Department of

Mathematics

Seminar Calendar
for events the day of Thursday, August 31, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2017             August 2017           September 2017
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1          1  2  3  4  5                   1  2
2  3  4  5  6  7  8    6  7  8  9 10 11 12    3  4  5  6  7  8  9
9 10 11 12 13 14 15   13 14 15 16 17 18 19   10 11 12 13 14 15 16
16 17 18 19 20 21 22   20 21 22 23 24 25 26   17 18 19 20 21 22 23
23 24 25 26 27 28 29   27 28 29 30 31         24 25 26 27 28 29 30
30 31


Thursday, August 31, 2017

11:00 am in 241 Altgeld Hall,Thursday, August 31, 2017

Polynomial Roth type theorems in Finite Fields

Dong Dong (Illinois Math)

Abstract: Recently, Bourgain and Chang established a nonlinear Roth theorem in finite fields: any set (in a finite field) with not-too-small density contains many nontrivial triplets $x$, $x+y$, $x+y^2$. The key step in Bourgain-Chang's proof is a $1/10$-decay estimate of some bilinear form. We slightly improve the estimate to a $1/8$-decay (and thus a better lower bound for the density is obtained). Our method is also valid for 3-term polynomial progressions $x$, $x+P(y)$, $x+Q(y)$. Besides discrete Fourier analysis, algebraic geometry (theorems of Deligne and Katz) is used. This is a joint work with Xiaochun Li and Will Sawin.

4:00 pm in 245 Altgeld Hall,Thursday, August 31, 2017

Symplectic non-squeezing for the cubic nonlinear Schrodinger equation on the plane

Monica Visan (UCLA)

Abstract: A famous theorem of Gromov states that a finite dimensional Hamiltonian flow cannot squeeze a ball inside a cylinder of lesser radius, despite the fact that the ball has finite volume and the cylinder has infinite volume. We will discuss an infinite-dimensional analogue of Gromov's result, in infinite volume. Specifically, we prove that the flow of the cubic NLS in two dimensions cannot squeeze a ball in $L^2$ into a cylinder of lesser radius. This is joint work with R. Killip and X. Zhang.