A formula with some applications to the theory of Lyapunov exponent I

Speaker: 

Xiaowen Zhu

Institution: 

UC Irvine

Time: 

Friday, November 4, 2016 - 1:00pm to 1:50pm

Location: 

RH 510M

 I will present an elementary   formula about the average expansion of certain products of  cocycles,  which allows us to reobtained some known results about Lyapunov exponent.  Those  results are  based on  a paper of  A.Avila and J.Bochi -A formula with some applications to the theory of Lyapunov exponent.   It may take me  two or three times to finish the proof.

 

Good Choices for Great Careers

Speaker: 

Mac Hyman

Institution: 

Tulane University

Time: 

Friday, December 2, 2016 - 4:00pm to 5:00pm

Host: 

Location: 

MSTB 120

The choices that scientists make early in their careers will impact them for a lifetime. I will use the experiences of scientists who have had great careers to identify universal distinguishing traits of good career choices that can guild decisions in education, choice of profession, and job opportunities to increase your chances of having a great career with long-term sustained accomplishments.
 
I ran a student internship program at Los Alamos National Laboratory for over 20 years. Recently, I have been tracking the careers past students and realized that the scientists with great careers weren't necessarily the top students, and that some of the most brilliant students now had some of the most oh-hum careers.
 
I will describe how the choices made by the scientists with great careers were based on following their passion, building their talents into a strength supporting their profession, and how they identified a supportive engaging work environment. I will describe some simple guidelines that can
help guide your choices, in school and in picking the right job that can lead to a rewarding career and more meaningful life.
 
The topic is important because, so far as I can tell, life is not a trial run - we have one shot to get it right. The choices you are making right now to planning your career will impact your for a lifetime.
 
Please join us for an engaging discussion on how to make the choices that
will lead to a great career.

Self-Avoiding random motion

Speaker: 

Greg Lawler

Institution: 

University of Chicago

Time: 

Thursday, February 23, 2017 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

The self-avoiding walk (SAW) is a model for polymers that assigns equal probability to all paths that do not return to places they have already been. The lattice version of this problem, while elementary to define, has proved to be notoriously difficult and is still open. It is initially more challenging to construct a continuous limit of the lattice model which is a random fractal. However, in two dimensions this has been done and the continuous model (Schram-Loewner evolution) can be analyzed rigorously and  used to understand the nonrigorous predictions about SAWs.  I will survey some results in this area and then discuss some recent work on this ``continuous SAW''.

Higher moments of arithmetic functions in short intervals: a geometric perspective

Speaker: 

Vlad Matei

Institution: 

University of Wisconsin

Time: 

Tuesday, November 29, 2016 - 2:00pm to 3:00pm

Host: 

Location: 

RH 340P

In joint work with Daniel Hast, we recast the paper of Jon Keating and Zeev Rudnick "The variance of the number of prime polynomials in short intervals and in residue classes" by studying the geometry of these short intervals through an associated highly singular variety. We manage to recover their results for a a general class of arithmetic functions up to a constant and also obtain information about the higher moments. Recently work of Brad Rodgers in "Arithmetic functions in short intervals and the symmetric group" gives new insight into the geometry of our variety.

Torsion subgroups of elliptic curves in elementary abelian 2-extensions

Speaker: 

Ozlem Ejder

Institution: 

USC

Time: 

Tuesday, November 22, 2016 - 2:00pm to 3:00pm

Host: 

Location: 

RH 340P

Let E be an elliptic curve defined over Q. The torsion subgroup of E over the compositum of all quadratic extensions of Q was studied by Michael Laska, Martin Lorenz, and Yasutsugu Fujita. Laska and Lorenz described a list of 31 possible groups and Fujita proved that the list of 20 different groups is complete.

In this talk, we will generalize the results of Laska, Lorenz and Fujita to the elliptic curves defined over a quadratic cyclotomic field i.e. Q(i) and Q(\sqrt{-3}).

Construction of certain explicit solutions to the Strominger system

Speaker: 

Teng Fei

Institution: 

Columbia University

Time: 

Tuesday, November 29, 2016 - 4:00pm

Location: 

RH 306

The Strominger system is a system of PDEs derived by Strominger in his
study of compactification of heterotic strings with torsion. It can be
thought of as a generalization of Ricci-flat metrics on non-Kähler
Calabi-Yau 3-folds. We present some new solutions to the Strominger
system on a class of noncompact 3-folds constructed by twistor
technique. These manifolds include the resolved conifold
Tot(O(-1,-1)->P1) as a special case.

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