistics, and discuss how one can build and solve a model for this problem. We'll discuss how to attack problems like this in general (what are the features of a good model, how to solve it, and so on). The only pre-requisite is simple calculus (no baseball knowledge is required, though Red Sox knowledge is always a plus).

##### BC Geometry/Topology Seminar

Schedule for the BC Geometry/Topology Seminar

##### BC Number Theory/Algebraic Geometry Seminar

Schedule for the BC Number Theory/Algebraic Geometry Seminar

Organizers: Avner Ash, Dubi Kelmer, Rob Gross

##### BC Colloquium Series
 October 13 2:30 – 3:30 p.m. Carney 309 Speaker: Izzet Coskun, University of Illinois, Chicago Title: Pictures and homogeneous spaces Abstract: Many important problems in representation theory have analogues in geometry. For example, decomposing tensor products of representations of GL(n) into irreducible representations is very closely tied to the geometry of the Grassmannian. Similarly, studying the restriction of a representation of GL(n) to subgroups such as SO(n) or SP(n) has geometric analogues in terms of the geometry of flag varieties. In this talk, I will show you how drawing a few  pictures can make studying such lofty problems a lot of fun. I will specifically concentrate on Littlewood-Richardson rules and geometric branching rules. I intend to make the talk accessible to anyone who is willing to be seduced by pictures. October 27 4:00 – 5:00 p.m. Fulton 230 Speaker: Richard Askey, University of Wisconsin Title: The binomial theorem, beta and gamma functions, and some extensions of each. Abstract: It is well known that the number of permutations of the set 1,2,...,n is n!. An extension of this where one counts inversions was posed as a problem by M. Stern in 1839. These will be the starting place to build up the binomial theorem, the extension of n! which we now write as the gamma function, the beta integral of John Wallis, Euler's integral representation of the gamma function as an integral, and the connection between these three things. This connection will be looked at in two different settings, the classical one which most of you know reasonable well, and what will be called q-extensions of these classical results into a world which has finally started to come into its own. November 9,  4.00 – 5.00 p.m. Carney 309 Speaker: András Stipsicz (Rényi Institute of Mathematics) Title:  3-dimensional contact topology Abstract: After reviewing results about the existence of tight contact structures on closed 3-manifolds, we show how to use Heegaard Floer theory (in particular, the contact Ozsvath-Szabo invariant) to verify tightness of certain contact structures on 3-maniolds given by surgery along specific knots in S^3 November 17,  2:30 – 3:30 p.m Carney 309 Speaker: Joseph Harris, (Harvard University) Title:  Title: The Interpolation Problem Abstract: See here. December 7,  4:15 – 5:15 p.m. Carney 309 Speaker: Ian Agol, (University of California, Berkeley) Title: Virtual properties of 3-manifolds Abstract: In his article "3-Dimensional manifolds, Kleinian groups, and hyperbolic geometry", William Thurston posed 24 problems related to the topology and geometry of Kleinian groups and hyperbolic 3-manifolds. We'll discuss four of the remaining open problems from this list, 15-18, having to do principally with finite-sheeted covers of hyperbolic 3-manifolds. We'll discuss how recent work of Kahn-Markovic and Wise implies that these problems are essentially equivalent, and the prospects for answering these questions combining their results. March 14, 2012 3:00 – 4:00 pm Carney 309 Speaker: Martin Moeller (Frankfurt) Title: Fuchsian differential equations and derivatives of theta functions Abstract: Usually the power series expansion of solutions to a Fuchsian differential equation with integral coefficients has huge denominators. One instance when the solution is actually integral was discovered by Apery and gave a proof of the irrationality of Zeta(3). We give another instance of such a special Fuchsian differential equation with integral expansion. It is related to derivatives of Hilbert theta functions. The proofs connect (Hilbert) modular forms to the geometry of billard tables. March 28, 2012 3:00 – 4:00 pm Carney 309 Speaker: Chen-Yu Chi (Harvard) Title: On the L^1-norm on the space of quadratic differentials Abstract: The spaces of quadratic differentials play essential roles in the studies of Riemann surfaces and their moduli spaces. Each of these spaces is equipped with a canonical norm. In 1971, Royden shows that two closed Riemann surfaces of genus greater than 1 are isomorphic if and only if their spaces of quadratic differentials are isometric with respect to their canonical norms. We will first review Royden's proof and then outline a program initiated in a joint-work with Yau which can be regarded as further developments in higher dimensions along the same direction. If time permits, we will also talk about a recent observation due to Stergios Antonakoudis. April 24, 2012 4:00 – 5:00 pm Carney 309 Speaker: Peter Kronheimer (Harvard) Title: Knots, webs and unitary representations Abstract: A basic invariant of a knot K in 3-space is the fundamental group, Π, of the knot complement; and a basic way to study any group such as Π is to look at its representations in a standard group G, such as a permutation group or a linear group. In the case of knot groups, representations of Π in dihedral groups contain information encoded in the Alexander polynomial of the knot. Already when we look at the case G=U(2), something emerges from the deep: if K is non-trivial then there always exists at least one non-abelian representation of Π in U(2). The proof of this result involves taking a distinguished set representations of Π in U(2) and assembling them to form an invariant of the knot K -- its instanton Floer homology group -- with surprising connections to both the Alexander polynomial and the Khovanov homology of the knot. In this talk, we will introduce some of these concepts, and look a little past the group U(2) to the case of U(N). In this case, it is natural to extend our objects of study, from knots to "webs", and to seek connections with the knot homology groups defined by Khovanov and Rozansky. May 3, 2012 3:00 – 4:00 pm Carney 309 Speaker: John Etnyre (Georgia Tech) Title: Curvature and (contact) topology Abstract: Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it.  This is joint work with Rafal Komendarczyk and Patrick Massot.

### 2010-2011 Seminar Schedule

Seminars will meet roughly monthly on Thursdays from 2:00-3:00 p.m.

