An exceptionally gifted mathematician and an extremely complex person, Floer exhibited, as one friend put it, a "radical individuality." Indeed, his revolutionary mathematical ideas, contradicting conventional wisdom, could only be inspired by such impetus, and can only be understood in this context. Helmut Hofer is the Hermann Weyl Professor at the Institute for Advanced Study (IAS) in Princeto...

Starting with a discussion on the intrinsic structure of images and their mathematical representation, this talk will address some of these mathematical problems, including variational models for image analysis and their connection to partial differential equations and a new paradigm in mathematical imaging using deep neural networks. Carola-Bibiane Schönlieb is Professor of Applied Mathematics...

Over the past decade, research at the interface of topology and neuroscience has grown remarkably fast. In this talk, after a very brief introduction to the necessary elements of neuroscience, Hess will survey the results obtained by her and her collaborators when applying topological tools to studying the relationship between brain structure and function, primarily in collaboration with the Blue...

There are many situations in geometry and group theory where it is natural, convenient or necessary to explore infinite groups via their actions on finite objects. But how much understanding can one really gain about an infinite group by examining its finite images? Sometimes little, sometimes a lot. In this colloquium talk, Bridson will sketch some of the rich history of this problem. Martin Bri...

Conditional Gradient Methods are an important class of methods to minimize smooth convex functions over polytopes. In this talk, Pokutta will give a broad overview of these methods and their applications and present some recent results both in traditional optimization and learning as well as in deep learning. Sebastian Pokutta is the Vice President of the Zuse Institute Berlin (ZIB) and a Profess...

Tree decompositions are a powerful tool in structural graph theory that is traditionally used in the context of forbidden graph minors. Connecting tree decompositions and forbidden induced subgraphs has so far remained out of reach. Recently, several results in this direction have been obtained. The talk will be a survey of these results. Maria Chudnovsky received her PhD from Princeton Universi...