Department of

Mathematics


Seminar Calendar
for events the day of Friday, December 11, 2015.

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Friday, December 11, 2015

3:00 pm in 141 Altgeld Hall,Friday, December 11, 2015

  "Topological dynamics of closed subgroups of $S_\infty$" by Andy Zucker (the talk will end at 5pm)

Hamed Khalilian (UIUC Math)

Abstract: This is the second talk on the paper mentioned in the title and it will go for two hours 3pm-5pm. In the first hour, I will present a new proof of the Kechris-Pestov-Todorsevich correspondence. In the second hour, I will discuss how the Ramsey degree of a Fraïssé class is related to the metrizability of the universal minimal flow of the automorphism group of its limit.

4:00 pm in 245 Altgeld Hall,Friday, December 11, 2015

The dynamics of Type II solutions to energy critical wave equations

Hao Jia (University of Chicago)

Abstract: The study of dynamics of energy critical wave equations has seen remarkable progresses in recent years, resulting in deeper understanding of the singularity formation, soliton dynamics, and global large data theory. I will firstly review some of the landmark results, with emphasis on the channel of energy inequalities discovered by Duyckaerts, Kenig and Merle. Applications in the study of global dynamics of defocusing energy critical wave equation with a trapping potential in the radial case will be presented in some detail. We remark that the channel of energy argument provides crucial control on the global dynamics of the solution, and seems to be the only tool currently available to measure dispersion in this context, when we do not assume any smallness condition. The channel of energy argument is however sensitive to dimensions, and in higher dimensions, it is less powerful. We will mention a new approach to eliminate the dispersive energy when the channel of energy argument fails. Lastly, a new Morawetz estimate in the context of focusing energy critical wave equations will be discussed. This estimate allows us to study the singularity formation in more details in the non-radial case, without size restriction. As a result, we can characterize the solution along a sequence of times approaching the singular time, up to every nontrivial scale, as modulated solitons. View talk at https://youtu.be/rIesHSI8c24