• November 4, Cushing 332
Prof. Katherine Merseth (Harvard) and Erica Litke (Harvard)
"Mathematical Tasks in the Secondary Classroom: The Development of an Analytic Tool"
• December 2, Fulton 513
Prof. Man Goo Park (Seoul National University of Education)
"Teaching and Learning Mathematics: Focused on Korean Case"
• February 3, Campion 139  Cancelled
Prof. William McCallum (Arizona)
"Preparing for the Common Core"
Abstract: When there were 50 different sets of state standards, there was an incentive for universities to keep teacher preparation program generic in order to prepare their students for a wide variety of curricular. Now, with over 40 states adopting the Common Core State Standards in Mathematics, universities have an opportunity as never before to develop focused teacher preparation programs based on consensus about what students should learn and when. I will present some thoughts on key focus areas and engage the audience present their own thoughts.
• February 17, Campion 139
Prof. William Schmidt (Michigan State University)
“Inequality for all: Why America needs Common Core Math Standards”
Abstract: Over 40 states have now officially adopted the Common Core Mathematics Standards. They must now be implemented into classrooms where the cultural and structural context may not be particularly supportive. This presentation focuses on what that context looks like and why, if not addressed, it could become the Achilles heel of what I believe is the best opportunity for improving mathematics learning for all students.
• March 24, Fulton 513  Cancelled
Dr. Liping Ma (Palo Alto)
• April 28, Campion 139
Prof. Karen King (NYU)
"The Impact on Student Achievement of Teachers' Use of Standards Based Instructional Materials"
Abstract: This effectiveness study explores the relationship between the use and adaptation of the Connected Mathematics Project instructional materials by middle grades teachers in an urban school district and their students’ achievement. All middle grades mathematics teachers in Newark, NJ Public Schools were surveyed using the Surveys of Enacted Curriculum and the CMP Implementation Survey. The 6th, 7th, and 8th grade students in these teachers’ first period classes completed the New Jersey Assessment of Knowledge and Skills for their grade.  Using hierarchical linear modeling with two levels, we found that both increased use and adaptation of the instructional materials were related to increased student achievement. Implications for further research on instructional materials implementation and the design and implementation of materials are discussed.
##### BC-MIT Number Theory Seminar

The organizers are Sol Friedberg and Ben Howard at BC, and Ben Brubaker and Bjorn Poonen at MIT.

 2010-2011 Tuesday, September 21 MIT - Room 56-114 Map of MIT 3:00 p.m. Kai-Wen Lan - Princeton/IAS "Vanishing theorems for torsion automorphic sheaves" abstract 4:30 p.m. Michael Rapoport - Bonn "The Langlands-Kottwitz method for the zeta function, beyond the parahoric case" abstract Tuesday, October 19 BC - 9 Lake Street, Room 035 (north of Commonwealth Avenue near the "B" line) Directions 3:00 p.m. Eyal Goren - McGill “Canonical subgroups over Hilbert modular varieties” abstract 4:30 p.m. Pierre Colmez - Jussieu “On the p-adic local Langlands correspondence for GL2” Tuesday, November 16 MIT - Room 56-114 Map of MIT 3:00 p.m. Brian Smithling - Toronto “On some local models for Shimura varieties” abstract 4:30 p.m. Matt Baker - Georgia Tech “Tropical and Berkovich analytic curves” abstract Tuesday, February 8 BC - Campion 009 Note room change Directions 3:00 p.m. Amanda Folsom - Yale "ell-adic properties of the partition function" abstract 4:30 p.m. Jordan Ellenberg - Wisconsin "Expander graphs, gonality, and Galois representations" abstract Tuesday, March 1 MIT - 4-159 Map of MIT 3:00 p.m. Michael Harris - Jussieu "The Taylor-Wiles Method for Coherent Cohomology" abstract 4:30 p.m. Laurent Clozel - Orsay “Presentation of the Iwasawa algebra of Gamma_1 SL_(2, Z_p)” abstract Tuesday, April 12 BC - Campion 009 Note room change Directions 3:00 p.m. Freydoon Shahidi - Purdue "Arthur Packets and the Ramanujan Conjecture" abstract 4:30 p.m. William Duke - UCLA “The interpretation and  distribution of cycle integrals of modular functions” abstract
##### BC Distinguished Lecturer in Mathematics series

The distinguished number theorist Peter Sarnak, Eugene Higgins Professor of Mathematics at Princeton University and permanent member of the Institute for Advanced Study's School of Mathematics, is the fourth annual Boston College Distinguished Lecturer in Mathematics. Prof. Sarnak was awarded the Polya Prize of the Society of Industrial & Applied Mathematics in 1998, the Ostrowski Prize in 2001, the Levi L. Conant Prize in 2003 and the Frank Nelson Cole Prize in Number Theory in 2005. He was elected a member of the National Academy of Sciences (USA) and Fellow of the Royal Society (UK) in 2002. Prof. Sarnak gave 3 lectures April 4-6, 2011, and met with Boston College students and faculty during his visit. For event pictures, please click here.

 Monday, April 4 5:00-6:00 p.m. Devlin 008 "Randomness in Number Theory" Tuesday, April 5 4:00-5:00 p.m. Cushing 209 "Thin groups and the affine sieve" Wednesday, April 6 4:15-5:15 p.m. Fulton 115 "Zeros of modular forms and ovals of random real projective curves"

##### BC Math Society/Mathematics Department Undergraduate Lecture
 Thursday, April 14 5:00-6:00 p.m. Carney 309 A recent BC graduate from the NSA's Women in Mathematics Society will speak on "The Secret Lives of Mathematicians: Defending the Nation In A Pair of Chuck Taylors."

