Mathematics Colloquium

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

Fall 2017

Date	Speaker	Title	Host(s)
September 8	Tess Anderson (Madison)	A Spherical Maximal Function along the Primes	Yang
September 15
September 22, 9th floor	Jaeyoung Byeon (KAIST)	Patterns formation for elliptic systems with large interaction forces	Rabinowitz & Kim
September 29		TBA
October 6	Jonathan Hauenstein (Notre Dame)	Real solutions of polynomial equations	Boston
October 13	Tomoko L. Kitagawa (Berkeley)	TBA	Max
October 20	Pierre Germain (Courant, NYU)	TBA	Minh-Binh Tran
October 27	Stefanie Petermichl (Toulouse)	TBA	Stovall, Seeger
We, November 1	Shaoming Guo (Indiana)	TBA
November 3	Robert Laugwitz (Rutgers)	TBA	Dima Arinkin
November 10	Reserved for possible job talks	TBA
November 17	Reserved for possible job talks	TBA
November 24	Thanksgiving break	TBA
December 1	Reserved for possible job talks	TBA
December 8	Reserved for possible job talks	TBA

Fall Abstracts

September 8: Tess Anderson (Madison)

Title: A Spherical Maximal Function along the Primes

Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.

September 22: Jaeyoung Byeon (KAIST)

Title: Patterns formation for elliptic systems with large interaction forces

Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.

October 6: Jonathan Hauenstein (Notre Dame)

Title: Real solutions of polynomial equations

Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.

Spring 2018

date	speaker	title	host(s)
March 30	Anne Gelb (Dartmouth)	TBA	Qin
April 6	Reserved	TBA	Melanie
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