- Time:
- 5:00pm - 6:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics Colloquium**Wednesday,1 February, 2023, 5-6 pm

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

**Venue:**Ramanujan Hall**Host:**Neela Nataraj**Speaker:**Jean-Pierre Raymond**Affiliation:**Paul Sabatier University, Toulouse**Title:**Stabilization of fluid flows using reduced order model based on spectral projections**Abstract:**We will present results concerning the stabilization of fluid flows, or systems coupling fluid flow equations with convection-diffusion equations. We are interested in the local stabilization around unstable stationary solutions. We build feedback laws (in the case of total information) for reduced models defined by spectral projection. We prove, in some of the studied cases, that the feedback law defined from the reduced model also stabilizes the initial system with an exponential decay rate a priori fixed. We also establish convergence rates of feedback laws for models approximated by a Finite Element Method towards the feedback law of the original model. This approach can be used by other type of approximation. This work is in collaboration with M. Badra (IMT).This numerical approach has been used in a series of papers with many collaborators (even if, as mentioned above, all the assumptions, ensuring convergence rates of approximate feedback laws, have not yet been proved in all these cases).

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Building connections between time series data, outbreak investigation, and phylogenetics to create predictive disease transmission models

Date and time: 2nd Feb 2023, 4-5 pm

Venue: Ramanujan Hall

Host: Siuli Mukhopadhyay

Speaker: Niket Thakkar

Affiliation: senior research scientist at the Institute for Disease Modeling, within the Bill & Melinda Gates Foundation.

Title: Building connections between time series data, outbreak investigation, and phylogenetics to create predictive disease transmission models

Abstract:

In this talk, I describe a biologically motivated signal processing approach for building a compartmental, stochastic process model of disease transmission, where the process's mean and variance have distinct dynamics. I apply the approach to COVID-19 time series data from Washington state from January 2020 to March 2021, and I find that the model's hidden states, like population prevalence, agree with survey and other estimates. Then, in the talk's second part, I demonstrate that the same model can be reframed as a branching process with a dynamic degree distribution. This perspective leads to a sampling approach to generate collections of approximate transmission trees, a transmission forest, which I use to estimate some higher order statistics, like the clustering of cases as outbreaks. I find that these predictions are consistent with related observations from outbreak investigations and phylogenetics, suggesting deeper connections between time series volatility and more individualistic measures of disease transmission. Finally, to conclude, I apply similar principles to data on measles transmission in Nigeria, to illustrate the generality of the ideas and to build in this case a more structured model capable of forecasting risk, and I describe how these models are currently being used to inform vaccination strategy.

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

Date and time: Thursday 2 February, 2023, 4 pm

Venue: Room 215

Host: Tony Puthenpurakal

Speaker: Tony Puthenpurakal

Affiliation: Mathematics Department, IIT Bombay

Title: A generalization of a theorem of Rees

Abstract:TBA

- Time:
- 6:30pm
- Location:
- Venue: meet.google.com/exp-duym-nrr
- Description:
**Virtual Commutative Algebra Seminar****Friday, 3 February, 2023, 6.30 pm****Host:**J. K. Verma**Venue**:**meet.google.com/exp-duym-nrr****Speaker:**Kevin Tucker**Affiliation:**University of Illinois Chicago, IL, USA**Title:**The Theory of F-rational Signature**Abstract:**The celebrated results of Smith, Hara, and Mehta-Srinivas connect rational singularities in characteristic zero after reduction to characteristic p > 0 with F-rational singularities. In recent years, a number of invariants defined via Frobenius in positive characteristics have been introduced as quantitative measures of F-rationality. These include the F-rational signature (Hochster-Yao), relative F-rational signature (Smirnov-Tucker), and dual F-signature (Sannai). In this talk, I will discuss new results in joint work with Smirnov relating each of these invariants. In particular, we show that the relative F-rational signature and dual F-signature coincide, while also verifying that the dual F-signature limit converges.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**==================****Presynopsis seminar**Monday, 6 Feb. 2023 11 am

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

**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

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

**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

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

**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

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

**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

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

**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

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

**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

- 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:
**Ph. D. Defence**Tuesday, 14 February 2023, 11.30 am

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

**Host:**Shripad Garge**Venue:**Ramanujan Hall**Speaker:****Arghya Pramanik****Title:****A Study in Topology and Geometry**