##### BC Geometry and Topology Seminar
 Thursday, September 16 Carney 309 2:00 p.m. Professor Martin Bridgeman (Boston College) will speak on “The orthospectra of finite volume hyperbolic manifolds with totally geodesic boundary and associated volume identities.” Abstract: Given a finite volume hyperbolic n-manifold $M$ with totally geodesic boundary, an orthogeodesic of $M$ is a geodesic arc which is perpendicular to the boundary. For each dimension n, we show there is a real valued function $F_n$ such that the volume of any $M$ is the sum of values of $F_n$ on the orthospectrum (length of orthogeodesics). For $n=2$ the function $F_2$ is the Rogers L-function and the summation identities give dilogarithm identities on the Moduli space of surfaces. Thursday, September 23 Carney 309 2:00 p.m. Professor Daniel Mathews (Boston College) will speak on “Sutured topological quantum field theory and contact elements in sutured Floer homology.” Abstract: We consider a type of topological quantum field theory, a “sutured TQFT”, inspired by the work of Honda-Kazez--Matic on sutured Floer homology: contact elements in the sutured Floer homology of product manifolds forms a sutured TQFT. This theory has curious connections to structures seen in physics and representation theory. As an application, we obtain a “contact geometry free” proof that the contact element in sutured Floer homology of a contact structure with Giroux torsion is zero. Thursday, September 30 Carney 309 2:00 p.m. Professor Genevieve Walsh (Tufts) will speak on “Knot commensurability and the Berge Conjecture.” Abstract: We discuss the problem of understanding commensurability classes of hyperbolic knots in S^3. We show that generically, there are at most three knots in a commensurability class. If there is more than one knot in such a commensurability class, the knots are fibered. We also discuss how this relates to understanding lens space surgeries along knots in lens spaces. This is joint work with M. Boileau, S. Boyer, and R. Cebanu. Thursday, October 7 Carney 309 2:00 p.m. Professor Gabriel Katz (MIT) will speak on "Topological Invariants of Gradient Flows on Manifolds with Boundary." Abstract: Let f: X —> R be a Morse function on a manifold X and v its gradient-like vector field. Classically, the topology of a closed X can be described in terms of the spaces of v-trajectories that link the singular points of f. On manifolds with boundary, the situation is somewhat different: there, a massive set of nonsingular functions is available. For such Morse data (f, v), the interactions of the gradient flow with the boundary dX take central stage. We will introduce and measure the convexity and concavity of a v-flow relative to dX. “Some manifolds are intrinsically more concave than others with respect to any gradient flow” is the main slogan of the talk. Stated differently, the intrinsic concavity of X is a reflection of its complexity. We will explain how this approach leads to new topological invariants, both of the flow v and of the manifold X. In 3D, we have a good grasp of these invariants and their connection to the classification of 3-folds. Thursday, October 14 Carney 309 2:00 p.m. Professor Refik Baykur (Brandeis) will speak on "Round handles and smooth four-manifolds." Abstract: In this talk, we will unfold the strong affiliation of round handles with smooth four-manifolds. Several essential topics that appear in the study of smooth four-manifolds, such as logarithmic transforms along tori, exotic smooth structures, cobordisms, handlebodies, broken Lefschetz fibrations, one and all, will come into play as we discuss the relevant interactions between them. Thursday, October 21 Carney 309 2:00 p.m. Professor Tao Li (Boston College) will speak on “Rank and genus of amalgamated 3-manifolds." Abstract: The rank conjecture says that, for a hyperbolic 3-manifold, the rank of its fundamental group equals its Heegaard genus. We will discuss constructions of counterexamples involving hyperbolic JSJ pieces and candidate hyperbolic counterexamples to this conjecture. Thursday, October 28 Carney 309 2:00 p.m. Professor Sucharit Sarkar (Columbia) will speak on “Grid diagrams and the Ozsvath-Szabo tau-invariant.” Abstract: The Ozsvath-Szabo knot invariant $\tau$ satisfies the inequality that $|\tau(K_1)-\tau(K_2)|\leq g$, whenever there is a genus $g$ knot cobordism joining $K_1$ to $K_2$. We will give a new proof of this fact using grid diagrams. This will lead to a new and entirely grid diagram-based proof of Milnor's conjecture that the unknotting number the torus knot $T(p,q)$ is $\frac{(p-1)(q-1)}{2}$. Thursday, November 4 Carney 309 2:00 p.m. Professor Adam Levine (Brandeis) will speak on "A Combinatorial Spanning Tree Model for Knot Floer Homology." Abstract: We provide an explicit description of complex, based on spanning trees of the black graph of a diagram of a knot K in S^3, that computes the knot Floer homology of K. The strategy is to iterate Manolescu's unoriented skein exact sequence for knot Floer homology, using twisted coefficients in a Novikov ring, to form a cube of resolutions in which the only nonzero groups correspond to the connected resolutions. This construction has intriguing similarities with Ozsvath and Szabo's spectral sequence from the reduced Khovanov homology of K to the Heegaard Floer homology of the double branched cover of K. This is joint work with John Baldwin. Thursday, November 11 Carney 309 2:00 p.m. Professor Vera Vertesi (MIT) will speak on “Invariants for Legendrian knots in Heegaard Floer Homology.” Abstract: This talk will concentrate on invariants for contact 3--manifolds in Heegaard Floer homology. They can be defined both for closed 3--manifolds, in this case they live in Heegaard Floer homology and for 3--manifolds with boundary, when the invariant is in sutured Floer homology. There are two natural generalizations of these invariants for a Legendrian knot K in a contact manifold M. One can directly generalize the definition of the contact invariant to obtain an invariant L(K), or one can take the complement of the knot, and compute the invariant for that: EH(M-K). At the end of the talk I would like to describe a map that sends EH(M-K) to L(K). This is a joint work with Andras Stipsicz. Thursday, November 18 Carney 309 2:00 p.m. Professor Joshua Greene (Columbia) will speak on “The lens space realization problem.” Abstract: I will discuss the classification of the lens spaces which arise by integral Dehn surgery along a knot in the three-sphere. A related result is that if surgery along a knot produces a connected sum of lens spaces, then the knot is either a torus knot or a cable thereof, confirming the cabling conjecture in this case. The proofs rely on Floer homology and lattice theory. Tuesday, February 8 Carney 309 4:00 p.m. Prof. Andy Cotton-Clay (Harvard) will speak on “Sharp fixed point bounds for surface symplectomorphisms in each mapping class.” Abstract: Let S be a closed, oriented surface, possibly with boundary, and consider a connected component H of the space of symplectomorphisms of S with no fixed points on the boundary. We give sharp bounds on the number of fixed points for symplectomorphisms f: S to S with f in mapping class H, both with and without nondegeneracy assumptions on the fixed points of f. These bounds often exceed those for non-area-preserving maps coming from Nielsen theory. This generalizes the Poincaré-Birkhoff fixed point theorem, which states that area-preserving twist maps of the cylinder have at least two fixed points, to arbitrary surfaces and mapping classes. For the nondegenerate case, our techniques involve Floer homology computations with certain twisted coefficients plus a method for obtaining fixed point bounds on entire symplectic mapping classes from such. In the possibly degenerate case, we additionally use quantum-cup-length-type arguments for certain cohomology operations we define on Nielsen summands of the Floer homology. Tuesday, March 1 Carney 309 4:00 p.m. Prof. Stephan Wehrli (Syracuse)will speak on "On Quiver Algebras and Floer homology." Abstract: In this talk, I will discuss a connection between certain Khovanov- and Heegaard Floer-type homology theories for knots, braids, and 3-manifolds. Specifically, I plan to explain how the bordered Floer homology bimodule associated to the branched double cover of a braid is related to a similar bimodule defined by Khovanov and Seidel. This is joint work with D. Auroux and E. Grigsby. Tuesday, March 15 Carney 309 4:00 p.m. Professor Tejas Kalelkar (Washington University, St. Louis) will speak on “Normal surfaces and incompressible surfaces in 3-manifolds.” Abstract: Let S be a surface embedded in a triangulated 3-manifold M. S is said to be normal if it intersects each tetrahedron of this triangulation 'nicely'. S is said to be incompressible if it is \pi_1 injective. Haken showed that if S is incompressible then with respect to each triangulation of M, the minimal PL-area surface isotopic to S is a normal surface. In this talk the converse will be proved, that is, if with respect to each triangulation of M, a minimal PL-area surface isotopic to S is normal then in fact S is incompressible. Tuesday, April 12 Carney 309 4:00 p.m. Professor Candice Price (University of Iowa) will speak on “A Knot Theory Application to Biology: An overview of DNA Topology.”Abstract: Abstract: There exist proteins, such as topoisomerases and recombinases, that change the topology of DNA. These changes can inhibit or aid in biological processes that involve the structure of DNA. Because the mechanism of many proteins involves interaction with double stranded DNA, applications of knot theory to problems involving these proteins have been extensively studied.  