Analysis and Mathematical Physics

The Kakeya Conjectures concern overlapping properties of direction-separated tubes in $\mathbb{R}^n$. They are elementary to state, but difficult to prove. In 2025, Wang-Zahl proved the Kakeya Set Conjecture for $n=3$. On October 6, OpenAI claimed...

For a closed manifold $(M,g)$ with isometry group, $G$, we will discuss the construction of $G$-invariant minimal hypersurfaces. Pitts-Rubinstein initiated the program to construct such hypersurfaces via min-max methods. The community has made...

Let X be a (nice) topological space, and suppose that we wish to know if X is homotopy equivalent to a simplicial complex of dimension $\leq n$. An obvious necessary condition is that the cohomology of X (with arbitrary coefficients) must be...

The goal of this work is to investigate the almost pressureless Euler-Poisson (EP) system with repulsive force in the large friction limit. The leading order equations in the limit are shown to be the hyperbolic-elliptic Keller-Segel (KS) system of...

*Please note start time change from 9:30 AM to 12:30 PM.