October 30th from 4:30pm – 5:30pm
@ Skiles 006
Reception at 4pm

Title: The Convexity Conjecture, the Kahn-Kalai Conjecture, and introduction to k-thresholds

Abstract: The "Convexity Conjecture" by Talagrand asks (very roughly) whether one can "create convexity" in constant steps regardless of the dimension of the ambient space. Talagrand also suggested a discrete version of the Convexity Conjecture and called it "my lifetime favorite problem," offering $1,000 prize for its solution. We introduce a reformulation of the discrete Convexity Conjecture using the new notion of "k-thresholds," which is an extension of the traditional notion of thresholds, introduced by Talagrand. Some ongoing work on understanding k-thresholds, along with a (vague) connection between the Kahn-Kalai Conjecture and the discrete Convexity Conjecture, will also be discussed. Joint work with Michel Talagrand.

Photo by Rod Searcey

 

About the Speaker

Jinyoung Park is an Assistant Professor of Mathematics at the Courant Institute, NYU. Her research interests include extremal and probabilistic combinatorics. She earned her Ph.D. in mathematics from Rutgers University in 2020, under the supervision of Jeff Kahn. Following her Ph.D., she was a postdoctoral researcher at the Institute for Advanced Study (IAS) and Stanford University before joining the faculty of the Courant Institute at NYU in 2023. Park received her bachelor's degree in mathematics education from Seoul National University in 2005 and worked as a secondary school mathematics teacher until 2011. She has received several honors and awards, including the AMS Conant Prize, the Dénes König Prize, and the Maryam Mirzakhani New Frontiers Prize.