Past BC Mathematics seminars

Thomas Banchoff (Brown University)

February 25, 2009

 "The Four-Dimensional Geometry and Theology of Salvador Dali"

Cosponsored 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.

Mark Reeder (Boston College) will speak in 309 Carney Hall at 3:15 p.m.

Benjamin Howard (Boston College) will speak in 309 Carney Hall at 3:15 p.m.

Avner Ash (Boston College) will speak in 309 Carney Hall at 3:15 p.m.

Jay Pottharst (Boston College) will speak in 309 Carney Hall at 3:15 p.m.

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.

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.

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.

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.

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.

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