Mathematics Colloquium

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

Spring 2019

date	speaker	title	host(s)
Jan 25	Beata Randrianantoanina (Miami University Ohio) WIMAW	TBA	Tullia Dymarz
Jan 30 Wednesday	Lillian Pierce (Duke University)	Short character sums	Boston and Street
Jan 31 Thursday	Dean Baskin (Texas A&M)	Radiation fields for wave equations	Street
Feb 1	Jianfeng Lu (Duke University)	TBA	Qin
Feb 5 Tuesday	Alexei Poltoratski (Texas A&M University)	TBA	Denisov
Feb 8	Aaron Naber (Northwestern)	A structure theory for spaces with lower Ricci curvature bounds	Street
Feb 15		TBA
Feb 22	Angelica Cueto (Ohio State)	TBA	Erman and Corey
March 4	Vladimir Sverak (Minnesota) Wasow lecture	TBA	Kim
March 8	Jason McCullough (Iowa State)	TBA	Erman
March 15	Maksym Radziwill (Caltech)	TBA	Marshall
March 29	Jennifer Park (OSU)	TBA	Marshall
April 5	Ju-Lee Kim (MIT)	TBA	Gurevich
April 12	Evitar Procaccia (TAMU)	TBA	Gurevich
April 19	Jo Nelson (Rice University)	TBA	Jean-Luc
April 26	Kavita Ramanan (Brown University)	TBA	WIMAW
May 3	Tomasz Przebinda (Oklahoma)	TBA	Gurevich

Abstracts

Lillian Pierce (Duke University)

Title: Short character sums

Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.

Dean Baskin (Texas A&M)

Title: Radiation fields for wave equations

Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.

Aaron Naber (Northwestern)

Title: A structure theory for spaces with lower Ricci curvature bounds.

Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.