Fall 2025
This seminar meets on Wednesdays 2:00-3:00 PM in Blocker 302.
The organizers are Simone Cecchini, Runije Hu, Qiaochu Ma, Jesus Sanchez Jr, Zhizhang Xie and Guoliang Yu.
| Date |
Speaker |
Affiliation |
Title |
Abstract |
| August 27, 2025 |
Qiaochu Ma |
Texas A&M University |
Small Scale Index Theory, Scalar Curvature, and Gromov’s Simplicial Norm |
View Abstract |
| September 3, 2025 |
Ryo Toyota |
Texas A&M University |
Twisted coarse Baum-Connes conjecture and relatively hyperbolic groups |
View Abstract |
| September 10, 2025 |
Simone Cecchini |
Texas A&M University |
Positive scalar curvature with point singularities |
View AbstractD |
| September 17, 2025 |
Jesus Sanchez Jr |
Texas A&M University |
Hypoelliptic Operators on Contact Manifolds |
View Abstract |
| September 24, 2025 |
Hongyi Liu |
Princeton University |
TBD |
TBD |
| October 1, 2025 |
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| October 8, 2025 |
Tao Mei |
Texas A&M University |
TBD |
TBD |
| October 15, 2025 |
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| October 22, 2025 |
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| October 29, 2025 |
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| November 5, 2025 |
Thomas Tony |
University of Muenster |
TBD |
TBD |
| November 12, 2025 |
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| November 19, 2025 |
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| November 26, 2025 |
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| December 3, 2025 |
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Scalar curvature encodes the volume information of small geodesic balls within a Riemannian manifold, making it, to some extent, the weakest curvature invariant. This raises a natural question: what topological constraints does scalar curvature impose on manifolds? In this talk, we shall show that for a manifold with a scalar curvature lower bound, the simplicial norm of certain characteristic classes can be controlled by its volume and isoperimetric constant. This is joint work with Guoliang Yu.
We introduce twisted coarse Baum–Connes conjecture with stable coarse algebras, a geometric analogue of the Baum–Connes conjecture with coefficients. We show that this twisted version has stronger permanence properties than the classical coarse Baum–Connes conjecture, particularly with respect to unions and subspaces. We apply this framework to relatively hyperbolic groups. For a finitely generated group $G$ that is hyperbolic relative to $\{H_1,\cdots,H_n\}$, it is known that $G$ satisfies coarse Baum-Connes conjecture if each $H_i$ does and $H_i$ admits finite-dimensional simplicial model of the universal space proper actions. Using our permanence results, we can show that $G$ satisfies twisted coarse Baum-Connes conjecture with stable coefficients, if and only if each $H_i$ does. This is a joint work with Jintao Deng.
Historically the elliptic differential operators have held a special place for their importance in mathematical physics as well as their ability to connect various subjects within pure mathematics. In recent years, the Fourier theoretic approach to elliptic operators has seen much progress in its extension to a wider class of operators, those which are hypoelliptic. In this talk we will use the extended Fourier theoretic approach to provide a construction of a new hypoelliptic operator on the Heisenberg group and discuss its properties and generalizations to contact manifolds. This is joint work with Andres Franco Valiente.
