Department of

Mathematics


Seminar Calendar
for events the day of Monday, October 24, 2016.

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Monday, October 24, 2016

4:00 pm in 241 Altgeld Hall,Monday, October 24, 2016

The Cohomological McKay Correspondence and Symplectic Cohomology

Mark McLean (Stony Brook University)

Abstract: Suppose that we have a finite quotient singularity C^n/G admitting a crepant resolution Y (i.e. a resolution with c_1 = 0). The cohomological McKay correspondence says that the cohomology of Y has a basis given by irreducible representations of G (or conjugacy classes of G). Such a result was proven by Batyrev when the coefficient field F of the cohomology group is Q. We give an alternative proof of the cohomological McKay correspondence in some cases by computing symplectic cohomology+ of Y in two different ways. This proof also extends the result to all fields F whose characteristic does not divide |G| and it gives us the corresponding basis of conjugacy classes in H^*(Y). We conjecture that there is an extension to certain non-crepant resolutions. This is joint work with Alex Ritter.

4:00 pm in 245 Altgeld Hall,Monday, October 24, 2016

Some Radon transforms and their discrete analogue

Xiaochun Li (Department of Mathematics, University of Illinois)

Abstract: We report some progress on certain Radon transforms and some discrete analogue. For instance, bilinear Hilbert transform along curves, discrete Strichartz estimate and its relation with weighted restriction, etc.

5:00 pm in 241 Altgeld Hall,Monday, October 24, 2016

Renyi Divergence and Noncommutative $L_p$ spaces

Li Gao (UIUC Math)

Abstract: We continue from last time.