In the 1980's, DeWitt Sumners and Claus Ernst developed the tangle model of protein-DNA complexes, using the mathematics of tangles to model DNA-protein binding. An n-string tangle is a pair (B,t) where B is a 3-dimensional ball and t is a collection of n non-intersecting curves properly embedded in B. The protein is seen as the 3-ball and the DNA bound by the protein as properly embedded curves in the 3-ball. In this talk, I will give definitions and a description of the tangle model with a biological example. Tuesday, April 26 Carney 309 4:00 p.m. Professor Peter Ozsvath (MIT) will speak on “Bordered Floer homology.” Abstract: Heegaard Floer homology is an invariant, defined in joint work with Zoltan Szabo, which associates to a four-manifold, a number; to a three-manifold, a vector space; and to a four-dimensional cobordism, a morphism of vector spaces. I will describe aspects of a lower-dimensional invariant, Bordered Floer homology, defined in joint work with Robert Lipshitz and Dylan Thurston, which associates to a two-manifold, a differential graded algebra; and to a three-manifold with boundary, a module over that algebra. I will also sketch how this invariant can be used to compute parts of the higher-dimensional theory.
##### All talks are in Carney 309 at 4:00 p.m.
 Thursday, October 7 Professor Solomon Friedberg (Boston College) will speak on “Eisenstein series and crystal graphs.” Abstract: The study of the Whittaker coefficients of Eisenstein series on reductive groups led Langlands to formulate his Conjectures. But the study of Whittaker coefficients on covers of such groups has not been carried out. In this talk I present a theorem for the simplest Eisenstein series on such a cover, showing that these series may be computed in a surprising way that involves the theory of crystal graphs. Thursday, October 14 David Hansen (Boston College) will speak on "Ranks of elliptic curves over (nearly) abelian extensions" Abstract: Given a modular elliptic curve E over a number field K, the theory of L-functions provides a powerful tool for studying the rank of E over K and over varying families of extensions of K. Most results of this flavor analyze the rank of E over "vertical" towers of abelian extensions of K. I will review these results, and then explain some recent progress on the corresponding question for some interesting "horizontal" families of abelian extensions. Thursday, October 21 Professor George McNinch (Tufts/MIT) will speak on “The special fiber of a parahoric group scheme.” Abstract: Let G be a connected and reductive algebraic group over the field of fractions K of a complete discrete valuation ring A with residue field k. Bruhat and Tits have associated with G certain smooth A-group schemes P -- called parahoric group schemes -- which have generic fiber P/K = G. The special fiber P/k of such a group scheme is a linear algebraic group over k, and in general it is not reductive. In some recent work, it was proved that P/k has a Levi factor in case G splits over an unramified extension of K. Even more recently, this result was (partially) extended to cover the case where G splits over a tamely ramified extension. The talk will discuss these results and some applications. In particular, it will mention possible applications to the description of the scheme-theoretic centralizer of suitable nilpotent sections in Lie(P)(A). Thursday, October 28 Professor Avner Ash (Boston College) will speak on "Reducible Galois representations and Hecke eigenclasses." Abstract: Serre's conjecture (now a theorem) was stated for irreducible Galois representations, but it could have been stated as well for reducible ones. When Warren Sinnott and I generalized the niveau 1 case to GL(n), we stated a conjecture for irreducible and reducible Galois representations. I have proved this conjecture for direct sums of one-dimensional characters with pairwise relatively prime conductors. This talk will describe the background and proof of this theorem. Thursday, November 11 Professor Andrew Ledoan (Boston College) will speak on “Zeros of partial sums of the Riemann zeta function.” Abstract: The Riemann zeta-function zeta(s) of the complex variable is defined in the half plane Re(s) > 1 by an absolutely convergent Dirichlet series 1+1/2^s+1/3^s+...which can be continued analytically to a meromorphic function in the complex plane with solely a simple pole situated at s = 1 with residue 1. The critical strip 0< Re(s) < 1 is the most important and mysterious region for zeta(s), and much attention has been given to the right half of the strip. Although a great deal is known and conjectured about the distribution of zeros of zeta(s), little is known about the zeros of its partial sums F_X(s) = 1+1/2^s+...+1/X^s, where X>1. By the absolute convergence of the Dirichlet series one sees that, even for X not very large, F_X(s) gives (at least away from the pole) a rather good approximation to zeta(s) with a remainder which is o(1) as X goes to infinity. To be more precise, zeta(s) is well-approximated unconditionally by arbitrarily short truncations of its Dirichlet series in the region sigma>1, |s-1| > 1/10. This is also true in the right half of the critical strip, if one assumes the Lindelof Hypothesis. In this talk, I will present recent results obtained in collaboration with S. M. Gonek on the distribution of zeros of F_X(s), in which we estimate the number of zeros up to height T, the number of zeros to the right of a given vertical line, and other aspects of their horizontal distribution. Thursday, November 18 Professor Sawyer Tabony (Boston College) will speak on “Finding Representation Theory in a Statistical Mechanical Model.” Tuesday, May 3 Professor Tasho Kaletha (IAS) will speak on “Simple wild L-packets.”Abstract:  In a recent paper, Gross and Reeder have described an interesting class of smooth representations of reductive p-adic groups, which they call simple supercuspidal representations. Guided by the conjectural framework of the Langlands correspondence, they analyse the structure of the expected Langlands parameters for these representations. These so called simple wild parameters are wildly ramified, but in a minimal way. In this talk we will report on a construction which explicitly associates to each simple wild parameter a finite set of simple supercuspidal representations, and furthermore provides a description of this set in terms of the Langlands dual group.
##### BC Colloquium Series
 Tuesday, February 15 Carney 309 4:00 p.m. Prof. Benedict Gross (Harvard) will speak on "Stable orbits and the arithmetic of curves." Abstract: Manjul Bhargava has recently made a great advance in the arithmetic of elliptic curves, giving the first bounds on the average rank of the group of rational points. He shows that the average order of the 2-Selmer group is equal to 3, by studying the stable orbits of the group PGL(2,Z) acting on the lattice of binary quartic forms.  In this talk, I will begin by reviewing some basic material on elliptic curves, defining the 2-Selmer group, and describing the stable orbits in this representation, whose invariants were determined by Hermite. If time permits, I will discuss a possible generalization of Bhargava's result to hyperelliptic curveswith a rational Weierstrass point. Tuesday, February 22 Carney 309 4:00 p.m. Prof. Danny Calegari (Caltech) will speak on "Stable commutator length in free groups." Abstract: Stable commutator length (scl) answers the question: “what is the simplest surface in a given space with prescribed boundary?” where “simplest” is interpreted in topological terms. This topological deﬁnition is complemented by several equivalent deﬁnitions - in group theory, as a measure of non-commutativity of a group; and in linear programming, as the solution of a certain linear optimization problem. On the topological side, scl is concerned with questions such as computing the genus of a knot, or finding the simplest 4-manifold that bounds a given 3-manifold. On the linear programming side, scl is measured in terms of certain functions called quasimorphisms, which arise from hyperbolic geometry (negative curvature) and symplectic geometry (causal structures). I will discuss how scl in free groups is connected to such diverse phenomena as the existence of closed surface subgroups in graphs of groups, rigidity and discreteness of symplectic representations, phase locking for nonlinear oscillators, and the theory of multi-dimensional continued fractions and Klein polyhedra.

