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Presynopsis seminar

Monday, 6 Feb. 2023 11 am

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Venue: Ramanujan Hall

Host: Rekha Santhanam

Speaker: Soumyadip Thandar

Affiliation: IIT Bombay

Title: Equivariant Intrinsic Formality

Pre Synopsis Seminar

Title: Topology of surfaces and classification of affine curves

Date: February 6, 2023(Monday)

Time: 12:00 PM to 1:00 PM

Venue: Ramanujan Hal

Lecture series on Lie groups 

Date and Time: Six Mondays at 4 pm
Tea: 3.50 pm
Venue: A1-A2, CDEEP, Mathematics Department
Host: Dipendra Prasad

Speaker: M. S. Raghunathan, CEBS, Mumbai

Title: Compact Lie groups and their representations

Abstract: In this course I will first talk about the structure theory of compact Lie groups, beginning with the fact that a compact connected Lie group is an almost direct product of the identity connected component of its centre and its commutator subgroup (which is closed subgroup) conjugacy of maximal tori and the fact that every element is contained in a maximal torus. In the course of proving these results, some results on the topology of compact Lie groups which will also be proved. I will then establish Weyl's theorem which asserts that if G is a compact connected Lie group and [G, G]=G, π_1(G,e) is finite (and hence the universal covering of a compact group whose abelianisation is trivial is  compact. 

Then I will introduce roots and weights and the Dynkin diagram of the compact group and sketch a proof of the fact that the Dynkin diagram determines the group locally. The remaining lectures will be devoted to representation theory. I will establish the bijective correspondence between 'Dominant Weights' and irreducible representations. The course will end with the Weyl Character Formula for the character of an irreducible representation corresponding to a 'dominant' weight. The entire theory is essentially the same as the representation theory of reductive algebraic groups. I will off and on indicate how the two are related.  

I will be assuming some familiarity with basic theory of Lie groups such as the correspondence between Lie sub-algebras of the Lie group and Lie subgroups of the Lie groups, also with some basic results from algebraic topology.
 

Algebraic Geometry  and Commutative Algebra seminar

Tuesday, 05 February 2023, 11:30 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR Mumbai (retd)

Title: Local Criterion for Flatness

Statistics Seminar

Tuesday, 7th February, 3:30 pm

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Venue: Ramanujan Hall

Host: Sanjeev Sabnis

Speaker: Sujit Ghosh

Affiliation: North Carolina State University

Title: Possible Hazards of Some Popular Hazard Rate Models

Abstract: The Cox proportional hazard (PH) model is widely used to determine the effects of risk factors and treatments on survival time of subjects that might be right censored. The selection of covariates depends crucially on the specific form of the conditional hazard model, which is often assumed to be PH, accelerated failure time (AFT), or proportional odds (PO). However, it is shown that none of these semiparametric models allow for the crossing of the survival functions and hence such assumptions, although popular, may adversely affect the selection of risk factors. Moreover, the most commonly used PH assumption may also be violated when there is a delayed effect of the risk factors. A sequence of Bernstein polynomials based model is instead presented which provides (i) a smooth estimator of the conditional hazard and can be shown to be a unique solution of a strictly convex optimization problem; making it computationally attractive, (ii) a model that encompasses PH structure, and (iii) large sample properties including consistency and convergence rates can be established under a set of mild regularity conditions. Empirical results based on several simulated data scenarios indicate the superior performances of the model, and thereby shown to avoid possible hazards of some of the commonly used hazard rate models. The presentation is based on some ongoing work and the following published articles: (i) Osman and Ghosh (2012) and (ii) Sheng and Ghosh (2019).

Algebraic Groups Seminar

Tuesday, 7 February 2023, 4 pm

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Venue: Room 215

Host:Shripad M. Garge

Speaker: Deepkumar Makadiya

Affiliation: IIT Bombay

Title: Linear algebraic groups, basic themes. II

Abstract: This lecture will be devoted to proving that every affine algebraic group is linear.

Mathematics Colloquium

Wednesday, 8 February, 4 pm

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Venue: Ramanujan Hall

Speaker: Dipendra Prasad

Affiliation: IIT Bombay

Title: A synopsis of compact Lie groups and their representations.

Abstract: I will give an overview lecture on the topics listed in the title with a view

to some questions being pursued by me and my students.

Statistics Seminar

Thursday 9 Feb. 2023, 2 pm

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Venue: Ramanujan Hall

Host: Ashish Das

Speaker: Prof. Bikas Kumar Sinha

Affiliation: ISI Kolkata

Title: Optimal Covariates Designs in Factorial Models

Abstract:This talk is based on papers on "Optimal experimental designs for models with covariates", "A new class of optimal designs in the presence of a quantitative covariate" and the book “Optimal Covariate Designs”. There are still open problems in this area of combinatorial designs.

Department of Mathematics

Virtual Commutative Algebra Seminar.

Speaker: Saugata Basu,
  Purdue University, West Lafayette, IN, USA
Date/Time: 10 February 2023, 6:30pm
(joining time 6:20 pm IST)

Gmeet link: meet.google.com/ujm-mmpg-ckq [1]

Title: Homology of symmetric semi-algebraic sets
Abstract: Studying the homology groups of semi-algebraic subsets of 
$\mathbb{R}^n$ and obtaining upper boundson the Betti numbers has been a 
classical topic in real algebraic geometry beginning with the work of 
Petrovskii and Oleinik, Thom, and Milnor. In this talk I will consider 
semi-algebraic subsets of $\mathbb{R}^n$ which are defined by symmetric 
polynomials and are thus stable under the standard action of the 
symmetric group $\mathfrak{S}_n$ on $\mathbb{R}^n$. The homology groups 
(with rational coefficients) of such sets thus acquire extra structure 
as $\mathfrak{S}_n$-modules leading to possible refinements on the 
classical bounds. I will also mention some connections with a 
homological stability conjecture.

Joint work (separately) with Daniel Perrucci and Cordian Riener.

For more information and links to previous seminars, visit the website 
of VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar