Differential Geometry Seminar

报告人 Speaker:Timothée Bénard (Warwick Mathematic Institute)
组织者 Organizer:Akito Futaki, 邓嘉龙
时间 Time:Tuesday 21:00-22:00
地点 Venue:Zoom Meeting ID: 271 534 5558 Passcode: YMSC

Zoom link: https://us06web.zoom.us/j/2715345558?pwd=eXRTTExpOVg4ODFYellsNXZVVlZvQT09



Upcoming talks

Speaker: Timothée Bénard (Warwick Mathematic Institute)

Title: Limit theorems on nilpotent Lie groups.  

Abstract: I will present limit theorems for random walks on nilpotent Lie groups, obtained in a recent work with Emmanuel Breuillard. Most works on the topic assumed the step distribution of the walk to be centered in the abelianization of the group. Our main contribution is to authorize non-centered step distributions. In this case, new phenomena emerge: the large-scale geometry of the walk depends on the increment average, and the limit measure in the central limit theorem may not have full support in the ambient group.


Speaker:  Javier Martínez-Aguinaga  (Universidad Complutense de Madrid)

Title: $h$-Principle for maximal growth distributions

Abstract: The existence and classification problem for maximal growth distributions on smooth manifolds has garnered much interest in the mathematical community in recent years. Prototypical examples of maximal growth distributions are contact structures on $3$-dimensional manifolds and Engel distributions on $4$-dimensional manifolds.


The existence and classification of maximal growth distributions on open manifolds follows from Gromov’s $h$-Principle for open manifolds. Nonetheless, not so much was known for the case of closed manifolds and several open questions have been posed in the literature throughout the years about this problem.


In our recent work [1] we show that maximal growth distributions of rank $> 2$ abide by a full h-principle in all dimensions,  providing thus a classification result from a homotopic viewpoint. As a consequence we answer in the positive, for $k > 2$, the long-standing open question posed by M. Kazarian and B. Shapiro more than 25 years ago of whether any parallelizable manifold admits a $k$-rank distribution of maximal growth.


[1].  Martínez-Aguinaga, Javier. Existence and classification of maximal growth distributions . Preprint. arXiv:2308.10762


Upcoming talks

Title: TBA

Abstract: TBA

Speaker: James Bonifacio (University of Mississippi)


Speaker: Mario Garcia Fernandez (Universidad Autónoma de Madrid)


Speaker: Jacopo Stoppa (Scuola Internazionale Superiore di Studi Avanzati)


Speaker: Gonçalo Oliveira (Instituto Superior Técnicon Lisbon)


Speaker: Jeffrey D. Streets (University of California, Irvine)


Speaker: Fernando Galaz-García (Durham University)


Past Talks

Speaker: Kajal Das  (Indian Statistical Institute)

Title: On super-rigidity of Gromov's random monster group Slides)

Abstract: In my talk, I will speak on the super-rigidity of Gromov's random monster group. It is a finitely generated random group $\Gamma_\alpha$ ( $\alpha$ is in a probability space $\mathcal{A}$) constructed using an expander graph by M. Gromov in 2000. It provides a counterexample to the Baum-Connes conjecture for groups with coefficients in commutative $C^*$-algebra. It is already known that it has global fixed point property for isometric affine action on $L^p$ spaces for $1< p<\infty$ (in particular, Property (T) ) for a.e. $\alpha$ due to Gromov and Naor-Silberman. It is also hyperbolically rigid, i.e., any isometric action of the group on a Gromov-hyperbolic space is elementary for a.e. $\alpha$ (due to Gruber-Sisto-Tessera). In this talk, I will discuss the following type of super-rigidity problem (motivated by Margulis super-rigidity theorem): for which countable group $G$, any collection of homomorphisms $\phi_\alpha:\Gamma_\alpha\rightarrow G$ have a finite image for a.e. $\alpha$? This question was first addressed for linear groups by Naor-Silberman. The super-rigidity follows immediately from the literature for groups with a-$L^p$-menablity and K-amenable groups. In this talk, we will show that $\Gamma_\alpha$ has super-rigidity with respect to the following groups $G$: mapping class group $MCG(S_{g,p})$, braid group $B_n$, automorphism group of a free group $Aut(F_n)$, outer automorphism group of a free group $Out(F_N)$ . We will also show a stability result of the class of groups $G$.