- 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