Wednesday, February 8, 2023
Time  Items 

All day 

1pm 
02/08/2023  1:00pm Abstract: Many statistical models for realworld data have the following structure. Let A be a low rank matrix, and E a matrix of the same dimension. The objective is to approximate a parameter f(A) from the noisy data A' = A + E. A represents the ground truth, A' the observable data, and E the noise. In statistical settings, E is taken to be random. While this setup is simple, it represents an extremely rich environment in which to study problems in data science. In this talk, I will discuss how spectral perturbation theory is employed to solve problems in statistics and data science. However, classical perturbation bounds, like the DavisKahan theorem, are wasteful in the random E setting. This motivates us to look at the problem through the lens of random matrix theory. I will discuss our improved spectral perturbation bounds and applications. Location:
AKW 200

4pm 
02/08/2023  4:15pm The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higherrank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the PattersonSullivan theory and introduce new results about Kleinian groups with small or large critical exponents.
Location:
LOM 214