- Time:
- 12:30pm
- Location:
- Room 216, Mathematics Department
- Description:
**Department of Mathematics****Geometric Group Theory Learning Seminar**Tuesday, 14th Feb 2023, 12:30 PM

**Host:**Rekha Santhanam**Venue:**Room 216**Speaker:**Radhika Gupta (TIFR)**Affiliation:**TIFR, Mumbai**Title:**Introduction to the seminar series**Abstract:**I will give a (biased) introduction to geometric group theory,mentioning some questions and some sample theorems.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic groups seminar**Tuesday, 14 February 2023, 4 pm

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

**Venue:**Ramanujan Hall**Host:**Shripad M. Garge**Speaker:**Shripad M. Garge**Affiliation:**IIT Bombay, Mumbai**Title:**Some examples I**Abstract:**We will see some examples to understand some of the basic concepts in the theory of linear algebraic groups.

- Time:
- 8:00am
- Location:
- Zoom
- Description:
**Statistics seminar**Wednesday, 15 February, 8.00 am

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

**Venue:**Zoom**Host:**Ayan Bhattacharya**Speaker:**Ayan Bhattacharya**Affiliation:**IIT Bombay**Title:**Online lecture series on extreme value theory**Abstract:**In Part I of this lecture series, I will try first to provide an overview of the modelling aspects, avoiding mathematical details as much as possible. A basic understanding of probability is a must. Basic real analysis is also a must (convergence of a sequence and sequence of functions are essential). It will involve some knowledge of the convergence concepts in probability. I will try to explain this whenever needed and feel free to ask any questions in case of any confusion. However, a good understanding of the convergence concepts in probability and functions will make the lectures more accessible and appealing.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry and Commutative Algebra seminar**Tuesday, 15 February 2023, 11:30 am

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

**Venue:**Ramanujan Hall**Host****:**Sudarshan Gurjar**Speaker****:**Nitin Nitsure**Affiliation****:**TIFR Mumbai (retd)**Title:**Local Criterion for Flatness

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Commutative Algebra Seminar**Thursday, 16 February, 4 pm

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

**Venue:**Ramanujan Hall**Host:**Tony Puthenpurakal**Speaker:**Prof. R. V. Gurjar**Affiliation:**IIT Bombay**Title:**Positively Graded Domains**Abstract:**I will continue my lectures on this topic. Following results will be discussed. 1. Demazure's construction of normal affine positively graded domains. Some applications of this will be discussed. 2. Flenner and Keiichi Watanabe's rationality of singularities criterion for positively graded affine domains. 3. A very general result I conjectured around 1990 and proved by O.Mathieu In 2002 will be discussed. It has some new consequences for rings of invariants of reductive algebraic group action on an affine space. 4. Divisor Class Groups of positively graded domains. Works of Brieskon Flenner, Samuel, Scheja-Storch, Anurag Singh etc, will be mentioned. The connection with the topology of these results will be discussed.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Ph. D. Defence**Friday, 17 February 2023, 11.00 am

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

**Host:**Jugal Verma**Venue:**Ramanujan Hall**Speaker:**Saipriya Dubey**Title:**Tight Hilbert polynomials and F-rational local rings

- Time:
- 4:00pm
- Location:
- A1-A2, CDEEP, Mathematics Department
- Description:
**Lecture series on Lie groups**Monday, 20 Feb at 4 pm

**Tea**: 3.50 pm==============================

**Venue:**A1-A2, CDEEP, Mathematics Department**Host:**Dipendra Prasad**Speaker**: M. S. Raghunathan**Affiliation:**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.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Algebraic Geometry Seminar**Tuesday, 21 February 2023, 11.30 am

===========================**Venue:**Ramanujan hall**Host:**Sudarshan Gurjar**Speaker:**Nitin Nitsure**Affiliation:**TIFR, Mumbai (retd)**Title:**Local Criterion of Flatness-II

- Time:
- 4:00pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
**Algebraic groups seminar**Tuesday, 21 February 2023, 4 pm

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

**Venue:**Room 113**Host:**Shripad M. Garge**Speaker:**Deepkumar Makadiya**Affiliation:**IIT Bombay, Mumbai**Title:**Linear algebraic groups, basic themes- III**Abstract:**We begin the study of Jordan decomposition in linear algebraic groups.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Bombay Seminar Series on Probability and Statistics (BSSPS)****===================================================****Venue:**Ramanujan Hall**Host:**Ayan Bhattacharya**Dates:**Thursday, 23 February 2023, 11.30 am and 4 pmFriday, 24 February 2023, 10 am

