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/
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