"Right Triangles and Elliptic Curves" by Professor Karl Rubin

The Mathematics Department at UCI, with the support of NSF RTG grant DMS-1044150, is proud to present "Right Triangles and Elliptic Curves," by Professor Karl Rubin.
 
The event is part of a math seminar series for undergraduates and will take place on February 16th from 12 to 1 p.m. in Natural Sciences 2, Room 1201. The event is free and open to the public.
 

Deformations of G2-structures with torsion

Speaker: 

Sergey Grigorian

Institution: 

Stony Brook

Time: 

Tuesday, April 10, 2012 - 4:00pm

Location: 

RH 306

We consider non-infinitesimal deformations of G2-structures on 7-dimensional
manifolds and derive a closed expression for the torsion of the deformed
G2-structure. We then specialize to the case where the deformation lies in
the seven-dimensional representation of G2 and is hence defined by a vector
v. In this case, we explicitly derive the expressions for the different
torsion components of the new G2-structure in terms of the old torsion
components and derivatives of v. In particular this gives a set of
differential equations for the vector v which have to be satisfied for a
transition between G2-structures with particular torsions. For some specific
torsion classes we then explore the solutions of these equations.

The mathematics of Multiwave Imaging

Speaker: 

Professor Plamen Stefanov

Institution: 

Purdue University

Time: 

Thursday, March 1, 2012 - 4:00pm

Location: 

RH 306

 
Thermoacoustic (TAT) and Photoacoustic Tomography (PAT) are examples of multiwave imaging methods allowing to combine the high imaging contrast of one wave (an electromagnetic or a photoacoustic one) with the high resolution of ultrasound. We present recent results obtained in collaboration with Gunther Uhlmann, Jianliang Qian and Hongkai Zhao on the mathematical theory behind TAT, PAT and other multiwave methods. We allows the acoustic speed to be variable, and consider the partial data case as well. We will also discuss the case of a discontinuous speed modeling brain imaging.  Numerical reconstructions will be shown as well.
Most of the progress is due to the use of microlocal methods. One of the goals of the talk is to show the usefulness of microlocal methods to solving real life problems.

Asymptotics of General Orthogonal Polynomials

Speaker: 

Brian Simanek

Institution: 

Caltech

Time: 

Thursday, March 1, 2012 - 2:00pm

Location: 

RH 306

This talk will focus on orthogonal polynomials whose corresponding measure of orthogonality is not supported on the real line or unit circle. In this setting, the orthonormal polynomials do not satisfy a three-term recurrence relation. However, many theorems from the classical settings of the real line and unit circle can be reformulated to apply to this more general situation. The first part of this talk will present some history and motivation for studying these polynomials and we will conclude by presenting some new results.

Trace map dynamics: general results with recent applications in the theory of orthogonal polynomials and classical Ising models (III)

Speaker: 

William Yessen

Institution: 

UC Irvine

Time: 

Friday, February 24, 2012 - 2:00pm

Location: 

RH 440R

In the previous two talks we established a dictionary between some properties of quasiperiodic (particularly Fibonacci) models and some geometric constructions arising as dynamical invariants for the Fibonacci trace map. In this talk we shall apply our findings to a specific model: the classical 1D Ising model with quasiperiodic magnetic field and quasiperiodic nearest neighbor interaction. In particular, we'll prove absence of phase transitions of any order and we'll investigate the structure of Lee-Yang zeroes in the thermodynamic limit (these are zeroes of the partition function as a function of the complexified magnetic field---while in finite volume the partition function is a polynomial whose zeroes fall on the unit circle, a challenge is to determine whether in infinite volume (thermodynamic limit) these zeroes accumulate on any set on the unit circle, and if so, to determine the structure of this set). The purpose of this work is to serve as rigorous justification to previously observed phenomena (mostly through numerical and some soft analysis). Should we have time, we'll also very briefly mention applications of the aforementioned dictionary to quasiperiodic Jacobi matrices/CMV matrices.

Image Restoration in the Presence of Rician Noise

Speaker: 

Melissa Tong

Institution: 

UCLA

Time: 

Thursday, February 16, 2012 - 11:00am

Location: 

RH 306

Magneto-Resonance (MR) images are believed to have Rician distributed noise. In this talk, we propose two variational models involving total variation (TV) regularization to denies images corrupted by Rician distributed noise. For the first model, we implement the L2 and Sobolev H1 gradient descent methods in our numerical simulations on synthetic 3D MR images of the brain. In addition, we show the existence of a minimizer and a maximum principle result. For the second model, we incorporate the image formation model in the data fidelity term together with the Rician noise assumption. We perform numerical experiments on High-Angular Resolution Diffusion Imaging (HARDI) data of the brain to show the validity of the proposed model.

The Urysohn sphere is rosy

Speaker: 

Dr Isaac Goldbring

Institution: 

UCLA

Time: 

Monday, February 27, 2012 - 4:00pm

Location: 

RH 440R

I will discuss the role that independence relations play in modern model theory, discussing the classes of stable, simple, and rosy theories along the way. I will then discuss why the Urysohn space is not
stable or simple, but is rosy. Part of the talk reflects joint work with Clifton Ealy.

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