Persistent homology, a popular method in Topological Data Analysis, encodes geometric information of data into algebraic objects called persistence modules. Invoking a decomposition theorem, these alg...
In the first part of the course we will provide a brief introduction to the spectrum of the Laplacian on Euclidean domains and Riemannian manifolds, along with a few basic examples, and their relation...
In the first part of the course we will provide a brief introduction to the spectrum of the Laplacian on Euclidean domains and Riemannian manifolds, along with a few basic examples, and their relation...
I will talk about a principal eigenvalue problem for a second-order elliptic operator with a very small diffusion coefficient in one direction. In this regime, how do the principal eigenvalue and the ...
The Flux Problem is a famous problem in condensed matter physics, solved by Lieb. It states that the magnetic flux through each plaquette of a square lattice in 2d (with either OBC/PBC or PBC/PBC) th...
This talk explores how random graphs, serving as simple models of quantum disordered systems, exhibit a delocalization-localization transition of the eigenstates of their adjacency matrices. I will pr...
Start of Winter School on Statistical Mechanics, Nonequilibrium Processes and Probability, which will take place February 17-28, 2025. All information available at https://sites.google.com/view/winter...
We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the mo...
