Mathematics Colloquium:

Wednesday, 14  February  2023, 4:00 pm

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Venue: Ramanujan hall

Host: Ravi Raghunathan

Speaker: Manish Patnaik

Affiliation: University of Alberta

Title: Eisenstein series and some variants on Loop Groups

Abstract: We will first review some aspects of the reduction theory for loop groups studied by Howard Garland in the 1970s. Following this, we explain how features of the Siegel domains in this setting essentially force certain cuspidal Eisenstein series on loop groups to be entire functions, in stark contrast to the finite-dimensional situation. 

Switching to the case of function fields, we then introduce, following ideas of Braverman and Kazhdan, new “regularized” cuspidal Eisenstein series for loop groups. These series are no longer entire and their Fourier coefficients encode (finite-dimensional) automorphic L-functions that have previously remained inaccessible by the standard Langlands-Shahidi method.

Probability and statistics seminar

Wednesday, 14th Feb, 4 pm--5pm

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Venue: Room 113, Maths Dept

Host: Siuli Mukhopadhyay

Speaker: Subhra Sankar Dhar

Affiliation:   IIT Kanpur

Title: Inspecting discrepancy between multivariate distributions using half-space depth

 Abstract: In this talk, we inspect whether a multivariate distribution is different from a specified distribution or not AND two multivariate distributions are equal or not. In the course of this study, a graphical toolkit using well-known half-spaced depth is proposed, which is a two-dimensional plot, regardless of the dimension of the data, and it is even useful in comparing high-dimensional distributions. The simple interpretability of the proposed graphical toolkit motivates us to formulate test statistics to carry out the corresponding testing of hypothesis problems. It is established that the proposed tests are consistent, and the asymptotic distributions of the test statistics under contiguous/local alternatives are derived, which enables us to compute the asymptotic power of these tests. Furthermore, it is observed that the computations associated with the proposed tests are unburdensome. Besides, these tests perform better than many other tests available in the literature when data are generated from various distributions such as heavy-tailed distributions, which indicates that the proposed methodology is robust as well. Finally, the usefulness of the proposed graphical toolkit and tests is shown on two benchmark real data sets. This is a joint work with Pratim Guha Niyogi (Johns Hopkins University, USA).