Unless stated otherwise, colloquia are scheduled for Thursdays 4:30-5:30pm in LN 2205 with refreshments served from 4:00-4:25 pm in the Anderson Memorial Reading Room.
Here you find some directions to Binghamton University and the Department of Mathematical Sciences.
Thursday, March 21st, 2013
Speaker:
Robert Bieri (University of Frankfurt and Binghamton University)
Title:
Subset of the (n-1)-sphere with no balanced n-tuples.
Time:
4:30 - 5:30 pm
Room: LN-2205
Thursday, April 4th, 2013
Speaker:
Farshid Hajir (UMass Amherst)
Title:
From D=B^2-4AC to non-abelian Cohen-Lenstra heuristics.
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: In his 1801 masterpiece, *Disquisitiones Arithmeticae*, Gauss laid the foundations not only of the arithmetic theory of quadratic forms, but also of algebraic number fields in general. Most of the conjectures he made there, about the frequency of occurrence of various groups as class groups of binary quadratic forms, are still open. But in the 1980s, Cohen and Lenstra formulated a simple heuristic which "explains" Gauss's observations in terms of the theory of abelian groups. In recent joint work with Nigel Boston and Michael Bush, we study the variation of pro-p fundamental groups, generalizing the Cohen-Lenstra heuristics to a non-abelian setting. In this expository talk for a general audience, I will sketch the outlines of this work.
Thursday, April 11th, 2013
Dean's Speaker Series in Geometry/Topology
Speaker:
Yuri Zarhin (Penn State)
Title:
One-dimensional polynomial maps, periodic orbits and multipliers.
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: We study the map that sends a monic degree n complex polynomial f(x) without multiple roots to the collection of n values of its derivative at the roots of f(x). We give an answer to a question posed by Ju.S. Ilyashenko.
Thursday, April 25th, 2013
Dean's Speaker Series in Geometry/Topology
Speaker:
Robert Jerrard (University of Toronto)
Title:
Weak solutions of an equation describing vortex filaments.
Time:
4:30 - 5:30 pm
Room: LN-2205
Abstract: An old conjecture, dating back to the early 20th century, holds that vortex filaments in ideal fluids in certain limits can be described by a geometric evolution equation called the binormal curvature flow. Smooth solutions of the binormal curvature flow are mostly well-understood. However, it is interesting and possibly useful to study rough solutions as well, for a couple of (probably orthogonal) reasons: because non-smooth vortex filaments may occur in physical fluids, and because some rough solutions of the binormal curvature flow are conjectured to exhibit very rich, peculiar (and probably nonphysical) behavior with surprising number-theoretic properties. This talk will describe the history of some of these conjectures, which remain completely open, as well as a recent proposal for a notion of very weak solutions of the binormal curvature flow which reveals some previously unexpected stability properties.
Wednesday, May 1st, 2013 [Note unsuaul day of the week! ]
Dean's Speaker Series in Geometry/Topology
Speaker:
Allan Greenleaf (Rochester)
Title:
Is there a general theory of Fourier integral operators?.
Time:
4:40 - 5:40 pm
Room: LN-2205
Abstract: Fourier integral operators (FIOs) are fundamental tools in the analysis of linear partial differential equations. FIOs can, as in Egorov's theorem, be used to conjugate partial differential operators to normal forms, which are then easier to analyze, and they are natural objects for studying the spectral geometry of Riemannian manifolds . These early applications of FIOs have since broadened, first to linear inverse problems, such as the Radon transform and its variants, and more recently to linearizations of nonlinear inverse problems, such as in exploration seismology. However, these applications often lead to situations where the assumptions of the standard FIO calculus are violated. This talk will describe the geometry, formulated in terms of singularity theory, behind these difficulties and assess the prospects for having a satisfactory general theory.