Events for 03/21/2025 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Danko Moisés Aldunate Bascuñán

Title: Nonlinear Dirac equation: characterization of a gap property for the linearized 1D Soler model

Abstract: We establish for the 1D Soler model with power nonlinearities $f(s)=s|s|^{p-1}$, $p>0$, that the upper-right block operator~$L_0$ of the linearized operator satisfies: its ground states $-2\omega$ and $0$ are its only two eigenvalues in the gap of its essential spectrum if only if $p\geq1$. Our second main result is the simplicity of generalized eigenfunction at the threshold of the essential spectrum for Dirac operators with potential. These results apply in particular to lower-left block operator~$L_\mu$.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 302

Speaker: Suchitra Pande, University of Utah

Title: A Gorenstein criterion in positive characteristics via the F-pure threshold

Abstract: This talk concerns singularities of local rings and numerical invariants used to detect mild singularities. Some classical notions of mild singularities include normal, Cohen-Macaulay and Gorenstein. However, when the ring has prime characteristic, the Frobenius map provides powerful new ways to detect mild singularities via the notions of F-purity and F-regularity. For instance, Hochster and Huneke proved that strongly F-regular rings are automatically normal and Cohen-Macaulay, but not always Gorenstein. In this talk, we will discuss a criterion for a strongly F-regular standard graded ring to be Gorenstein. This criterion was conjectured by Hirose, Watanabe and Yoshida and relies on the relationship between the F-pure threshold and another classical invariant of graded rings called the a-invariant. In this talk, we will discuss a proof of this conjecture, extending previous partial results of Singh, Takagi and Varbaro, and De Stefani and Núñez-Betancourt. We will review the relevant preliminary notions before presenting the proof.

Geometry Seminar

Time: 4:00PM - 4:50PM

Location: BLOC 302

Speaker: Demetre Kazaras, Michigan State University

Title: Scalar curvature and codimension 2 collapse

Abstract: This talk is about the structure of Riemannian 3-manifolds satisfying a lower bound on their scalar curvature. These manifolds are models for spatial geometry in general relativity. Our motivational question will be "How flat is an isolated gravitational system with very little total mass?" Objects like gravity wells and black holes can distort geometry without accumulating much mass, making this a subtle question. In addition to discussing progress, I will present a "drawstring" construction, which modifies a manifold near a given curve, reducing its length with negligible damage to a scalar curvature lower bound. Unexpected examples are produced with relevance to a few problems. This construction extends ideas of Basilio-Dodziuk-Sormani and Lee-Naber-Neumayer, and is based on joint work with Kai Xu.

Noncommutative Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Demetre Kazaras, Michigan State University

Title: Scalar curvature and codimension 2 collapse

Abstract: This talk is about the structure of Riemannian 3-manifolds satisfying a lower bound on their scalar curvature. These manifolds are models for spatial geometry in general relativity. Our motivational question will be "How flat is an isolated gravitational system with very little total mass?" Objects like gravity wells and black holes can distort geometry without accumulating much mass, making this a subtle question. In addition to discussing progress, I will present a "drawstring" construction, which modifies a manifold near a given curve, reducing its length with negligible damage to a scalar curvature lower bound.  Unexpected examples are produced with relevance to a few problems. This construction extends ideas of Basilio-Dodziuk-Sormani and Lee-Naber-Neumayer, and is based on joint work with Kai Xu.

Student/Postdoc Working Geometry Seminar

Time: 5:00PM - 6:00PM

Location: BLOC 302

Speaker: Yevgeniya Tarasova, Univedrsity of Michigan

Title: An introduction to liaison