Workshop on Mathematical Physics in honor of Craig Tracy

Workshop on Mathematical Physics in honor of Craig Tracy, October 30 2021

All talks held in room 1147 of the Mathematics Science Building, University of California, Davis

Directions to the Mathematical Sciences Building can be found at math.ucdavis.edu.

There is no charge for parking on weekends.
Parking at UCD .

This will be a hybrid workshop. Talks will be live and speakers will be at the workshop, but the talks will also be broadcast over zoom. The zoom link is at the very bottom of this page.

Please register for the conference so we can have adequate supplies of coffee and food.
A registration form is found below.
There is a separate registration form for the banquet, also found below. Space is limited so please sign up by the deadline of Oct 22.

Schedule

Note: Times have been changed from the original posted times. The times below are correct.

9:30 AM Coffee

10:00 AM
Iain Johnstone
Title: PCA, likelihood ratios, and a transition to the Tracy-Widom law

11:05 AM
Herbert Spohn
Department of Mathematics, Technical University Munich and MSRI Berkeley
Title: The hydrodynamic scale for integrable many-body systems

1:10 PM
Alexander Its
Department of Mathematics, Indiana University-Purdue University
Title: ISOMONODRTOMY ASPECTS OF THE TT* EQUATIONS OF CECOTTI AND VAFA. IWASAWA FACTORIZATION AND ASYMPTOTICS.

2:15 PM
Axel Saenz
Department of Mathematics, Oregon State University
Title: TASEP back in time

3:15 PM Coffee

3:30 PM
Estelle Basor
American Institute of Mathematics
Title: Some reflections on asymptotics of determinants and their applications and the work of Craig Tracy.

Register

To register for the workshop please fill in the form at the below link
Workshop registration.

or by pasting the text below into a web browser
https://docs.google.com/forms/d/e/1FAIpQLScVqhvPPJiyB8PWUAEGrasj8HHGA9wF2C26ehuEzLsZclQT7A/viewform

Banquet

There will be a banquet in the evening. To register for the banquet please fill in the form by using the below link
Banquet Sign Up.

or by pasting the text below into a web browser
https://docs.google.com/forms/d/e/1FAIpQLSf2w_0NSesIZqOq7xGnLps3Vjb0SjL-idGU8AZnBbfKBe5q3Q/viewform

Abstracts

Alexander Its
Titiel: ISOMONODRTOMY ASPECTS OF THE TT* EQUATIONS OF CECOTTI AND VAFA. IWASAWA FACTORIZATION AND ASYMPTOTICS
The talk is concerned with the global asymptotic analysis of the tt* - Toda equation, 2(w i ) t ¯t = −e 2(w i+1 −w i ) + e 2(w i −w i+1 ) , where, for all i, w i = w i+n+1 (periodicity),w i = w i ( | t | ) (radial condi- tion), and w i + w −i−1 = 0 (“anti-symmetry”). The problem has been intensively studied since the early 90s work of Cecotti and Vafa. In these work a prominent role of the tt*- equations in the classification of supersymmetric field theories had been revealed and a series of important conjectures about their solutions has been formulated. Assuming n = 3 (the first case beyond the known Painlev´e III situation), we study the question using a combination of methods from p.d.e., isomonodromic deformations (Riemann-Hilbert method), and loop groups (Iwasawa factorization). We place these global solutions into the broader context of solutions which are smooth near 0. For such solutions, we compute explicitly the Stokes data and connection matrix of the associated meromorphic system, in the resonant cases as well as in the non-resonant case. This allows us to give a complete picture of the monodromy data, holomorphic data, and asymptotic data of the global solutions and prove some of Cecotti-Vafa conjectures. In the talk, the above mentioned results will be presented in detail with an outline of the key steps in their derivation. Also, the relation to 1998 work of Tracy and Widom on the tt*-Toda equation will be discussed. This is a joint work with Martin Guest and Chang-Shou Lin

Axel Saenz
Title: TASEP back in time
The (totally) asymmetric simple exclusion process, the (T)ASEP, is an interacting particle system on the integer line that is exactly solvable. In the late 2000s, C. Tracy and H. Widom discovered the Tracy-Widom distribution in the fluctuations of a particle in the bulk for the ASEP with the so-called step initial conditions. This was a groundbreaking result, which has fostered much research activity.
In this talk, I will introduce a Markov process that maps the TASEP back in time for the step initial conditions. I motivate this Markov process by considering the action of the Yang-Baxter equations on the TASEP. This result is based on a collaboration with L. Petrov (U VA).

Herbert Spohn
Title: The hydrodynamic scale for integrable many-body systems
From the statistical physics side there is currently much interest in the hydrodynamic description of the Lieb-Liniger delta-Bose gas and similar integrable systems. We discuss the underlying concepts. For the Ablowitz-Ladik discretized version of the nonlinear Schroedinger equation generalized Gibbs ensembles are introduced and the structure of average conserved fields and their currents is elucidated.

Estelle Basor
Title: Some reflections on asymptotics of determinants and their applications and the work of Craig Tracy.
This talk will survey results that describe the asymptotics of determinants of structured matrices and operators. We will highlights some applications and the connections to some of the early work of Craig Tracy and then the links to his later fundamental contributions to random matrix theory.

Access by Zoom

For those who will not be present in Davis, the workshop will be braodcast over zoom using the following link: Workshop on Mathematical Physics in honor of Craig Tracy Topic: Tracy Workshop
Time: Oct 30, 2021 10:00 AM Pacific Time (US and Canada)

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