MenuEvents for 04/01/2022 from all calendars
Noncommutative Geometry Seminar
Time: 08:00AM - 09:00AM
Location: ZOOM
Speaker: Zhizhang Xie, Texas A&M University
Title: Comparisons of scalar curvature, mean curvature and dihedral angle, and their applications
Abstract: In this talk, I will review Gromov’s dihedral extremality and rigidity conjectures regarding comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. These conjectures have profound implications in geometry and mathematical physics such as the positive mass theorem. I will explain the recent work on positive solutions to these conjectures, and some related applications (such as a positive solution to the Stoker conjecture). The talk is based on my joint works with Jinmin Wang and Guoliang Yu.
URL: Event link
Noncommutative Geometry Seminar
Time: 09:15AM - 10:15AM
Location: ZOOM
Speaker: Jinmin Wang, Texas A&M University
Title: Gromov's dihedral rigidity conjecture and index theory on manifolds with corners
Abstract: In this talk, I will explain the key ideas of our recent work on positive solutions to Gromov's dihedral extremality and rigidity conjectures. One of the main ingredients is a new index theory on manifolds with corners (more generally, manifolds with polytope singularities), which is of independent interest on its own. Our approach is based on the analysis of differential operators arising from conical metrics. The comparison of dihedral angles enters into the study of these differential operators in an essential way. This is based on my joint works with Zhizhang Xie and Guoliang Yu.
URL: Event link
Working Seminar on Banach and Metric Spaces
Time: 10:00AM - 11:30AM
Location: BLOC 302
Speaker: Luis Eduardo Aceves, Texas A&M University
Title: Unconditional martingale differences
Several Complex Variables Seminar
Time: 10:20AM - 11:10AM
Location: ZOOM
Speaker: Gian Maria Dall'Ara and Samuele Mongodi, Scuola Normale Superiore and Politenico di Milano
Title: The Levi core: basic properties and applications
Abstract: In the first part of this talk, Samuele will present briefly the construction of the core of the Levi distribution, highlighting the links with other known geometric invariants of boundaries of pseudoconvex domains, like finite-type points, local maximum sets, Levi currents. He will also sketch a parallel between the sequence of derived distributions from the Levi distribution to the core and Kohn's algorithm of multipliers' ideals. In the second half of the talk, Gian Maria will discuss two ways in which the Levi core can be applied to problems in SCV, specifically he will address the question of whether the DF index of a domain is 1, the exact regularity of the d-bar Neumann problem, and subelliptic estimates. The subellipticity part is yet unpublished.
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: Zoom
Speaker: Theo McKenzie, Berkeley
Title: Many nodal domains in random regular graphs
Abstract: If we partition a graph according to the positive and negative components of an eigenvector of the adjacency matrix, the resulting connected subcomponents are called nodal domains. Examining the structure of nodal domains has been used for more than 150 years to deduce properties of eigenfunctions in both continuous and discrete space. Dekel, Lee, and Linial observed that according to simulations, most eigenvectors of the adjacency matrix of random regular graphs have many nodal domains, unlike dense Erdős-Rényi graphs. In this talk, we show that for the most negative eigenvalues of the adjacency matrix of a random regular graph, there is an almost linear number of nodal domains. Joint work with Shirshendu Ganguly, Sidhanth Mohanty, and Nikhil Srivastava.
Algebra and Combinatorics Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 302
Speaker: Chun-Hung Liu, TAMU
Title: A decomposition theorem for immersion-free graphs with no 3-edge-cut
Abstract: Structural decomposition theorems for graphs with forbidden minors and topological minors have been proved and led to many applications. Graph immersions is a notion related to graph minors and topological minors, and many analogous open problems about immersions have been proposed. In this talk we address the fundamental problem about the structure of a graph with forbidden immersions. We prove that every graph with no edge-cut of size 3 that forbids a fixed graph H as an immersion can be decomposed into graphs that are "nearly simpler" than H. The condition for having no 3-edge-cut is necessary to have a clean theorem.
