Rare events for point process limits of random matrices.

Speaker: 

Diane Holcomb

Speaker Link: 

http://math.arizona.edu/~dianeholcomb/

Institution: 

University of Arizona

Time: 

Tuesday, January 27, 2015 - 11:00am to 12:00pm

Host: 

Michael C. Cranston

Location: 

RH 306

The Gaussian Unitary and Orthogonal Ensembles (GUE, GOE) are some of the most studied Hermitian random matrix models. When appropriately rescaled the eigenvalues in the interior of the spectrum converge to a translation invariant limiting point process called the Sine process. On large intervals one expects the Sine process to have a number of points that is roughly the length of the interval times a fixed constant (the density of the process). We solve the large deviation problem which asks about the asymptotic probability of seeing a different density in a large interval as the size of the interval tends to infinity. Our proof works for a one-parameter family of models called beta-ensembles which contain the Gaussian orthogonal, unitary and symplectic ensembles as special cases.

Brownian Motion in Three Dimensions Conditioned to have the Origin as a Recurrent Point

Speaker: 

Patrick Fitzsimmons

Institution: 

UCSD

Time: 

Tuesday, January 20, 2015 - 11:00am to 12:00pm

Host: 

Michael C. Cranston

Location: 

RH 306

I will discuss aspects of a polymer model based on three-dimensional Brownian motion conditioned to hit (and keep returning to) the origin 

introduced by Mike Cranson and co-authors.   The construction and certain properties of this conditioned Brownian motion will be approached from two points of view (i) Dirichlet forms, and (ii) excursion theory. The latter gives a nice interpretation of the Johnson-Helms example from martingale theory. It turns out that this diffusion process is not a semimartingale, even though its radial part is just a one-dimensional Brownian motion reflected at the origin. 

 

(This talk is based on joint work with Liping Li of Fudan University.)

Selected problems in dynamical systems

Speaker: 

Anton Gorodetski

Institution: 

UC Irvine

Time: 

Tuesday, December 9, 2014 - 1:00pm to 2:00pm

We will discuss some problems (related to piecewise isometris, sums and products of Cantor sets, dynamics of the Fibonacci trace map etc.) that are in the scope of current interests of the dynamical systems seminar. Many of the problems can be considered as potential research projects by the interested graduate students. 

We're Going to the Moon: The N-body problem

Speaker: 

Jeremy Pecharich

Institution: 

Pomona College

Time: 

Monday, December 8, 2014 - 4:00pm to 5:00pm

Location: 

NS2, 1201

It is May 25, 1961, President Kennedy announced that the United States would land a person on the moon. But, in 1961 nobody actually knew how to get to the moon! It wasn't until 1963 that a viable flight path to the moon was found to exist. We will discuss the mathematics that made this path possible and some of the long history of the N-body problem.

Professor Zhiqin Lu selected as an Eisenbud Professor for the MSRI Spring 2016 Program in Differential Geometry

Congratulations to Professor Zhiqin Lu for being selected as an "Eisenbud Professor" for the MSRI Spring 2016 program in Differential Geometry. The “Eisenbud Professorship” is an endowed chair position named for Professor David Eisenbud, director of MSRI, to support distinguished visiting profesors at MSRI. A link to the MSRI Differential Geometry program can be found here.

Professor Qing Nie elected a Fellow of the American Physical Society (APS)

Congratulations to Professor Qing Nie, who was elected as a Fellow of the American Physical Society. Election to Fellowship in the American Physical Society is limited to no more than one half of one percent of the membership in the American Physical Society. The criterion for election is exceptional contributions to the physics enterprise; e.g., outstanding physics research, important applications of physics, leadership in or service to physics, or significant contributions to physics education. Fellowship is a distinct honor signifying recognition by one's professional peers. 

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