How big is infinity?

Speaker: 

Professor Matt Foreman

Institution: 

UC Irvine

Time: 

Wednesday, April 8, 2009 - 5:00pm

Location: 

RH 594

Is infinity plus one equal to one plus infinity? What is infinity times
zero? Is infinity even a number? What are numbers anyway? Are there
different sizes of infinity? How does infinity come up in ordinary
mathematics? Do we need infinity to add real numbers?

I will survey these puzzles and give some rigorous answers.

Hodge groups of superelliptic jacobians

Speaker: 

Yuri Zarhin

Institution: 

Pennsylvania State University

Time: 

Thursday, May 7, 2009 - 2:00pm

Location: 

RH 306

The Hodge group (aka special Mumford-Tate group) of a complex abelian variety $X$ is a certain linear reductive algebraic group over the rationals that is closely related to the endomorphism ring of $X$. (For example, the Hodge group is commutative if and only if $X$ is an abelian variety of CM-type.) In this talk I discuss" lower bounds" for the center of Hodge groups of superelliptic jacobians. (This is a joint work with Jiangwei Xue.)

Compressive Sensing: RIP-free Theory and Efficient Algorithms

Speaker: 

Professor Yin Zhang

Institution: 

Rice University

Time: 

Monday, May 4, 2009 - 4:00pm

Location: 

RH 306

We will first introduce basic ideas of Compressive Sensing (CS), which
is an emerging
(some would say revolutionary) methodology in signal, image and data
processing.
The theory for CS has so far been built largely on a notion called
Restricted Isometry
Property or RIP. We will point out drawbacks of RIP-based analyses and
introduce
results from a non-RIP analysis including some new extensions. We will
also discuss
some related optimization algorithms.

Large deviations from equilibrium measure for zeros of random holomorphic fields.

Speaker: 

Professor Steve Zelditch

Institution: 

Johns Hopkins

Time: 

Wednesday, April 8, 2009 - 2:00pm

Location: 

RH 306

An old result of Kac-Hammersley says that the complex zeros of a Gaussian
random polynomial \sum_{j = 0}^N a_j z^j with i.i.d. normal coefficients a_j, concentrate
on the unit circle. This seems counter intuitive at first, since the zeros could be anywhere.
We will explain this paradox and show that there is a very general result that empirical measures
of complex zeros tend to `equilibrium measures'. We then give a large deviations principle showing
that the probability of deviation from equilibrium measure is exponentially small.

Perturbed simple random walk

Speaker: 

Professor Ben Morris

Institution: 

UC Davis

Time: 

Tuesday, June 2, 2009 - 11:00am

Location: 

RH 306

A random walk is called recurrent if it is sure to return to its starting point and transient otherwise. A famous result of Polya is that simple symmetric random walk on the integer lattice is recurrent in dimensions 1 and 2, and transient in higher dimensions. We study random walks that are small perturbations of simple random walk. Our main result is that if the dimension is high enough then these random walks are transient.

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