Research Seminars @ Illinois

View Full Calendar

Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

Tomer Schlank (U Chicago): Random Links and Arithmetic Statistics

Event Type
Seminar/Symposium
Sponsor
UIUC math department
Location
Altgeld 241
Date
Sep 10, 2024   11:00 am  
Views
43
Originating Calendar
Topology Seminar

Étalé homotopy is a theory that enables the study of algebraic and arithmetic concepts through geometric perspectives. Barry Mazur observed that, from this viewpoint, square-free integers are analogous to links in three-dimensional space. We will explore this analogy and propose a way to give it a statistical flavor. Informally, we assert that a random square-free integer of size approximately X resembles the closure of a random braid on roughly logX strands. We will make this statement more precise by introducing a number-theoretical analog for a family of numerical link invariants (called Kei's) and use this analogy to propose a conjecture regarding their asymptotic behavior. We will also present a few cases where this conjecture has been proven.

link for robots only