The space of metrics on an algebraic variety

Speaker: 

Ben Weinkove

Institution: 

Northwestern University

Time: 

Thursday, November 9, 2017 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

 The space of (Kahler) metrics on a projective algebraic variety can be given a natural infinite dimensional Riemannian structure.  This leads to the notion of a geodesic in the space of metrics.  I will discuss a recent result on the optimal regularity of these geodesics and how this relates to nonlinear PDEs and canonical metrics.  This is joint work with J. Chu and V. Tosatti.

Some problems on the distribution of prime numbers

Speaker: 

Yitang Zhang

Institution: 

UC Santa Barbara

Time: 

Thursday, November 16, 2017 - 4:00pm to 5:00pm

Host: 

Location: 

NSII 1201

We briefly describe some ideas and techniques that lead to solutions to certain problems in number theory, such as the bounded gaps between prime numbers, and others. This talk will be made understandable to general math audiences; technical details will be avoided.

Deep learning in vision and language intelligence

Speaker: 

Xiaodong He

Institution: 

Microsoft Research

Time: 

Thursday, May 25, 2017 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

Deep learning, which exploits multiple levels of data representations that give rise to hierarchies of concept abstraction, has been the driving force in the recent resurgence of Artificial Intelligence (AI). In this talk, I will summarize rapid advances in cognitive AI, particularly including comprehension, reasoning, and generation across vision and natural language, and applications in vision-to-text captioning, text-to-image synthesis, and reasoning grounded on images for question answering and dialog. I will also discuss future AI breakthrough that will benefit from multi-modal intelligence, which empowers the communication between humans and the real world and enables enormous scenarios such as universal chat-bot and intelligent augmented reality.

Harmonic measure in higher co-dimension

Speaker: 

S. Mayboroda

Institution: 

U. Minnesota

Time: 

Thursday, April 13, 2017 - 4:00pm

Location: 

RH 306

 

 

Over the past century an effort to understand dimension and structure of the harmonic measure spanned many spectacular developments in Analysis and in Geometric Measure Theory. Uniform rectifiability emerged as a natural geometric condition, necessary and sufficient for classical estimates in harmonic analysis, boundedness of the harmonic Riesz transform in L^2, and, in the presence of some background topological assumptions, for suitable scale invariant estimates on harmonic functions. While many of geometric and analytic problems remain relevant in sets of higher co-dimension (e.g., a curve in $\RR^3$), the concept of the harmonic measure is notoriously missing. In this talk, we introduce a new notion of a "harmonic" measure, associated to a linear PDE, which serves the higher co-dimensional sets. We discuss its basic properties and give large strokes of the argument to prove that our measure is absolutely continuous with respect to the Hausdorff measure on Lipschitz graphs with small Lipschitz constant.

 

 

Applications of Tauberian theorems to counting arithmetic objects

Speaker: 

Ramin Takloo-Bighash

Institution: 

UIC

Time: 

Thursday, March 16, 2017 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

The talk will start with some remarks on the role that zeta functions and Tuberian theorems have played in number theory in the last 180 years starting essentially with Dirichlet's proof of his Arithmetic Progression Theorem. The remainder of the talk will be devoted to giving a survey of recent applications of Tauberian theorems to counting arithmetic objects. 

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