The Mathematical Gazette is published weekly by the Worcester Polytechnic Institute Mathematical Sciences Department. It provides a list of mathematical seminars and colloquia in the Massachusetts area.

##### BC-MIT Joint Number Theory Seminar

The organizers are Sol Friedberg and Ben Howard at BC, and Ben Brubaker and Bjorn Poonen at MIT.

### 2009/2010

 September 22 MIT 3:00 p.m. Yiannis Sakellaridis - University of Toronto "A 'relative' Langlands program and periods of automorphic forms" 4:30 p.m. Matthew Emerton - Northwestern University "p-adically completed cohomology and the p-adic Langlands program" October 20 BC 3:00 p.m. Ze'ev Rudnick - Tel-Aviv University and IAS "Statistics of the zeros of zeta functions over a function field" 4:30 p.m. Haruzo Hida - UCLA "Characterization of abelian components of the 'big' Hecke algebra" November 17 MIT 3:00 p.m. Akshay Venkatesh - Stanford University "Torsion in the homology of arithmetic groups" 4:30 p.m. Ken Ono - University of Wisconsin "p-adic coupling of harmonic Maass forms" February 9 BC 3:00 p.m. Gautam Chinta - CUNY "Orthogonal periods of Eisenstein series" 4:30 p.m. Mihran Papikian - Pennsylvania State University "On the arithmetic of modular varieties of D-elliptic sheaves" March 9 MIT 3:00 p.m. Elena Mantovan - Caltech "l-adic etale cohomology of PEL Shimura varieties with non-trivial coefficients" 4:30 p.m. Karl Rubin - UC Irvine "Selmer ranks of elliptic curves in families of quadratic twists" April 13 BC 3:00 p.m. Shou-Wu Zhang - Columbia University "Calabi-Yau theorem and algebraic dynamics" 4:30 p.m. Ching-Li Chai - University of Pennsylvania "CM lifting of abelian varieties"

### 2009-2010

 Professor Benson Farb (University of Chicago) will be speaking this spring as the department's third annual Boston College Distinguished Lecturer in Mathematics. Professor Farb is an internationally renowned mathematician who specializes in the interaction between geometry, topology and group theory.
 March 10 4:00 p.m. McGuinn 121 "Geometry and the Imagination (with applications)" Abstract: Geometry and geometric reasoning underlie all of science. In this talk I will explore a few fundamental geometric notions, including symmetry, dimension (including dimensions bigger than 3), and orientation (i.e. left-handed vs. right-handed). I will give some examples illustrating important applications in chemistry, biology and physics, from the weak nuclear force to understanding the Thalidomide tragedy. Some questions to ponder before the talk: How can you turn a left sneaker into a right sneaker without ripping or bending the sneaker at all? Why do mirrors reflect left/right but not up/down? This talk is intended for all who are interested in mathematics. March 11 4:00 p.m. Cushing 212 "Topology, dynamics and geometry of surfaces (and their remarkable relationships)" Abstract: Surfaces can be considered from many different angles: their shape (i.e. topological structure), their geometry (e.g. curvature), and the behavior of fluid flows on them. In this talk I will describe three beautiful theorems, one for each of these aspects of surfaces. I will also try to explain the remarkable fact that these seemingly completely different viewpoints are intimately related. This talk will be geared towards those with some familiarity with calculus. March 12 3:00 p.m. Higgins 265 "Representation theory and homological stability"Abstract: Homological stability is a remarkable phenomenon in the study of groups and spaces. For certain sequences G_n of groups, for example G_n=GL(n,Z), it states that the homology group H_i(G_n) does not depend on n for big enough n. There are many natural sequences G_n, from pure braid groups to congruence groups to Torelli groups, for which homological stability fails horribly. In these cases the rank of H_i(G_n) blows up to infinity, and in many (e.g. the latter two) cases almost nothing is known about H_i(G_n); indeed there may be no nice "closed form" for the answers. While doing some homology computations for the Torelli group, Tom Church and I found what looked to us like the shadow of a broad pattern. In order to explain it and formulate a specific conjecture, we came up with a notion of "stability of a sequence of representations of group G_n". We began to realize that this notion can be used to make other predictions: from group representations to Malcev Lie algebras to the homology of congruence groups. Some of these predicitions are known results, while others are not known. In this talk I will explain our broad conjectural picture via some of its many instances. No knowledge of either representation theory or group homology will be assumed. This talk is intended for a mathematically sophisticated audience.

