Events for 03/04/2022 from all calendars

Algebra and Combinatorics Seminar

Title: CombinaTexas

Abstract: Conference website: https://www.math.tamu.edu/conferences/combinatexas/

Noncommutative Geometry Seminar

Time: 08:00AM - 09:00AM

Location: ZOOM

Speaker: Bernhard Hanke, Augsburg University

Title: Surgery, bordism and scalar curvature

Abstract: One of the most influential results in scalar curvature geometry, due to Gromov-Lawson and Schoen-Yau, is the construction of metrics with positive scalar curvature by surgery. Combined with powerful tools from geometric topology, this has strong implications for the classification of such metrics. We will give an overview of the method and point out some recent developments.

URL: Event link

Noncommutative Geometry Seminar

Time: 08:00AM - 09:00AM

Location: ZOOM

Speaker: Johannes Ebert, University of Münster

Title: Rigidity theorems for the diffeomorphism action on spaces of positive scalar curvature

Abstract: The diffeomorphism group, Diff(M), of a closed manifold acts on the space, R+(M), of positive scalar curvature metrics. For a basepoint, g, we obtain an orbit map σg : Diff(M) → R+(M) which induces a map on homotopy groups (σg)∗ : π∗(Diff(M)) → π∗( R+(M)). The rigidity theorems from the title assert that suitable versions of the map (σg)∗ factors through certain bordism groups. A special case of our main result asserts that (σg)∗ has finite image if M is simply connected, stably parallelizable, and of dimension at least 6. The results of this talk are from joint work of the speaker with Oscar Randal–Williams.

URL: Event link

Working Seminar on Banach and Metric Spaces

Time: 10:30AM - 11:30AM

Location: BLOC 302

Speaker: Ryan Malthaner, Texas A&M University

Title: Embedding trees into Banach spaces

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Jake Fillman, Texas State University

Title: Spectral properties of the unitary almost-Mathieu operator

Abstract: We introduce a unitary almost-Mathieu operator, which is a one-dimensional quasi-periodic quantum walk obtained from an isotropic two-dimensional quantum walk in a uniform magnetic field. We will discuss background information, the origins of the model, its interesting spectral features, and key ideas needed in proofs of the main results. [Joint work with Christopher Cedzich, Darren C. Ong, and Zhenghe Zhang]

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 306

Speaker: Igor Zelenko , TAMU

Title: Morse inequalities for eigenvalue branches of generic families of self-adjoint matrices

Abstract: The talk is based on the joint work with Gregory Berkolaiko. The eigenvalue branches of families of self-adjoint matrices are not smooth at points corresponding to repeated eigenvalues (called diabolic points or Dirac points). Generalizing the notion of critical points as points for which the homotopical type of (local) sub-level set changes after the passage through the corresponding value, in the case of the generic family we give an effective criterion for a diabolic point to be critical for those branches and compute the contribution of each such critical point to the Morse polynomial of each branch, getting the appropriate Morse inequalities as a byproduct of the theory. The motivation comes from the Floquet-Bloch theory of Schrodinger equations with periodic potential and other problems in Mathematical Physics.