We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and logarithmic in the error. This is an exponential improvement over previous algorithms which were analyzed in the usual Euclidean, “commutative” metric (for which the above problem is not convex).
Let F be a family of subsets over a domain X that is closed under taking intersections. Such structures are abundant in various fields of mathematics such as topology, algebra, analysis, and more. In this talk we will view these objects through the lens of convexity.
We will focus on an abstraction of the notion of weak epsilon nets:
given a distribution on the domain X and epsilon>0,
a weak epsilon net for F is a set of points that intersects any set in F with measure at least epsilon.
A basic but difficult question in the analytic theory of automorphic forms is: given a reductive group G and a representation r of its L-group, how many automorphic representations of bounded analytic conductor are there? In this talk I will present an answer to this question in the case that G is a torus over a number field.
We will hear from two passionate creators of successful mentoring programs in math for high school kids in educationally challenged environments. They will give back-to-back talks about their experiences and educational insights.