### 2009-2010

 October 157:30 p.m. Dr. Paul Garvey - MITRE "MITRE and Systems Engineering"Dr. Garvey is Chief Scientist, and a Director, for the Center for Acquisition and Systems Analysis - a division at The MITRE Corporation. He is internationally recognized and widely published in cost analysis, cost uncertainty analysis, and in the application of advanced decision analytic methods to problems in engineering systems risk analysis and management. He is an alumnus of the BC Mathematics department. April 7   5:00 p.m. Carney Dr. Amir Aczel - visiting Boston College "Mathematics, Physics, and the LHC: the Largest Machine Ever Built"Abstract: In late February this year, the Large Hadron Collider at the international physics laboratory in Switzerland, CERN, began crashing protons at energy levels never seen before since the Big Bang, and will increase these levels over the next few years. The reason for this unprecedented \$10 billion effort is the search for new particles, including the mysterious Higgs boson, the so-called "God particle," believed to give all particles in the universe their mass. If the Higgs is found, along with other possible particles, this will be a major triumph not only for physics, but also for mathematics: Mathematical theories, including Lie groups, underlie much of the foundation that allows physicists to predict the existence of new particles. We will survey this fascinating topic.

#### BC Geometry and Topology Seminar

Martin Bridgeman, Eli Grigsby, Tao Li and Rob Meyerhoff conduct this seminar on the BC Campus.

### 2009-2010

#### BC Number Theory/Representation Theory Seminar

Avner Ash and Jay Pottharst conduct this seminar on the BC Campus.

### 2009-2010

 April 84:00 p.m. Carney 309 Andre Reznikov - IAS/Bar Ilan University "Gelfand pairs and identities for automorphic periods"Abstract: I will discuss how the notion of Gelfand pairs from the representation theory leads to various identities for automorphic periods. These include the classical Rankin-Selberg integral, its anisotropic analog, and many other identities. Time permitting, I will discuss some applications towards bounds for L-functions. April 153:00 p.m. Carney 309 Jens Funke - University of Durham "Spectacle cycles and modular forms of half-integral weight"Abstract: The classical Shintani lift is the adjoint of the Shimura correspondence. It realizes periods of even weight cusp forms as Fourier coefficients of a half-integral modular form. In this talk we revisit the Shintani lift from a (co)homological perspective. In particular, we extend the lift to Eisenstein series and give a geometric interpretation of this extension. This is joint work with John Millson.

#### BC Colloquium Series

Martin Bridgeman, Rob Gross, Tao Li and Jay Pottharst conduct this seminar on the BC Campus.

### 2009-2010

 October 14:00 p.m. McGuinn 521 Lounge Rob Kirby - University of California, Berkeley "Broken fibrations for 4-manifolds"Abstract: I will discuss the existence and uniqueness theorems for broken fibrations of arbitrary orientable, smooth 4-manifolds over either S^2, B^2, or S^1 x I. Existence always holds, and there is a nice set of moves relating different broken fibrations for a given 4-manifold. November 3 3:00 p.m. Carney 309 Sonal Jain - New York University "The minimum canonical height on an elliptic surface"Abstract: TBA April 27  4:00 p.m. Carney 309 Cameron Gordon - University of Texas at Austin "The unknotting number of a knot"Abstract: The unknotting number u(K) of a knot K is the minimal number of times you must allow K to pass through itself in order to unknot it. Although this is one of the oldest and most natural knot invariants, it remains mysterious. We will survey known results on u(K), including relations with 4-dimensional smooth topology, and describe some joint work with John Luecke on algebraic knots with u(K)=1. We will also discuss several open questions.

#### Mathematics Education Seminar Series

This monthly seminar series in Mathematics Education is supported by Teachers for a New Era (TNE), and is organized by Profs. Solomon Friedberg (Mathematics) and Lillie Albert (Teacher Education).

### 2009/2010

 October 8 McGuinn 334 Dr. Andrew Chen President, EduTron Corporation "Cross Cultural Lore! A session on mathematical achievement in the U.S. and abroad" October 29 McGuinn 334 Prof. Deborah Hughes Hallett University of Arizona "Literacy: Teaching the Role of Numbers and Numeracy" December 3 McGuinn 334 Prof. Paul Sally University of Chicago "Algebra Initiative in the Chicago Public Schools" February 4 Canceled Dr. Liping Ma Author, Knowing and Teaching Elementary Mathematics "The learning of fractions: How can it be built on the learning of whole numbers?" February 25 McGuinn 334 Prof. Alan Schoenfeld University of California at Berkeley "How We Think" April 15 McGuinn 521 Prof. Yeap Ban Har National Institute of Education, Nanyang Technological University, Singapore "Mathematics Teaching and Learning in Singapore Schools" April 27  McGuinn 334 Prof. Sybilla Beckmann University of Georgia "What Is Worth Focusing on in Math Courses for Elementary Teachers, and Why?

#### BC-MIT Number Theory Seminar

The organizers are Sol Friedberg and Ben Howard at BC, and Ben Brubaker and Kiran Kedlaya at MIT. Further details

### 2008/2009

 September 23 MIT 3:00 p.m. Wee Teck Gan - UC San Diego 4:30 p.m. Daniel Bump - Stanford October 28 BC 3:00 p.m. Steve Kudla - Toronto 4:30 p.m. Chris Skinner - Princeton November 18 BC 3:00 p.m. Henri Darmon - McGill 4:30 p.m. Peter Sarnak - Princeton February 17 MIT 3:00 p.m. Brooke Feigon - Toronto 4:30 p.m. Kartik Prasanna - Maryland March 17 BC 3:00 p.m. Dorian Goldfeld - Columbia 4:30 p.m. Brian Conrad - Stanford April 28 MIT Matt Papanikolas Texas A&M Dinakar Ramakrishnan Caltech

### 2008-2009

Ravi Vakil (Stanford University)

Professor Ravi Vakil will be speaking this spring as the department's second annual Boston College Distinguished Lecturer in Mathematics. Prof. Vakil is a renowned algebraic geometer who has received the Presidential Early Career Award for Scientists and Engineers, the Andre-Aisenstadt Prize from the CRM in Montreal, an American Mathematical Society Centennial Fellowship, a Frederick E. Terman fellowship, and an Alfred P. Sloan Research Fellowship. He will be the Mathematical Association of America's 2009 Hedrick Lecturer. He also received Stanford's 2004-05 Dean's Award for Distinguished Teaching and the Brown Faculty Fellowship.

