ACO Seminar - Dylan Altschuler September 4, 2025 3:00pm — 4:00pm Location: In Person - CNA Room, Wean Hall 7281 Speaker: DYLAN ALTSCHULER , Postdoctoral Researcher, Department of Mathematics Sciences, Carnegie Mellon University https://dylanaltschuler.github.io/ Dimension reduction, universal approximation, and nonlinear spectral gaps When can a low–regularity object, such as a metric space or a graph, be embedded into a high regularity object, such as a normed space? This is a fundamental question in metric geometry, specifically the Ribe program, with wide-ranging applications in algorithm design, geometric group theory, and functional analysis. Traditional approaches to such problems rely on heavy machinery from analysis and geometry. We will introduce a recent program—joint with P. Dodos, K. Tikhomirov, and K. Tyros—towards developing direct combinatorial and probabilistic methods for studying (random) graph embeddings. Some highlight results include the resolution of a long–standing question on the asymptotics of Bourgain’s metric dimension reduction modulus, as well as a solution to an outstanding problem of Jon Kleinberg.No prior knowledge of metric geometry will be assumed; the first portion of the talk will aim to give a high-level overview of some of the key definitions, techniques, and questions in the field.4:00 pm → Jane Street-sponsored tea and cookies in Wean 6220. For More Information: rkrueger@andrew.cmu.edu Add event to Google Add event to iCal
