webcal

Time:

11:30am

Location:

Room No. 105, Department of Mathematics

Description:

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) Brauer-Severi 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 `non-separated 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.
We will show how specialization of points can look very different in this algebraic space X, which illustrates the need for modifying the valuative criterion for universal closedness of morphisms when we wish to generalize from schemes to algebraic spaces. Further generalization to algebraic stacks needs a further modification in the valuative criteria, to be addressed later.

Time:

3:00pm

Location:

Ramanujan Hall, Department of Mathematics

Description:

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 high-dimensional 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 non-identical observations, and also identify the limit distribution by using free probability. We also propose a graphical test of independence under these assumptions.

Time:

4:00pm

Location:

Ramanujan Hall, Department of Mathematics

Description:

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 high-dimensional means under missing observations seems to be very rare in the literature. We propose a new two-sample test for high-dimensional 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 non-trivial extension of the two-sample 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.

Time:

4:00pm

Location:

https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09

Description:

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 well-posed-ness and error estimates for the mixed methods.

Time:

4:00pm

Location:

Room No. 114, Department of Mathematics

Description:

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.