


Algebraic Geometry Seminar 

Date 
27 Feb Tuesday, 11.30 am 
Venue 
Room 105 
Host 
Sudarshan Gurjar 
speaker 
Nitin Nitsure 
Affiliation 
Bhaskaracharya Pratishthana 
Title 
Galois descent in topology, algebra, and geometry. 
Abstract: We will begin by introducing Galois descent, and giving diverse examples of effective Galois descent to produce `twisted forms' in topology, algebra and geometry: (1) The Mobius band is a twisted form of a cylinder. (2) The division algebra H of Hamilton quaternions is a twisted form of the 2 x 2 matrix algebra M over real numbers R. (3) The real algebraic groups SO(2,R) and SU(2) are twisted forms of GL(1,R) and SL(2,R) respectively. (4) BrauerSeveri varieties are twisted forms of projective spaces. We will then connect the questions of twisted forms and effective Galois descent to the 1st cohomology set of the Galois group. After this, we will turn to the general problem of effective Galois descent for schemes (of which (3) and (4) are examples). We will show that: (A) Under a certain condition, effective Galois descent holds for schemes. (B) But more generally, effective Galois descent always holds for algebraic spaces. (C) The `nonseparated affine line' over R has as a twisted form an algebraic space X over R that is not a scheme, which shows that Galois descent (and so etale descent or flat descent) is not always effective for schemes. 
Annual Progress Seminar 

Date 
27 Feb Tuesday, 3 pm 
Venue 
Ramanujan Hall 
Host 
Monika Bhattacharjee 
speaker 
Raunak Shevade 
Affiliation 
IIT Bombay 
Title 
Limiting spectral distribution of large Kendall's correlation matrix and its application 
Abstract: The limiting spectral distribution (LSD) of highdimensional Kendall's correlation matrix and tests of independence based on this matrix have been studied in the literature when observations are absolutely continuous with respect to the Lebesgue measure, and are independent and identically distributed. We investigate the LSD of this matrix under much weaker assumptions which accommodate discrete and/or nonidentical observations, and also identify the limit distribution by using free probability. We also propose a graphical test of independence under these assumptions.
Annual Progress Seminar 

Date 
Tuesday, 27 Feb, 4 pm 
Venue 
Ramanujan Hall 
Host 
Monika Bhattacharjee 
speaker 
Shiv Kumar Yadav 
Affiliation 
IIT Bombay 
Title 
Two sample tests for high dimensional means under missing observations 
Abstract: Statistical test for highdimensional means under missing observations seems to be very rare in the literature. We propose a new twosample test for highdimensional means based on independent observations with missing values. The critical region of the proposed test is based on a bootstrap estimate of the sample quantiles of the proposed test statistic. Unlike the existing tests, this test does not require any distributional assumptions or any particular correlation structure of the covariance matrices. We establish the Gaussian approximation result for the proposed test statistic which is a nontrivial extension of the twosample Gaussian approximation result with no missing values. The rate of accuracy of the bootstrap approximation of the sample quantile of the proposed test statistic is also derived. This Gaussian approximation result and the accuracy of the bootstrap estimators together provide the theoretical guarantees on the size and power of the proposed test.
Annual progress seminar 

Date 
27 Feb Tuesday, 4 pm 
Venue 
https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09 

Zoom ID 695 068 4207 Passcode 802747 
Host 
Neela Nataraj 
speaker 
Shivani Goel 
Affiliation 
IIT Bombay 
Title 
Mixed finite element method 
Abstract 
In this talk, we discuss mixed variational formulation and mixed finite element method for the Poisson and Stokes problems. We will discuss the wellposedness and error estimates for the mixed methods. 
Algebraic groups seminar 

Date 
27 Feb Tuesday, 4 pm 
Venue 
Room 114 
Host 
Shripad Garge 
speaker 
Shripad Garge 
Affiliation 
IIT Bombay 
Title 
Quotients 
Abstract 
We prove the existence of a quotient of a linear algebraic group G by a closed subgroup H. 