 March 31 "Hidden polynomials in geometry" Abstract: A number of recent developments in geometry have hinged on unexpected polynomials appearing in geometric phenomena. Interpreted appropriately, this behavior is in retrospect visible in the doodling I did as a child. I'll use this doodle as a jumping-off point. It will lead inevitably to ideas from topology, geometry, a Hilbert problem, and the work of several Fields Medalists. Gasson Hall, Room 202 at 3:00 p.m. This talk is intended for all who are interested in mathematics. March 31 "Murphy's Law in algebraic geometry: Badly-behaved moduli spaces" Abstract: We consider the question: "How bad can the deformation space of an object be?" (Alternatively: "What singularities can appear on a moduli space?") The answer seems to be: "Unless there is some a priori reason otherwise, the deformation space can be arbitrarily bad." I show this for a number of important moduli spaces, parametrizing objects such as smooth curves in projective space, smooth projective surfaces, and plane curves with nodes and cusps. This justifies Mumford's philosophy that even moduli spaces of well-behaved objects should be arbitrarily bad unless there is an a priori reason otherwise. This is good news, not bad: we now have a complete constructive understanding of the singularities of these fundamental spaces. I will begin by telling you what "moduli spaces" and "deformation spaces" are, and then explain our question and its answer. Gasson Hall, Room 202 at 4:30 p.m. This talk is intended for a broad but mathematically sophisticated audience. April 1 "A geometric Littlewood-Richardson rule" Abstract: I will describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are 1; this is important for applications. This rule should be seen as a generalization of Pieri's rule to arbitrary Schubert classes, by way of explicit homotopies. It has a straightforward bijection to other Littlewood-Richardson rules, such as tableaux and Knutson and Tao's puzzles. This gives the first geometric proof and interpretation of the Littlewood-Richardson rule. It has a host of geometric consequences, which I may describe, time permitting. The rule also has an interpretation in K-theory, suggested by Buch, which gives an extension of puzzles to K-theory, and in fact a Littlewood-Richardson rule in equivariant K-theory (ongoing work with Knutson). The rule suggests a natural approach to the open question of finding a Littlewood-Richardson rule for the flag variety, leading to a conjecture, shown to be true up to dimension 5. Finally, the rule suggests approaches to similar open problems, such as Littlewood-Richardson rules for the symplectic Grassmannian and two-step flag varieties.  McElroy Conference Room at 3:00 p.m. This talk is intended for a mathematically sophisticated audience.

#### BC Math Society/Mathematics Department Undergraduate Lecture

 2008-2009 Thomas Banchoff (Brown University) February 25, 2009 "The Four-Dimensional Geometry and Theology of Salvador Dali" Co-sponsored by the Department of Mathematics, the Boston College Mathematics Society, the Department of Fine Arts, the Department of Theology, and the Jesuit Institute Abstract: Throughout his career, Salvador Dali was fascinated by mathematics and science, and he incorporated many geometric ideas and symbols into his paintings, especially his religious paintings. Where did he get his ideas and how did he carry them out? This presentation will feature images and stories from ten years of conversations with Dali, about the Fourth Dimension, impossible perspectives, catastrophe theory, art history and medieval philosophy. The talk will be illustrated by computer-generated images and animations, and is intended for a broad audience.

#### BC Geometry and Topology Seminar

Martin Bridgeman, and Rob Meyerhoff conduct this seminar on the BC Campus.

 September 23 Yi Ni (AIM and MIT) will speak in 251 Carney Hall at 2:00 p.m. "Dehn surgeries that reduce the Thurston norm of a fibered manifold" Abstract: Suppose K is a knot on the fiber of a surface bundle over the circle. If we do surgery on K with slope specified by the fiber, then the Thurston norm of the homology class of the fiber will decrease in the new manifold. We will show that the converse is also true. Namely, if a Dehn surgery on a winding number 0 knot in a fibered manifold reduces the Thurston norm of the homology class of the fiber, then the knot must lie on the fiber and the slope is the natural one. September 25 Scott Taylor (Colby College) will speak in 251 Carney Hall at 2:00 p.m. "Adding a 2-handle to a sutured manifold" Abstract: Sutured manifold theory has long been used to study Dehn surgery on knots in 3-manifolds. It has not often been used to study 2-handle addition, a natural generalization of Dehn surgery. If a component F of a simple 3-manifold N has genus two, sutured manifold theory is particularly effective for studying degenerating separating curves on F. (A curve is degenerating if attaching a 2-handle to it creates a non-simple 3-manifold N[a].) For example, suppose that the boundary of N consists of tori and the genus two surface F containing essential separating curves a and b. Then if N[a] is reducible and N[b] is non-simple, a and b are istopic on F. Similar sutured manifold theory techniques are useful for studying knots and links obtained by "boring" a split link or unknot. Such a perspective allows a theorem to be proved which is a generalization of two seemingly unrelated theorems. The first theorem generalized is the superadditivity of genus under band connect sum (Gabai, Scharlemann) and the second is the fact that a tunnel for a tunnel number one knot or link can be slid and isotoped to be disjoint from a minimal genus Seifert surface (Scharlemann, Thompson). As time permits, I will discuss other applications of sutured manifold theory to questions about bored split links and unknots. December 8 Yoav Moriah (Technion and Yale University) will speak in 251 Carney Hall at 3:00 p.m. "Horizontal Dehn surgery and distance of Heegaard splittings" Abstract: Given a 3-manifold M with a Heegaard surface S of genus g at least 2 and an essential simple closed curve c in S, we can obtain a new Heegaard splitting by changing the gluing of the two handlebodies/compression bodies by a Dehn twist to some power m along c. If c is "sufficiently complicated", measured a priori by a parameter n, then there is at most a single value so that the obtained Heegaard splitting is of smaller distance than n-1. Furthermore, the curves c with this property are "generic" in the set of essential simple closed curves c in S. (Joint with M. Lustig) March 17 Bill Menasco (SUNY at Buffalo) will speak in 251 Carney Hall at 1:00 p.m. "Legedrian and Lorenz knots" April 15 Elmas Irmak (Bowling Green State University) will speak in 251 Carney Hall at 1:00 p.m. "Mapping Class Groups and Complexes of Arcs on Surfaces" Abstract: I will talk about a joint work with J.D. McCarthy: Each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface, and the group of automorphisms of the arc complex is naturally isomorphic to the quotient of the extended mapping class group of the surface by its center. I will also talk about my similar results on nonorientable surfaces.

#### BC Number Theory/Representation Theory Seminar

Jay Pottharst and Mark Reeder conduct this seminar on the BC Campus.

