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.

Bio:
Dr. Fan Cheng received the bachelor degree in computer science and engineering from Shanghai Jiao Tong University in 2007, and the PhD degree in information engineering from The Chinese University of Hong Kong in 2012. From 2012-2014, he was a postdoctoral fellow in the Institute of Network Coding, The Chinese University of Hong Kong. From 2015-2016, he was a research fellow in the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. As of 2016, he has been  an associate professor  in the Department of Computer Science and Engineering, Shanghai Jiao Tong University, China. His research interests include information theory and machine learning. https://ichengfan.github.io/