- Mon, February 26, 2024
- Tue, February 27, 2024
- Wed, February 28, 2024
- Fri, March 1, 2024
- Wed, March 6, 2024

- Time:
- 9:30am
- Location:
- https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09
- Description:
**Annual Progress Seminar****Date****Monday, 26 Feb, 9.30 am****Venue**https://us06web.zoom.us/j/6950684207?pwd=VkNmYzFBd0c0QWx3azhJODJ0QUp1Zz09

**Zoom ID :**6950684207**Passcode :**802747**Host**Neela Nataraj

**speaker**Aamir Yousuf

**Affiliation**IIT Bombay, Monash Univ.

**Title**Semi and fully discrete analysis of lowest-order non-standard finite element methods for the biharmonic wave problem.

**Abstract:**

- Time:
- 4:00pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
**Annual Progress Seminar****Date****26 Feb, Monday, 4 pm****Venue****Room 114****Host**Shripad Garge

**speaker**Deep Makadiya

**Affiliation**IIT Bombay

**Title**Twisted Chevalley groups over commutative rings

**Abstract**We discuss some results on the structure of twisted Chevalley groups over commutative rings with 1.

- 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****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.

- Time:
- 11:00am - 12:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Annual Progress seminar

Wed, 28 Feb 11:00 am -12:00 pm

==================================

Venue: Ramanujan Hall

Host: Suresh Kumar

Speaker: Vikrant Desai (174093013)

Title: Mean field games with degenerate diffusions

Abstract: We study mean field games with degenerate diffusions. We prove

the existence of a mean field equilibrium for class of mean field games with state dynamics given by controlled degenerate diffusions.

- Time:
- 1:30pm
- Location:
- https://meet.google.com/xtn-rapo-jsd
- Description:
**Pre-synopsis Seminar****Date**Wednesday 28 Feb, 1.30 pm

**Venue****Host**Sivaji Ganesh Sista

**speaker**Lalit Kumar

**Affiliation****IIT Bombay****Title**Kirchhoff type quasilinear space-time fractional PDE with memory

**Abstract:**In this seminar, we discuss three types of Kirchhoff-type PDE with memory involving usual time derivative, fractional time derivative, and fractional Laplacian. In the first half, we focus on well-posedness and regularity results. Then, we derive a semi-discrete error analysis of Galerkin FEM by defining a modified Ritz-Volterra projection operator. Finally, we develop fully discrete formulations and implement some examples to validate the proven theoretical results.

- Time:
- 3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Statistics Seminar**Date

**28 Feb Wednesday, 3 pm**Venue

Ramanujan Hall

**Host**Sanjeev Sabnis

**speaker**Girish Aras

**Title**Modern drug development and a brief History of drug regulation in the USA

**Abstract:**In the first half of the talk, I will introduce key ideas and methodologies of causal inference in the scientific foundations of evidence-based medicine. I will trace the history (20th century) of modern drug development through the evolution of the law known as The Food, Drugs and Cosmetic Act. The law was instituted and further evolved in response to some major global health events/crises. The US Congress gave sweeping powers to the FDA to interpret and execute the law to develop a drug approval process based on empirical data and science. We will also trace the law’s impact on global drug policies. In that context, we will discuss ‘adequate and well-controlled studies and the role of statistics in the process. We will discuss some of the important examples on the way.**Bio of the speaker:**As a statistician, I worked in academia, the federal government, and the Biotechnology/Pharma industry. I was in leadership and supervisory positions in the government (Department of Biostatistics at Center for Drug Development and Research, Food and Drug Administration), and in the pharma industry at Johnson & Johnson (large pharma), Amgen (mid-size pharma when I began there) and Esperion (small biotech).**The early**years of my career (about 10 years) were in academic positions starting as a lecturer at Bombay University followed by several years at the University of California, Santa Barbara with a brief sojourn to IIT, Mumbai. I continued methodological research and publishing during my time in the government and industry as well. Currently, I offer statistical and regulatory consulting services to pharmaceutical companies specializing in strategic and secondary review of submission modules, DMC statistical membership, strategic reviews of protocols, and statistical analysis plans mostly in dermatology, immunology, cardiovascular, and antiviral therapeutic areas. I am an elected Fellow of the American Statistical Association.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics Colloquium****Date****28 Feb, Wed, 4 pm****Venue****Ramanujan Hall****Host**Ravi Raghunathan

