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4:00pm to 5:00pm - Zoom https://uci.zoom.us/j/97796361534 - Applied and Computational Mathematics Wuchen Li - (University of South Carolina) Mean-Field Games for Scalable Computation and Diverse Applications Abstract: Mean field games (MFGs) study strategic decision-making in large populations where individual players interact via specific mean-field quantities. They have recently gained enormous popularity as powerful research tools with vast applications. For example, the Nash equilibrium of MFGs forms a pair of PDEs, which connects and extends variational optimal transport problems. This talk will present recent progress in this direction, focusing on computational MFG and engineering applications in robotics path planning, pandemics control, and Bayesian/AI sampling algorithms. This is based on joint work with the MURI team led by Stanley Osher (UCLA). |
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1:00pm to 2:00pm - RH 440R - Dynamical Systems Grigorii Monakov - (UC Irvine) Stationary random walks on SL(k, R) I will give an overview of the most important results about stationary random walks on SL(k, R). We will talk about Lyapunov exponent and their properties, such as positivity of the top exponent, simplicity and regularity of the spectrum and others. We will also mention other limit theorems, such as central limit theorem and law of iterated logarithm. The talk is based on the monograph ``Random walks on groups and random transformations'' by Alex Furman. |
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2:00pm to 3:00pm - 510R Rowland Hall - Combinatorics and Probability Marcelo Sales - (UCI) Set representation of sparse graphs and hypergraphs Let $G$ be a graph on $n$ vertices. Given an integer $t$, we say that a family of sets $\{A_x\}_{x \in V}\subset 2^{[t]}$ is a set representation of $G$ if $$xy \in E(G) \iff A_x \cap A_y = \emptyset$$ Let $\overline{\theta}_1(G)$ be the smallest integer $t$ with such representation. In this talk I will discuss some of the bounds on $\overline{\theta}_1$ for sparse graphs and related problems. Joint work with Basu, Molnar, Rödl and Schacht. |
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1:00pm - RH 306 - Harmonic Analysis Polona Durcik - (Chapman University) Quantitative norm convergence of triple ergodic averages for commuting transformations We establish a quantitative result on norm convergence of triple ergodic averages with respect to three general commuting transformations by proving an r-variation estimate, r > 4, in the norm. We approach the problem via real harmonic analysis, using the recently developed techniques for bounding singular Brascamp-Lieb forms. It is not known whether such norm-variation estimates hold for all r>=2 as in the analogous cases for one or two commuting transformations, or whether such estimates hold for any r<infinity for more than three commuting transformations. This is joint work with Christoph Thiele and Lenka Slavikova. |