Almost commuting elements of real rank zero C*-algebras.

Speaker: 

Ilya Kachkovskiy

Institution: 

UCI

Time: 

Thursday, October 10, 2013 - 2:00pm

Location: 

RH 340P

The classical Huaxin Lin's theorem shows that the distance from a matrix A to the set of normal matrices can be estimated in terms of its self-commutator [A,A*]. We obtain a quantitative version of this theorem, "optimal" with respect to the power of self-commutator. Under certain assumptions on A, our approach can be extended to the case of general bounded operators in Hilbert spaces and to elements of C*-algebras of real rank zero. The results are joint with Professor Yuri Safarov from King's College London.

Separating strong saturation properties of ideals on small cardinals II

Speaker: 

Monre Eskew

Institution: 

UCI

Time: 

Monday, October 7, 2013 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 440R

The topic of this talk is inspired by measure-theoretic questions raised by Ulam: What is the smallest number of countably additive, two valued measures on R such that every subset is measurable in one of them?  Under CH, the minimal answer to this question has several equivalent formulations, one of which is the maximal saturation property for ideals on aleph_1, aleph_1-density.  Our goal is to show that these equivalences are special to aleph_1.  In the second talk, we will continue with construction of normal ideals of minimal possible density on a variety of spaces from almost-huge cardinals.  This generalizes a result of Woodin.

Recovering point sources in unknown inhomogeneous environments

Speaker: 

Kui Ren

Institution: 

University of Texas, Austin

Time: 

Monday, October 14, 2013 - 4:00pm to 5:00pm

Host: 

Hongkai Zhao

Location: 

RH306

Reconstructing point sources in the Helmholtz equation from boundary or far-field measurements has many practical applications. There have been extensive studies on the reconstruction problem in homogeneous media and known inhomogeneous media. We study here the point source identification problem in an unknown inhomogeneous medium. We propose a two-step procedure to reconstruct both the medium and the point sources inside the medium with differential data. We present some stability results for the reconstruction as well as some numerical simulations with synthetic data. This is a joint work with Yimin Zhong.

Lipschitz inverse shadowing and structural stability

Speaker: 

Dmitry Todorov

Institution: 

Chebyshev laboratory, Saint-Petersburg, Russia

Time: 

Tuesday, November 5, 2013 - 2:00pm to 3:00pm

Location: 

RH 440R

There is known a lot of information about classical or standard shadowing. It is also often called a pseudo-orbit tracing property (POTP). Let M be a closed Riemannian manifold. Dieomorphism f : M \to M is said to have POTP if for a given accuracy any pseudotrajectory with errors small enough can be approximated (shadowed) by an exact trajectory. A similar denition can be given for flows.

Most results about this property prove that it is present in certain hyperbolic situations. Quite surprisingly, recently it has been proven that a quantitative version of it is in face equivalent to hyperbolicity (structural stability).

There is also a notion of inverse shadowing that is a kind of a converse to the notion of classical shadowing. Dynamical system is said to have inverse shadowing property if for any (exact) trajectory there exists a pseudotrajectory from a special class that is uniformly close to the original exact one.

I will describe a quantitative (Lipschitz) version of this property and why it is equivalent to structural stability both for dieomorphisms and for flows.

On the Mumford-Tate conjecture for abelian foufolds

Speaker: 

Bin Zhao

Institution: 

UC Los Angeles

Time: 

Tuesday, November 5, 2013 - 2:00pm to 3:00pm

Location: 

RH 340P

The Mumford-Tate conjecture is a deep conjecture which relates the arithmetic and the geometry of  abelian varieties defined over number fields. The results of Moonen and Zarhin indicate that this conjecture holds for almost all absolutely simple abelian fourfolds. The only exception is when the abelian varieties have no nontrivial endomorphism. In this talk we will begin with an introduction to the Mumford-Tate conjecture and a brief summary of known results towards it. Then we sketch a proof of this conjecture in the above 'missing' case for abelian fourfolds.

Risk, Return and Ross Recovery

Speaker: 

Dr. Peter Carr

Speaker Link: 

http://www.math.nyu.edu/research/carrp/

Institution: 

Morgan Stanley

Time: 

Monday, October 7, 2013 - 5:30pm to 6:30pm

Location: 

Natural Sciences 2, room 1201

Math Finance Seminar

Dr. Peter Carr

Global Head of Market
Modeling Managing Director
Morgan Stanley

Title: Risk, Return and Ross Recovery

Abstract: Recently, Stephen Ross has shown that the real-world transition probabilities of a finite state Markov chain can be recovered from Arrow Debreu security prices by assuming that the pricing kernel enjoys transition independence. We motivate this restriction by deriving it as a consequence of restricting the form and dynamics of the numeraire portfolio. Working with a diffusion process for a short interest rate, we indicate how one can recover real world transition probabilities on both bounded and unbounded domains.

Light refreshments will be served.

 

Separating strong saturation properties of ideals on small cardinals I

Speaker: 

Monroe Eskew

Institution: 

UCI

Time: 

Monday, September 30, 2013 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 440R

The topic of this talk is inspired by measure-theoretic questions raised by Ulam: What is the smallest number of countably additive, two valued measures on R such that every subset is measurable in one of them?  Under CH, the minimal answer to this question has several equivalent formulations, one of which is the maximal saturation property for ideals on aleph_1, aleph_1-density.  Our goal is to show that these equivalences are special to aleph_1.  In the first talk, we will show how to get normal ideals of minimal possible density on a variety of spaces from almost-huge cardinals.  This generalizes a result of Woodin.
 

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