# Calendar

## Yesterday

## Higher regularity of inverse mean curvature flow in $\mathbb{R}^n$.

We will continue to prove the mean curvatures of the surfaces driven by inverse mean curvature flow in a finite time have a uniformly strictly positive lower bound which only depends on the gross geometric property of initial star-shaped surface. This result can be applied to prove the global solution of inverse mean curvature flow on $C^1$ initial star-shaped mean convex surface.### Automorphic Forms and Representation Theory Seminar, Professor Jonathan Mboyo Esole, Northeastern University, WTHR 360

Thursday, Apr 27 1:30 pm - 2:30 pm

## Pushforward and Euler characteristic of crepant resolutions of Weierstrass models

I will introduce a new pushforward formula that streamlines the computations of intersection numbers in projective bundles. As an application, I will explain how it has been recently used to compute generating functions for Euler characteristic of crepant resolutions of Weierstrass models.### PDE Seminar, Dr. Jamie Taylor, Oxford University and Kent State University, REC 317

Thursday, Apr 27 3:30 pm - 4:30 pm

## Deriving the Oseen-Frank theory for liquid crystals from a mean-field free energy

There are a variety of models for the describing systems of liquid crystals (certain anisotropic fluids), depending on the length scales one is interested in. Heuristic arguments are well known for obtaining the macroscopic Oseen-Frank model from the mesocopic mean-field models, which can relate large scale elastic behaviour to pairwise molecular interactions. In this talk we will formalise such arguments through techniques of Gamma-convergence, obtaining the local Oseen-Frank model as a Gamma limit of a non-local mean field free energy in the limit of large sample size. The non-local nature of the problem means boundary conditions in particular cause technical difficulties, so we first consider periodic domains. The results in this simpler setting then provide results for models with bounded domains and Dirichlet-like boundary conditions.## Today

### CCAM Lunch seminar, Prof. Vaneet Aggarwal, Purdue University, REC 114

Friday, Apr 28 11:30 am - 12:30 pm

## Deterministic Sampling Conditions for Tensor Completion

In this talk, we will consider the problem of multi-dimensional data completion. We will investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries, for completability of a low-rank tensor. An algebraic geometric analysis on the tensor manifold can lead to a characterization of the algebraic independent polynomials based on the sampling pattern which is related to the problem of data completion. Having understood the deterministic sampling conditions, the probabilistic conditions will be guaranteed to determine when the proposed deterministic conditions on the sampling patterns hold with high probability. The number of measurements needed to recover tensors are shown to be of a much lower order as compared to that when the data is converted to a matrix.## Next Week

## The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory

The Lojasiewicz-Simon gradient inequality is a generalization, due to Leon Simon (1983), to analytic or Morse-Bott functionals on Banach manifolds of the finite-dimensional gradient inequality, due to Stanislaw Lojasiewicz (1963), for analytic functions on Euclidean space. We shall discuss several recent generalizations of the Lojasiewicz-Simon gradient inequality and a selection of their applications, such as global existence and convergence of Yang-Mills gradient flow over four-dimensional manifolds and discreteness of the energy spectrum for harmonic maps from Riemann surfaces into analytic Riemannian manifolds.## Two Weeks

### Department of Mathematics Colloquium, Prof. Irene Fonseca, Carnegie Mellon University, TBD

Tuesday, May 9 4:30 pm - 5:30 pm