Colloquia 2012-2013

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Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Spring 2012

date speaker title host(s)
Jan 23, 4pm Saverio Spagnolie (Brown) Hydrodynamics of Self-Propulsion Near a Boundary: Construction of a Numerical and Asymptotic Toolbox Jean-Luc
Jan 27 Ari Stern (UCSD) Numerical analysis beyond Flatland: semilinear PDEs and problems on manifolds Jean-Luc / Julie
Feb 3, 2:25pm, B215 Travis Schedler (MIT) Symplectic resolutions and Poisson-de Rham homology Andrei
Feb 3 Akos Magyar (UBC) On prime solutions to linear and quadratic equations Street
Feb 10 Melanie Wood (UW Madison) Counting polynomials and motivic stabilization local
Feb 17 Milena Hering (University of Connecticut) TBA Andrei
Feb 24 Malabika Pramanik (University of British Columbia) TBA Benguria
March 2 Guang Gong (University of Waterloo) TBA Shamgar
March 16 Charles Doran (University of Alberta) TBA Matt Ballard
March 19 Colin Adams and Thomas Garrity (Williams College) Which is better, the derivative or the integral? Maxim
March 23 Martin Lorenz (Temple University) TBA Don Passman
March 30 Wilhelm Schlag (University of Chicago) TBA Street
April 6 Spring recess
April 13 Ricardo Cortez (Tulane) TBA Mitchell
April 18 Benedict H. Gross (Harvard) TBA distinguished lecturer
April 19 Benedict H. Gross (Harvard) TBA distinguished lecturer
April 20 Robert Guralnick (University of South California) TBA Shamgar
May 4 Mark Andrea de Cataldo (Stony Brook) TBA Maxim
May 11 Tentatively Scheduled Shamgar

Abstracts

Mon, Jan 23: Saverio Spagnolie (Brown)

"Hydrodynamics of Self-Propulsion Near a Boundary: Construction of a Numerical and Asymptotic Toolbox"

The swimming kinematics and trajectories of many microorganisms are altered by the presence of nearby boundaries, be they solid or deformable, and often in perplexing fashion. When an organism's swimming dynamics vary near such boundaries a question arises naturally: is the change in behavior fluid mechanical, biological, or perhaps due to other physical laws? We isolate the first possibility by exploring a far-field description of swimming organisms, providing a general framework for studying the fluid-mediated modifications to swimming trajectories. Using the simplified model we consider trapped/escape trajectories and equilibria for model organisms of varying shape and propulsive activity. This framework may help to explain surprising behaviors observed in the swimming of many microorganisms and synthetic micro-swimmers. Along the way, we will discuss the numerical tools constructed to analyze the problem of current interest, but which have considerable potential for more general applicability.

Fri, Feb 3: Akos Magyar (UBC)

On prime solutions to linear and quadratic equations

The classical results of Vinogradov and Hua establishes prime solutions of linear and diagonal quadratic equations in sufficiently many variables. In the linear case there has been a remarkable progress over the past few years by introducing ideas from additive combinatorics. We will discuss some of the key ideas, as well as their use to obtain multidimensional extensions of the theorem of Green and Tao on arithmetic progressions in the primes. We will also discuss some new results on prime solutions to non-diagonal quadratic equations of sufficiently large rank. Most of this is joint work with B. Cook.

Fri, Feb 10: Melanie Wood (local)

Counting polynomials and motivic stabilization

We will begin with the problem of counting polynomials modulo a prime p with a given pattern of root multiplicity. Here we will discover phenomena that point to vastly more general patterns in configuration spaces of points. To see these patterns, one has to work in the ring of motives--so we will describe this place where a space is equivalent to the sum of its pieces. We will then be able to describe how these patterns in the ring of motives are related to theorems in topology on the homological stability of configuration spaces. This talk is based on joint work with Ravi Vakil.