- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**==================****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

- Time:
- 12:00pm-1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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

- Time:
- 4:00pm
- Location:
- A1-A2, CDEEP, Mathematics Department
- Description:
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, MumbaiTitle: 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.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**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

- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**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).

- Time:
- 4:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**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 viewto some questions being pursued by me and my students.

- Time:
- 2:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**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.

- Time:
- 6:30pm
- Location:
- Gmeet link: meet.google.com/ujm-mmpg-ckq
- Description:
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