Marcos Jardim — UNICAMP, Brazil 

 Monday, 4 May, at 4:30.

Title: Ideals with Three Generators 

Abstract: In joint work with Nejad and Simis, we introduced the Bourbaki degree of a plane curve as a measure of how far it is from being free. We now observe that all the arguments can be generalised to graded ideals with three generators, and we introduce the Bourbaki degree and related concepts in this setting. This is joint work with Felipe Monteiro, Abbas Nejad, and Zaqueu Ramos.

Luca Dieci- School of Mathematics, Georgia Institute of Technology, USA

Thursday, 25 June, at 3:30 p.m.

Title: Optimal Trajectories for Optimal Transport

Abstract: We present a solution to a discrete optimal transport problem in a non-uniform environment. To solve the optimal transport problem, we construct the cost matrix and then apply classical solvers for discrete optimal transport. The main challenge lies in forming the cost matrix, which requires determining the optimal trajectory between two points. For this purpose, we formulate and solve the associated Euler–Lagrange equation.We provide verifiable sufficient conditions for the optimality of the solution and numerically validate the computation of the cost matrix. We illustrate the results and the performance of the algorithms through several numerical examples in two and three spatial dimensions. We also extend the results to the non-autonomous setting.

This is joint work with Daniyar Omarov, University of Alberta–PIMS, Canada.