4:00pm  TBA  Logic Set Theory Kevin Duanmu  (UC Berkeley) Mixing times and Hitting times for general Markov processes using Nonstandard Analysis Nonstandard analysis, a powerful machinery derived from mathematical logic, has had many applications in probability theory as well as stochastic processes. Nonstandard analysis allows construction of a single objecta hyperfinite probability spacewhich satisfies all the first order logical properties of a finite probability space, but which can be simultaneously viewed as a measuretheoretical probability space via the Loeb construction. As a consequence, the hyperfinite/measure duality has proven to be particularly in porting discrete results into their continuous settings. In this talk, for every generalstatespace discretetime Markov process satisfying appropriate conditions, we construct a hyperfinite Markov process which has all the basic order logical properties of a finite Markov process to represent it. We show that the mixing time and the hitting time agree with each other up to some multiplicative constants for discretetime generalstatespace reversible Markov processes satisfying certain condition. Finally, we show that our result is applicable to a large class of Gibbs samplers and MetropolisHasting algorithms. 
11:00am to 12:00pm  RH 340N  Combinatorics and Probability Kyle Luh  (Harvard University) Eigenvalue gaps of sparse random matrices We will discuss some recent work on quantifying the gaps between eigenvalues of sparse random matrices. Before these results, it was not even known if the eigenvalues were distinct for this class of random matrices. We will also touch upon how these results relate to random graphs, the graph isomorphism problem and nodal domains. This is joint work with Van Vu and Patrick Lopatto. 
2:00pm to 3:00pm  510R  Working Group in Information Theory Kathryn Dover  (UCI) Submodularity of Entropy, Han's Inequality, and Shearer’s Lemma Working Group in Information Theory is a selfeducational project in the department. Techniques based on information theory have become essential in highdimensional probability, theoretical computer science and statistical learning theory. On the other hand, information theory is not taught systematically. The goal of this group is to close this gap. This week, we will discuss Section 1.4 and 1.5 of the lecture notes of Wu and Polyanski:

4:00pm  RH306  Differential Geometry Paula BurkhardtGuim  (UC Berkeley) Pointwise lower scalar curvature bounds for C^0 metrics via regularizing Ricci flow We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C^0 metrics. We show the following: that our definitions are stable under greaterthansecondorder perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from C^0 initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C^0 initial data. 
2:00pm to 3:00pm  RH 340 P  Mathematical Physics Lior Alon  (Technion) On a universal limit conjecture for the nodal count statistics of quantum graphs

3:00pm to 4:00pm  RH 440R  Number Theory Alexandra Florea  (Columbia University) Moments of cubic Lfunctions over function fields I will focus on the mean value of $L$functions associated to cubic characters over $\mathbb{F}_q[t]$ when $q \equiv 1 \pmod 3$. I will explain how to obtain an asymptotic formula which relies on obtaining cancellation in averages of cubic Gauss sums over functions fields. I will also talk about the corresponding nonKummer case when $q \equiv 2 \pmod 3$ and I will explain why this setting is somewhat easier to handle than the Kummer case, which allows us to prove some better results. This is joint work with Chantal David and Matilde Lalin.

1:00pm  RH 440R  Cryptography Alice Silverberg  (UCI) Introduction to NTRU encryption This talk will give an introduction to NTRU encryption. 
3:00pm to 4:00pm  RH 440R  Nonlinear PDEs Antonio De Rosa  (Courant Institute, NYU) Elliptic integrands in geometric variational problems I will present the recent tools I have developed to prove existence and regularity properties of the critical points of anisotropic functionals. In particular, I will provide the anisotropic extension of Allard's celebrated rectifiability theorem and its applications to the anisotropic Plateau problem. Three corollaries are the solutions to the formulations of the Plateau problem introduced by Reifenberg, by HarrisonPugh and by AlmgrenDavid. Furthermore, I will present the anisotropic counterpart of Allard's compactness theorem for integral varifolds. To conclude, I will focus on the anisotropic isoperimetric problem: I will provide the anisotropic counterpart of Alexandrov's characterization of volumeconstrained critical points among finite perimeter sets. Moreover I will derive stability inequalities associated to this rigidity theorem. Some of the presented results are joint works with De Lellis, De Philippis, Ghiraldin, Gioffré, Kolasinski and Santilli. 
4:00pm  PSCB 140  Graduate Seminar Jen McIntosh  (NSA) The #1 job to take after graduation Dr. Jen McIntosh is a UCI alum who started at the National Security Agency (NSA) over 15 years ago as an Applied Research Mathematician. Her journey with NSA has been typically atypical, in that most mathematicians have a world of choice and opportunities to explore as interests and mission needs evolve  whether mathy or not. Currently she is in the Senior Technical Development Program (STDP), a mid to latecareer program designed to foster expertise in areas of strategic importance to the Agency. Her current passion is bridging math, psychology, business, and other areas that make up decision science  enhancing decisionmaking with information and data. She'll talk a little about her journey, the diversity of mathematical fields she's practiced (from common sense to cryptanalysis), and she'll dedicate most of the time for questions about life at NSA and the wealth of career opportunities for mathematicians at any phase of their careers. 