MenuEvents for 03/01/2024 from all calendars
Stochastic Processes Seminar
Time: 10:00AM - 11:00AM
Location: BLOC 302
Speaker: Alexander Roitershtein, TAMU
Title: Balancing art and money in pursuit of a Kelly-type optimality
Abstract: We will discuss a model of an art collector driven by two competing long-term objectives, namely sustainable financial health and maintaining the collection. Mathematically, our model is a peculiar two-dimensional random linear system. In some examples, combining theoretical insights with intensive simulations, we are able to show that the two goals can be reconciled. The talk will focus on the story rather than on exact mathematical details, and will be accessible to students. Among other things, I am planning to discuss a connection between (evasive) Lyapunov exponents, Mobius transformations, continued fractions, inverse Gaussian distributions, and (mysterious) Furstenberg measures, and what it all has to do with investment portfolios, cultural economics, coexistence equilibria, and Bell Labs in the '50s.
Algebra and Combinatorics Seminar
Time: 2:00PM - 2:50PM
Location: BLOC 302
Speaker: Alex Lubotzky, Weizmann Institute of Science
Title: Uniform stability of high-rank Arithmetic groups
Abstract: (Joint with the workshop "Groups and dynamics".) Lattices in high-rank semisimple groups enjoy several special properties like super-rigidity, quasi-isometric rigidity, first-order rigidity, and more. In this talk, we will add another one: uniform ( a.k.a. Ulam) stability. Namely, it will be shown that (most) such lattices D satisfy: every finite-dimensional unitary "almost-representation" of D ( almost w.r.t. to a sub-multiplicative norm on the complex matrices) is a small deformation of a true unitary representation. This extends a result of Kazhdan (1982) for amenable groups and Burger-Ozawa-Thom (2013) for SL(n,Z), n>2. The main technical tool is a new cohomology theory ("asymptotic cohomology") that is related to bounded cohomology in a similar way to the connection of the last one with ordinary cohomology. The vanishing of H^2 w.r.t. to a suitable module implies the above stability. The talk is based on a joint work with L. Glebsky, N. Monod, and B. Rangarajan.
