Seminar Information
Thursdays, 11am AP&M 6402
University of California, San Diego
La Jolla, CA 920930112
Map
Organizer: Todd Kemp
Email: tkemp@math.ucsd.edu
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Fall 2018 Schedule
Sept 27   Nikhil Srivastava, UC Berkeley
 
Concentration for Sums of Random Matrices with Markov Dependence
There are many wellknown concentration results for sums of independent random matrices, e.g. those of Rudelson, AhlswedeWinter, Tropp, and Oliveira.
We move beyond the independent setting, and prove a Chernofftype bound for sums of matrixvalued random variables sampled via a random walk on an
reversible Markov chain, confirming a conjecture due to Wigderson and Xiao. Our proof is based on a new multimatrix extension of the GoldenThompson
inequality which follows from complex interpolation methods.
(Joint work with A. Garg, Y. Lee, and Z. Song.)



Oct 25   LiCheng Tasi, Columbia University
 
Lowertail large deviations of the KPZ equation
Regarding time as a scaling parameter, we prove the onepoint, lower tail Large Deviation Principle (LDP) of the KPZ equation, with an explicit rate function.
This result confirms existing physics predictions. We utilize a formula from [Borodin Gorin 16] to convert LDP of the KPZ equation to calculating an exponential
moment of the Airy point process, and analyze the latter via stochastic Airy operator and Riccati transform.



Nov 8   Joshua Frisch, Caltech
 
Proximal actions, Strong amenability, and infinite conjugacy class groups.
A topological dynamical system (i.e. a group acting by homeomorphisms on a compact topological space) is said to be proximal
if for any two points $p$ and $q$ we can simultaneously push them together i.e. there is a sequence $g_n$ such that
$\lim g_n(p)=\lim g_n (q)$. In his paper introducing the concept of proximality Glasner noted that whenever $\mathbb{Z}$ acts proximally
that action will have a fixed point. He termed groups with this fixed point property "strongly amenable" and showed that nonamenable
groups are not strongly amenable and virtually nilpotent groups are strongly amenable. In this talk I will discuss recent work precisely
characterizing which (countable) groups are strongly amenable.



Nov 15   Noah Forman, University of Washington
 
The diffusion analogue to a treevalued Markov chain
In '99, David Aldous conjectured that a certain natural "random walk" on the space of binary combinatorial trees
should have a continuum analogue, which would be a diffusion on the GromovHausdorff space of continuum trees.
This talk discusses ongoing work by FPalRizzoloWinkel that has recently verified this conjecture with a
pathwise construction of the diffusion. This construction combines our work on dynamics of certain projections
of the combinatorial treevalued random walk with our previous construction of intervalpartitionvalued diffusions.



"Winter" 2019 Schedule
Jan 10   Tom Kurtz, University of Wisconsin


Spring 2019 Schedule
Apr 4   Elizabeth and Mark Meckes, Case Western University


