Tuesday, May 11, 2021
Time  Items 

All day 

9am 
05/11/2021  9:00am Eisenstein series are key objects in the theory of automorphic forms. They are an important tool in the study of automorphic $L$functions, and they figure out in the spectral decomposition of the $L^2$space of automorphic forms. In recent years, new constructions of global integrals generating identities relating Eisenstein series were discovered. In 2018 Ginzburg and Soudry introduced two general identities relating Eisenstein series on split classical groups (generalizing MÅ“glin 1997, GinzburgPiatetskiShapiroRallis 1997, and CaiFriedbergGinzburgKaplan 2016), as well as double covers of symplectic groups (generalizing Ikeda 1994, and GinzburgRallisSoudry 2011). We consider the Kronecker product embedding of two general linear groups, $\mathrm{GL}_{m}(\mathbb{A})$ and $\mathrm{GL}_{n}(\mathbb{A})$, in $\mathrm{GL}_{mn}(\mathbb{A})$. Now, similarly to Ginzburg and Soudry's construction, we use a degenerate Eisenstein series of $\mathrm{GL}_{mn}(\mathbb{A})$ as a kernel function on $\mathrm{GL}_{m}(\mathbb{A}) \otimes \mathrm{GL}_{n}(\mathbb{A})$. Integrating it against a cusp form on $\mathrm{GL}_{n}(\mathbb{A})$, we obtain a 'semidegenerate' Eisenstein series on $\mathrm{GL}_{m}(\mathbb{A})$. Locally, we find a nice relation to the local GodementJacquet integral. Location: 
4pm 
05/11/2021  4:00pm In this talk, we explore the geometry of the handlebody group, i.e. the mapping class group of a handlebody. This talk will include a heuristic description of hierarchically hyperbolic spaces, and using this description, we will see that the handlebody group of genus two is a hierarchically hyperbolic group (HHG). Then, by analyzing the structure of the maximal hyperbolic space associated to the handlebody group and utilizing the characterization of stable subgroups of HHGs, I will show that the stable subgroups of the genus two handlebody group are precisely those subgroups whose orbit maps are quasiisometric embeddings into the disk graph. Lastly, we will see that various properties of the genus two handlebody group do not hold for higher genus handlebody groups. Location: 