Research Seminars @ Illinois

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

Special Colloquium - Eric Chen University of California, Berkeley

Event Type
Seminar/Symposium
Sponsor
Rui Antonio Loja Fernandes
Location
Altgeld 245
Date
Feb 29, 2024   4:00 - 4:50 pm  
Speaker
Eric Chen
Contact
Rui Fernandes
E-Mail
ruiloja@illinois.edu
Views
144
Originating Calendar
Mathematics Colloquium & Named Lectures

Title: Features of Ricci flow smoothing and singularities in four dimensions

Abstract: The Ricci flow, introduced by Hamilton in the 1980s, is a geometric-analytic tool that has since found many applications including Perelman's resolution of the Poincaré and Thurston's Geometrization conjectures, which classify three-dimensional compact manifolds and generalize the classical uniformization theorem for two-dimensional surfaces. The flow is a parabolic evolution equation which tends to smooth out a Riemannian metric on a manifold, but it may also encounter singularities; both are important features which can help us understand the topology of the manifold.  When moving to four dimensions, conical singularities are an important new class of singularities that arise.  I will discuss work on the existence of asymptotically conical expanding Ricci solitons in dimension four, joint with Richard Bamler, which may play a role in resolving these singularities and help in the ongoing construction of a theory of four-dimensional Ricci flow with surgery for the purpose of new applications.

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