Speaker：

Fan Cheng 程帆

(Shanghai Jiao Tong University)

Time：

Tues., 9:00-10:00 am, Mar. 25, 2025

Venue：

Jing Zhai 105 （清华大学静斋）

Online：

Zoom Meeting ID: 271 534 5558

Passcode: YMSC

Abstract：

Heat equation in mathematical physics and Gaussian channel in information theory are equivalent as the fundamental solution to heat equation is given by the heat kernel (Gaussian distribution). Gaussian completely monotone conjecture (GCMC) states that the entropy of the solution to heat equation is completely monotone in time t. GCMC was originally introduced in 2013 by obtaining the sign of the third derivative. Related study may date back to de Bruijn, C. E. Shannon, H. P. McKean, E. Lieb, M. Costa, and C. Villani, etc.

In this talk, we will talk about the progress, history and future of GCMC, including its application to the Gaussian interference channel and its connection with the hodge theory method for log-concave sequence by J. Huh.