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3:00pm to 4:00pm - 340P Rowland Hall - Differential Geometry Pak-Yeung Chan - (National Tsing Hua University) Flying wing construction of steady Ricci solitons Ricci solitons are generalizations of the Einstein manifolds and are self similar solutions to the Ricci flow. In particular, steady Ricci solitons are eternal solutions to the Ricci flow. In this talk, we will discuss the flying wing construction of some Kahler and Riemannian steady Ricci solitons of nonnegative curvature. This is based on joint work with Ronan Conlon and Yi Lai, as well as with Yi Lai and Man-Chun Lee. |
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4:00pm to 5:00pm - 306 Rowland Hall - Differential Geometry Adrian Chun-Pong Chu - (Cornell University) Enumerative problems for minimal surfaces with prescribed genus We will present the enumerative min-max theory, which relates the number of genus g minimal surfaces in 3-manifolds to topological properties of the set of all embedded surfaces of genus ≤g. As a consequence, we can show that in every 3-sphere of positive Ricci curvature, there exist ≥5 minimal tori (confirming a conjecture by B. White (1989) in the Ricci-positive case), ≥4 minimal surfaces of genus 2, and ≥1 minimal surface of genus g for all g. This is based on a joint work with Yangyang Li and Zhihan Wang. |
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3:00pm to 4:00pm - RH 306 - Number Theory John Cullinan - (Bard College) The group theory of elliptic curves in towers of finite fields If E and E' are elliptic curves defined over a finite field k such that E(k) and E'(k) have the same order, what is the likelihood that they define isomorphic groups? In this talk we will address this question from two points of view: fix E, vary p, and fix p, vary E. This is recent and ongoing work with Nathan Kaplan of UC Irvine. |
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4:00pm - NS2 1201 - Colloquium Dan Romik - (UC Davis) The moving sofa problem: a meandering journey from curiosity to serious mathematics The moving sofa problem asks for the largest area of a planar shape that can move around a right-angled corner in an L-shaped hallway. Initially posed by Leo Moser in 1966, the problem became a well-known example of an elementary geometry question that is extremely difficult to answer, and was open until its solution in 2024 by Jineon Baek. In this talk I will explain the basics of moving sofa theory, survey the milestone developments in the subject including my own work and how it inspired Baek's groundbreaking proof, and show entertaining moving sofa animations. I will make a halfhearted (and probably unsuccessful) attempt to draw general philosophical conclusions around the use of computer-based experimentation in mathematical discovery. The main goal of the talk will be to convince you that serious mathematical ideas are often hiding just around the corner. No prerequisite knowledge will be assumed, other than familiarity with the challenges of navigating furniture around obstacles. |