Title: Higher-Order Graphon Theory: Fluctuations, Inference, and Degeneracies Abstract: Motifs (patterns of subgraphs), such as edges and triangles, encode important structural information about the geometry of a network. Consequently, counting motifs in a large network is an important statistical and … Read more

Title: Scaling limit of stochastic gradient descents over large networks Abstract: Wasserstein gradient flows often arise from mean-field interactions of exchangeable particles. In many interesting applications however, the "particles" are edge weights in a graph whose vertex labels are exchangeable … Read more

Title: Limit Theorems for Recursive Cell-splitting Schemes Abstract: Random tessellations form a central class of models considered in stochastic geometry. They are used in a number of concrete applications ranging from metallography to wireless telecommunication, to name just two. Especially … Read more

Title: Large deviations in data science: some initial examples Abstract: The theory of large deviations has become a cornerstone of modern probability theory. It has proven particularly useful in the analysis and design of efficient stochastic numerical methods. Examples include … Read more

Title: Probabilistic solutions of singular free boundary problems Abstract: The main focus of the talk will be on a new, probabilistic, concept of solution to singular free boundary problems, in which boundary points may move at infinite speed. I will … Read more

Title: A Notion of Stability for Solutions of Random Optimization Problems Abstract: Consider the Euclidean traveling salesman problem with n random points on the plane. Suppose that one of the points is shifted to a new random location. This gives … Read more

Title: Some topics in spatial networks Abstract: There is a huge 21st century literature on quantitative aspects of networks. One aspect is spatial networks, that is networks embedded in the plane, exemplified by road networks. The recent book "Spatial Networks: … Read more