Events for 04/08/2022 from all calendars

Noncommutative Geometry Seminar

Time: 08:00AM - 09:00AM

Location: ZOOM

Speaker: Weiping Zhang, Nankai University

Title: Deformations of Dirac operators

Abstract: Deformations of Dirac operators have played important roles in various aspects in geometry and topology. In this expository talk I will discuss some of these applications.

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Noncommutative Geometry Seminar

Time: 09:15AM - 10:15AM

Location: ZOOM

Speaker: Guangxiang Su, Chern Institute of Mathematics

Title: Nonnegative scalar curvature and area decreasing maps on complete foliated manifolds

Abstract: Let $(M,g^{TM})$ be a noncompact complete Riemannian manifold of dimension $n$, and $F\subseteq TM$ be an integrable subbundle of $TM$. Let $g^F=g^{TM}|_{F}$ be the restricted metric on $F$ and $k^F$ be the associated leafwise scalar curvature. Let $f:M\to S^n(1)$ be a smooth area decreasing map along $F$, which is locally constant near infinity and of non-zero degree. We show that if $k^F> {\rm rk}(F)({\rm rk}(F)-1)$ on the support of ${\rm d}f$, and either $TM$ or $F$ is spin, then $\inf (k^F)<0$. As a consequence, we prove Gromov's sharp foliated $\otimes_\varepsilon$-twisting conjecture. Using the same method, we also extend two famous non-existence results due to Gromov and Lawson about $\Lambda^2$-enlargeable metrics (and/or manifolds) to the foliated case. This is a joint work with Xiangsheng Wang and Weiping Zhang.

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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 martingales differences II

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Reuven Hodges, UCSD

Title: Classifying Levi-spherical Schubert varieties

Abstract: A Schubert variety in the complete flag variety GL_n/B is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic subgroup has an open dense orbit. I will present some recent work, joint with Alexander Yong and Yibo Gao, giving a classification of Levi-spherical Schubert varieties in terms of spherical elements of a symmetric group. As part of this we will discuss the combinatorics of Demazure modules and their key polynomials. I will also discuss a conjectural extension of the classification to other Lie types.