### 2008-2009

 September 18 Mark Reeder (Boston College) will speak in 309 Carney Hall at 3:15 p.m. October 23 Benjamin Howard (Boston College) will speak in 309 Carney Hall at 3:15 p.m. November 6 Avner Ash (Boston College) will speak in 309 Carney Hall at 3:15 p.m. November 13 Jay Pottharst (Boston College) will speak in 309 Carney Hall at 3:15 p.m. April 23 Riad Masri (University of Wisconsin) will speak in 309 Carney Hall at 4:00 p.m. "Equidistribution of Heegner points and integer partitions" Abstract: A classical problem in number theory concerns the asymptotic growth of the function p(n) which counts the number of partitions of a positive integer n. This problem led Hardy and Ramanujan to invent what is now known as the "circle method". In this talk, I will explain how the equidistribution of Galois orbits of Heegner points on X_0(6) can be used to obtain a new asymptotic formula for p(n). The resulting error term sharpens those obtained by Rademacher and D.H. Lehmer in the 1930s. This is joint with Amanda Folsom.

#### BC Colloquium Series

Martin Bridgeman, Rob Gross, Ben Howard and Jay Pottharst conduct this seminar on the BC Campus.

### 2008-2009

 October 2 Dan Margalit (Tufts University) will speak in 309 Carney Hall.  Refreshments at 4:00 p.m, followed by a talk at 4:15. "Homologies of mapping class groups" Abstract: The mapping class group is the group of topological symmetries of a surface. By understanding the homology and cohomology of the mapping class group and its subgroups, we gain insight into its finiteness properties (finite generation, finite presentability, etc.) and we can also classify topological invariants of surface bundles. In this talk, we will introduce basic notions about the mapping class group and explain how to compute its low dimensional homology groups. Then, we will explain some recent work with Mladen Bestvina and Kai-Uwe Bux concerning the homology of the Torelli subgroup of the mapping class group, the group of elements acting trivially on the homology of the surface. In particular, we answer a question of Mess by proving that the cohomological dimension of the Torelli group for a genus g surface is 3g-5. November 4 Eriko Hironaka (Florida State University) will speak in 309 Carney Hall at 1:00 p.m.. "Families of mapping classes with small dilatation" Abstract: R. Penner showed that the logarithm of the least dilatation of mapping classes on an oriented genus g surface is asymptotic to 1/g. In joint work with E. Kin, we construct a sequence of mapping classes with small dilatations improving on explicit bounds found previously by Penner and Bauer. Our examples arise as mapping classes associated to labeled graphs. For such mapping classes, we discuss the relation between dilatation and the spectral radius of the graph, and show how dilatation is affected by edge subdivision. December 4 Richard Kenyon (Brown University) will speak in 309 Carney Hall.  Refreshments at 4:00 p.m, followed by a talk at 4:15. "Dimers and Harnack curves" Abstract: A polynomial P(z,w) with real coefficients is said to be Harnack if the real components of P(z,w)=0 satisfy a certain simple geometric property. These polynomials are somewhat analogous to one-variable polynomials with only real, negative roots. We describe a surprising parameterization of the space of all Harnack polynomials, coming from the dimer model of statistical mechanics. March 25 Bill Goldbloom Bloch (Wheaton College) will speak in 309 Carney Hall.  Talk at 4:30. "Navigating the Mathematical and Literary Labyrinths in Jorge Luis Borges' story "The Library of Babel" " Abstract: Jorge Luis Borges, the poet, essayist, librarian, and master crafter of short stories, was arguably the most influential writer in Spanish in the 20th century. An autodidact, he read and reread works by (among others) Bertrand Russell on the foundations and philosophy of mathematics, and these kinds of considerations explicitly directed the arcs of many of his short stories. "The Library of Babel" is perhaps his most famous story, and in its scant seven pages, he deploys simple combinatorial ideas to help create a miasmic atmosphere in the service of raising issues about the meaningfulness of our existence. The story also evokes ideas from three-dimensional manifold theory, real analysis, and graph theory; and, moreover, it is open to an interpretation from the theory of computation. This talk will touch on a number of these themes and along the way illustrate how a mathematician can become (to everyone's surprise) a literary theorist. April 7 Teruyoshi Yoshida (Harvard University and Cambridge University) will speak in 309 Carney Hall. Talk at 3:00, followed by refreshments at 4:00. "Arithmetic Geometry related to Local Langlands Correspondence" Abstract: To be announced

### 2013-2014 Seminar Schedule

Tuesday, March 11, 2014: Diane J. Briars, Ph.D.
Campion Hall, Room 139, 3:30-4:30 p.m.

Diane J. Briars, Ph.D., a mathematics education consultant, is president-elect of the National Council of Teachers of Mathematics and will serve two years (2014 and 2015) as president beginning in April 2014.

Title: Effective Teaching Practices to Ensure All Students Are “Common-Core Ready”

Abstract: What are the most effective teaching practices to ensure that all students build the conceptual understanding, procedural fluency, and proficiency in the Standards for Mathematical Practice called for in the Common Core State Standards for Mathematics? This talk describes eight research-based Mathematical Teaching Practices, along with the conditions, structures and policies needed to support them to turn the opportunity afforded by CCSSM into reality in every classroom, school and district.

Tuesday, April 29, 2014: Professor Marta Civil
Higgins Hall Auditorium, Room 300, 5:00 p.m.

Marta Civil is a Distinguished Professor of Mathematics Education at The University of North Carolina at Chapel Hill.

Title: Language, Culture and Mathematics: English Language Learners in the Mathematics Classroom

October 10, 2013: Prof. Jim Lewis (Nebraska). McGuinn 521

Title: Teaching Teachers Mathematics

Abstract: What mathematics should teachers know and how should they come to know that mathematics? The Mathematical Education of Teachers II argues that the mathematical knowledge needed for teaching differs from that of other professions and that teachers need mathematics courses that develop a solid understanding of the mathematics they will teach. The publication also urges greater involvement of mathematicians in teacher education. We will discuss the MET2 recommendations and report on efforts at the University of Nebraska-Lincoln to create mathematics courses for teachers and to work in partnership with mathematics educators to educate mathematics teachers able to educate K-12 students who graduate college and career ready.

Biography: W. James “Jim” Lewis is Aaron Douglas professor of mathematics and Director of the Center for Science, Mathematics, and Computer Education at the University of Nebraska-Lincoln. He was the Carnegie Foundation’s 2010 Nebraska Professor of the Year, and received the UNL Chancellor’s Commission on the Status of Women Award for his support of opportunities for women in the mathematical sciences.

December 5, 2013 in Campion 139

Dr. Jason Zimba (Student Achievement Partners).

Title: The Common Core State Standards for Mathematics

Description: I will speak about the design of the standards, their implications for mathematics education, and the state of implementation efforts—aiming to leave abundant time for questions.