Georgia Institute of Technology College of Sciences

This is a part of the GT MAP activities.  GT MAP is a place for research discussion and collaboration. We welcome participation of any researcher interested in discussing his/her project and exchange ideas with Mathematicians.

This seminar will be held in Skiles 006  starting at 3PM, and refreshments at Skiles Atrium.

A couple of members of Prof. Chen's group will present their research

3:00 PM - 3:45PM Prof. Yongxin Chen will give a talk

3:45PM -- 4:00PM Break with Discussions

4:00PM - 4:25PM Second talk by Prof. Yongxin Chen

4:25PM - 5PM Discussion of open problems stemming from the presentations.

Title: measure-valued splines and matrix optimal transport 

Abstract: Two recent extensions of optimal mass transport theory will be covered. In the first part of the talk, we will discuss measure-valued spline, which generalizes the notion of cubic spline to the space of distributions. It addresses the problem to smoothly interpolate (empirical) probability measures. Potential applications include time sequence interpolation or regression of images, histograms or aggregated datas. In the second part of the talk, we will introduce matrix-valued optimal transport. It extends the optimal transport theory to handle matrix-valued densities. Several instances are quantum states, color images, diffusion tensor images and multi-variate power spectra. The new tool is expected to have applications in these domains. We will focus on theoretical side of the stories in both parts of the talk.

Bio

Prof. Yongxin Chen received his B.S. in mechanical engineering from Shanghai Jiao Tong University, China, in 2011, and a Ph.D. degree in mechanical engineering, under the supervision of Tryphon Georgiou, from University of Minnesota in 2016.  He currently serves as an assistant professor in the Daniel Guggenheim School of Aerospace Engineering at Georgia Institute of Technology. Before joining Georgia Tech, he had a one-year research fellowship at Memorial Sloan Kettering Cancer Center from August 2016 to August 2017 and was an assistant professor in the Department of Electrical and Computer Engineering at Iowa State University from August 2017 to August 2018.