**speaker**Meera Mainkar

**Affiliation**Central Michigan University, Mt. Pleasant

**Title**Preserve one, preserve all

**Abstract:**The classical theorem of Beckman and Quarles states the following: A function from the Euclidean plane to itself that preserves unit distances must preserve all distances. We will discuss some key steps of the proof. We will also discuss our recent result generalizing this theorem. This is joint work with Ben Schmidt. We will try to make the talk accessible to a wide audience.

- Time:
- 4:00pm
- Location:
- Room No. 105, Department of Mathematics
- Description:
**Algebraic Groups seminar****Date**Friday, 1st March, 4 pm

**Venue**Room 105

**Host**Dipendra Prasad

**speaker**Deep Makadiya

**Affiliation****IIT Bombay****Title**Regular elements of semi-simple algebraic groups

**Abstract:**We will discuss a variety of topics in Algebraic groups through reading some of the papers that have become classics in the subject. The first few seminars will be on the paper by Robert Steinberg, Regular elements of semi-simple algebraic groups Publications mathématiques de l'I.H.É.S., tome 25 (1965), p. 49-80

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Analysis seminar****Date**Friday, 1 Mar, 4 pm

**Venue**Ramanujan Hall

**Host**Saikat Mazumdar

**speaker**Saikat Mazumdar

**Affiliation****IIT Bombay****Title**Taming explosions by blowing up

**Abstract:**In this talk, I will consider the question of compactness of (approximate) solutions to some Yamabe-type problems. We will see that by appropriately blowing up the singularities a finer analysis often reveals some analytical or geometric rigidity, thereby ruling out explosions. This establishes uniform bounds which implies compactness (in the appropriate topology) and gives existence and non-existence results.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics colloquium

Wednesday, March 6th, 4 pm

==================

Speaker: Leila Schneps

Affiliation: Institut de Mathématiques de Jussieu Paris

Title: Alexander Grothendieck: his life, his mathematics, and his writings.

Abstract: Alexander Grothendieck was arguably the most original, most influential, and

the most prolific mathematician of the 20th century. After retiring from active mathematics

in his early 40's, he contributed to several newer fundamental insights. This lecture will

reflect on some of the enigma around him, before and after ``retirement".Bio from Wikipedia:

Leila Schneps is an American mathematician and fiction writer at the Centre national de la recherche scientifique working in number theory. Schneps has written general audience math books and, under the pen name Catherine Shaw, has written mathematically themed murder mysteries.

Schneps earned a B.A. in Mathematics, German Language and Literature from Radcliffe College in 1983.[1] She completed a Doctorat de Troisième Cycle in Mathematics at Université Paris-Sud XI-Orsay in 1985 under the supervision of John H. Coates with a thesis on

*p*-adic L-functions attached to elliptic curves, a Ph.D. in Mathematics in 1990 with a thesis on*p*-Adic L-functions and Galois groups, and Habilitation at Université de Franche-Comté in 1993, with a thesis on the Inverse Galois problem.Schneps held various teaching assistant positions in France and Germany until the completion of her Ph.D. in 1990, then worked as a postdoctoral assistant at the ETH in Zurich, Switzerland, for one year. In 1991 she was awarded a tenured research position at CNRS, the French National Centre for Scientific Research, at the University of Franche-Comté in Besançon. During the late 1990s Schneps also had short-term visiting researcher assignments at Harvard University, Princeton's Institute for Advanced Study, and MSRI at Berkeley.