**Speaker:**Prof. Arup Bose**Affiliation:**ISI, Kolkata**Title:**Non-commutative probability and its connections to random matrices**Abstract:**In this talk, the connection of the non-commutative probability to the large-dimensional random matrices will be discussed. This talk will be accessible to a wide audience.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Statistics Seminar**Thursday, 23 February 2023, 2.30 pm

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

**Venue:**Ramanujan Hall**Host:**Ayan Bhattacharya**Speaker:**Prof. Rishideep Roy**Affiliation:**Indian Institute of Management Bangalore**Title:**Some results in interacting particle systems**Abstract:**We will introduce two disease spread models, the frog model and the rumour model. In the frog model we show co-existence of multiple rumours first for finite types of rumours, followed by infinite co-existence, on Z^d. In rumour models we show the speed of spread of rumours on the integer line.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Bombay Seminar Series on Probability and Statistics (BSSPS)****===================================================****Venue:**Ramanujan Hall**Host:**Ayan Bhattacharya**Dates:**Thursday, 23 February 2023, 11.30 am and 4 pmFriday, 24 February 2023, 10 am

**Speaker:**Prof. Arup Bose**Affiliation:**ISI, Kolkata**Title:**Non-commutative probability and its connections to random matrices**Abstract:**In this talk, the connection of the non-commutative probability to the large-dimensional random matrices will be discussed. This talk will be accessible to a wide audience.

- Time:
- 10:00am - 11:00am
- Location:
- Room 216, Mathematics Department
- Description:
PhD defence seminar: Title: Totally positive field extensions and pythagorean closures of formally real fields. Day-Date: Friday, 24.02.2023 Time: 10 AM - 11 AM Venue: Room no 216, Department of Mathematics.

- Time:
- 10:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Bombay Seminar Series on Probability and Statistics (BSSPS)****===================================================****Venue:**Ramanujan Hall**Host:**Ayan Bhattacharya**Dates:**Thursday, 23 February 2023, 11.30 am and 4 pmFriday, 24 February 2023, 10 am

**Speaker:**Prof. Arup Bose**Affiliation:**ISI, Kolkata**Title:**Non-commutative probability and its connections to random matrices**Abstract:**In this talk, the connection of the non-commutative probability to the large-dimensional random matrices will be discussed. This talk will be accessible to a wide audience.

- Time:
- 5:30pm
- Location:
- Venue: Gmeet link: meet.google.com/pur-voek-uvo
- Description:
**Virtual Commutative algebra seminar**Friday, 24 February

**2023**, 5:30pm IST===============================

**Host:**J. K. Verma**Venue:**Gmeet link: meet.google.com/pur-voek-uvo**Speaker:**Luis Duarte**Affiliation:**University of Genoa, Genoa, Italy**Title:**Perturbations of ideals in local rings**Abstract:**Let I be an ideal of a Noetherian local ring R. We study how properties of the ideal change under small perturbations, that is, when I is replaced by an ideal J which is the same as I modulo a large power of the maximal ideal. In particular, assuming that R/J has the same Hilbert function as R/I, we show that the Betti numbers of R/J coincide with those of R/I. We also compare the local cohomology modules of R/J with those of R/I.For more information and links to previous seminars, visit the website of VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar

- Time:
- 4:00pm
- Location:
- A1-A2, CDEEP, Mathematics Department
- Description:
**Lecture series on Lie groups**Monday, 27 Feb at 4 pm

**Tea**: 3.50 pm==============================

**Venue:**A1-A2, CDEEP, Mathematics Department**Host:**Dipendra Prasad**Speaker**: M. S. Raghunathan**Affiliation:**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 center 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.I will be assuming some familiarity with the basic theory of Lie groups such as the correspondence between Lie sub-algebras of the Lie group and Lie subgroups of the Lie groups, and also with some basic results from algebraic topology.

- Time:
- 4:15pm
- Location:
- Conference room, Department of Mathematics
- Description:
**Presynopsis seminar**Monday, 28 Feb. 2023, 4.15 pm

**Venue:**Conference room**Host:**Siuli Mukhopadhyay**Speaker:**Savita Pareek**Affiliation:**IIT Bombay**Title:**On Some Problems in Mixed Effect Models