Mode: In-Person Title: Colding-Minicozzi entropies in Cartan-Hadamard manifolds Abstract: I will discuss a family of functionals defined on submanifolds of Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy of submanifolds of Euclidean space. These quantities are monotone under mean curvature flow … Read more

Mode: In-Person Title: Spatiotemporal analysis of single-cell and spatial genomics data Abstract: The emerging single-cell and spatial genomics techniques allow us to elucidate the governing rules of multicellular systems with an unprecedented resolution and depth. These datasets are often high-dimensional, … Read more

Mode: In-Person Title: Physical rigidity of Frenkel-Gross connection Abstract: A G-connection over a smooth complex curve is called physically rigid if it is determined by its local monodromies. We show that the Frenkel-Gross connection is physically rigid, thus confirming the … Read more

With funding provided by the PDE group’s NSF RTG grant, we are excited to announce the return of the UNC PDE Mini-schools and wanted to invite you to the first of these. The mini-schools are structured around a series of … Read more

Mode: In-Person Title: Nodal sets of eigenfunctions of sub-Laplacians Abstract: Nodal sets of eigenfunctions of elliptic operators on compact manifolds have been studied extensively over the past decades. In a recent work, we initiated the study of nodal sets of … Read more

Mode: In-Person Title: On positivity for flag manifolds and Hessenberg spaces Abstract: “Positivity” is a phenomenon involving the intersection of subvarieties in the presence of enough structure to ensure that intersection points are positively oriented, among other generalizations. It has … Read more

Mode:In-Person Title: Pieri formulas for the quantum K-theory of cominuscule Grassmannians Abstract: The quantum K-theory ring QK(X) of a flag variety X encodes the K-theoretic Gromov-Witten invariants of X, defined as arithmetic genera of Gromov-Witten varieties parametrizing curves meeting fixed … Read more