April 1, 2024 - April 5, 2024
Public Access Category: All |
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- Time:
- 11:30am
- Description:
Algebraic geometry seminar
Date
Tuesday, 2 April, 11.30 am
Venue
Room 215
Host
Sudarshan Gurjar
speaker
Nitin Nitsure
Affiliation
Bhaskaracharya Pratishthana, Pune
Title
Overview and summary of my 50 lectures on Algebraic Stacks and
Moduli spaces, 2022-24.Abstract
I gave a series of about 50 lectures on Algebraic Stacks and Moduli spaces in the Department of Mathematics, IIT-B, spread across four semesters from 2022 to 2024. This is the final lecture of this series, in which I will summarise the main themes, and make suggestions for further study.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic groups Seminar
Date
Tuesday, April 2, 2024, 4 pm
Venue
Ramanujan Hall
Host
Shripad M. Garge
speaker
Akash Yadav
Affiliation
IIT Bombay
Title
Connected solvable groups
Abstract
We begin studying connected, solvable, linear algebraic groups starting with the Lie-Kolchin theorem.
- Time:
- 4:00pm-5:00pm
- Location:
- Room 215, Mathematics Department
- Description:
Commutative Algebra Seminar
Date
Tuesday, 2 April, 2024, 4-5 pm
Venue
Room 215
Host
Tony J. Puthenpurakal
speaker
Om Prakash
Affiliation
IIT Bombay
Title
Numerical Semigroups and associated Semigroup Rings-I
Abstract
In this series of two lectures, we will study numerical semigroups and their associated semigroup rings. Initially, we will define numerical semigroups, state their fundamental properties, and introduce relevant invariants. Subsequently, we aim to prove the following fundamental results: (i) The Frobenius number of a numerical semigroup S equals the degree, viewed as a rational function, of the Hilbert series of the numerical semigroup ring k[S]. (ii) The Cohen-Macaulay type of the numerical semigroup ring $k[S]$ corresponds to the number of pseudo-Frobenius elements of $S$. Consequently, we derive a well-known result concerning Gorenstein numerical semigroup rings (credited to Kunz) asserting that k[S] is Gorenstein if and only if S is symmetric.
- Time:
- 4:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
Algebraic groups Seminar
Date
Thursday, 4 April, 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 continue with the seminar on Algebraic groups reading the paper of Robert Steinberg, Regular elements of semi-simple algebraic groups Publications mathématiques de l’I.H.É.S., tome 25 (1965), p. 49-80
- Time:
- 10:15am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Topology and Related Topics Seminar
Date
Friday, 5 April 2024, 10.15 am
Venue
Ramanujan Hall
Host
Rekha Santhanam
speaker
Sudarshan Gurjar
Affiliation
IIT Bombay
Title
Vector bundles and Characteristic Classes
Abstract
This is the third talk in the series of three talks. We will give an introduction to the characteristic classes of a vector bundle. Characteristic classes are invariants of a vector bundle taking values in the singular cohomology of the base and satisfying the obvious functoriality property concerning pullback. They are the measure of the non-triviality of the vector bundle.
The background assumed will depend on the audience present.
- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic geometry seminar
Date
Friday, 5 April, 11.30 am
Venue
Ramanujan Hall
Host
Sudarshan Gurjar
speaker
Nitin Nitsure
Affiliation
Bhaskaracharya Pratishthana, Pune
Title
Introduction to the Tohoku (1957) paper of Grothendieck-part 1
Abstract
In 1957, Alexander Grothendieck published a long paper in
two parts in the Tohoku Mathematical Journal, Japan,
whose title can be translated as `On some points of homological
algebra'. This paper revolutionized the subject of homological
algebra and it sheds unifying light on topics in diverse areas such as group theory, Lie theory, number theory, algebraic topology, etc. It had profound applications to Algebraic Geometry, which were made apparent by Grothendieck and his school in the next few decades. The ideas of abelian categories and additive functors between them, and their derived functors, come from this paper. The famous `Grothendieck spectral sequence' first appeared here. I will give a series of two talks, introducing this paper's ideas and reporting some subsequent developments.
The first talk will assume no prior knowledge except of the basics of groups, rings, and modules at an undergraduate level. In it,
I will explain the historical context, and introduce the paper's themes in simple terms. The second talk will assume some
acquaintance with Algebraic Geometry.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Analysis seminar
Date
Friday, April 5, 4 pm - 5 pm
Venue
Ramanujan Hall
Host
Chandan Biswas
speaker
Prachi Mahajan
Affiliation
IIT Bombay
Title
The Squeezing function & the Fridman invariant
Abstract
The squeezing function and its dual, the Fridman invariant, are biholomorphic invariants, both of which capture the coarse metric geometry of the given domain. I will describe some results on the squeezing function and Fridman invariant such as their boundary behavior, their utility in classifying the unit ball under various hypotheses, and estimates near the boundary of the given domain. In the second part, I will compare this pair of invariants by showing that they are both equally capable of determining the boundary geometry of a bounded domain if their boundary behavior is apriori known.