Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.


Past events in this series

Mon, 12 Jun 2023

16:30 - 17:30

Breaking glass optimally and Minkowski's problem for polytopes

Jian-Guo Liu
(Duke University)
Motivated by a study of least-action incompressible flows, we study all the ways that a given convex body in Euclidean space can break into countably many pieces that move away from each other rigidly at constant velocity, following geodesic motions in the sense of optimal transport theory. These we classify in terms of a countable version of Minkowski's geometric problem of determining convex polytopes by their face areas and normals. Illustrations involve various intriguing examples both fractal and paradoxical, including Apollonian packings and other types of full packings by smooth balls.
Wed, 28 Jun 2023

16:00 - 17:00


Giuseppe Rosario Mingione
(University of Parma)


Tue, 04 Jul 2023

17:00 - 18:00

Fractional Sobolev lsometric lmmersions of Planar Domains

Siran Li
(NYU Shanghai)

We discuss $C^1$-regularity and developability of isometric immersions of flat domains into $\mathbb{R}^3$ enjoying a local fractional Sobolev $W^{1+s;2/s}$-regularity for $2/3 \leq s < 1$, generalising the known results on Sobolev (by Pakzad) and H\"{o}lder (by De Lellis--Pakzad) regimes. Ingredients of the proof include analysis of the weak Codazzi equations of isometric immersions, the study of $W^{1+s;2/s}$-gradient deformations with symmetric derivative and vanishing distributional Jacobian determinant, and the theory of compensated compactness. Joint work with M. Reza Pakzad and Armin Schikorra.