4. Commutative Algebra Seminar
Speaker: R. V. Gurjar (TIFR, Mumbai (retired))
Title: Local Analytic Geometry
Time, Day and Date: 12:30 - 2:00 p.m., Tuesday, October 1
Venue: Room 215, Department of Mathematics
 

Combinatorics Seminar
Speaker: Anand Srivastav (Kiel University, Germany)
Title: Chromatic number of randomly augmented graphs
Time, Day and Date: 4:00 - 5:00 p.m., Tuesday, October 1
Venue: Room 114

Abstract: https://drive.google.com/open?id=1EQxBeQKYytlkBAHQf7gaTpgLzzr36WAh

Algebraic Groups Seminar
Speaker:  Shripad Garge (Department of Mathematics, IIT Bombay)
Title: Geometric questions related to the Bruhat decomposition II
Time, Day and Date: 4:00 - 6:00 p.m., Tuesday, October 1
Venue: Ramanujan Hall, Department of Mathematics
Abtract: We study some geometric aspects of the Bruhat decomposition.

Speaker: Dr Renu Joshi, IISER Bhopal

Time, Day and Date: 2.30 pm, Thursday, October 3, 2024.

Google Meet Link: https://meet.google.com/fqv-owns-ydv

Title: The Schur Multiplier and Non-inner Automorphism Conjecture

Abstract: The Schur multiplier M(G) of a finite group G is defined as H^2(G, ℂ×), where ℂ× is the trivial G-module. Several authors have determined upper bounds on the order, rank, and exponent of M(G). If G is a p-group of a maximal class of order p^n and 4 ≤ n ≤ p+1, we demonstrate that the Schur multiplier M(G) is an elementary abelian p-group. Additionally, the case n = p+1 answers a question raised by Primož Moravec.

In 1973, Berkovich asked if every finite non-abelian p-group has a non-inner automorphism of order p, for any prime p. This problem is solved in the positive direction for several classes of p-groups. In 2017, it was proven for p-groups of co-class 3 for p≠3. Consequently, the following question arises: Does the non-inner automorphism conjecture hold for finite 3-groups of co-class 3? Our current work focuses on 3-groups of co-class 3. We will discuss our progress and findings in this direction.

Complex Algebraic Surfaces
Speaker: Ronnie Sebastian (Department of Mathematics, IIT Bombay)
Title: Ruled Surfaces
Time, Day and Date: 3:30 - 5:00 p.m., Thursday, October 3
Venue: Room 114, Department of Mathematics

Abstract: We will continue with Chapter 3 in Beauville.

Algebraic Groups Seminar
Speaker: Deep Makadiya (Department of Mathematics, IIT Bombay)
Title: Nilpotent conjugacy classes
Time, Day and Date: 4:00 - 5:30 p.m., Friday, October 4
Venue: Room 215, Department of Mathematics

Abtract:We will continue the analysis of nilpotent conjugacy classes using the book by Collingwood and McGovern.

Number theory seminar
Speaker: Keshav Aggarwal (Department of Mathematics, IIT Bombay)

Title: Tate's thesis learning seminar

Time, day and date: 11:30:00 AM - 1:00:00 PM, Monday, October 7, 2024

Venue: Room No .215, Department of Mathematics

Commutative Algebra seminar
Speaker: Om Prakash (Department of Mathematics, IIT Bombay)

Title: Affine semigroups and semigroup rings

Time, day and date: 12:30:00 PM - 2:00:00 PM, Tuesday, October 8, 2024

Venue: Room No .215, Department of Mathematics

Algebraic groups seminar
Speaker: Deep Makadiya (Department of Mathematics, IIT Bombay)

Title: Two-dimensional root systems

Time, day and date: 4:00:00 PM - 6:00:00 PM, Tuesday, October 8, 2024

Venue: Ramanujan Hall, Department of Mathematics

Number theory seminar
Speaker: Animesh Sinha (Department of Mathematics, IIT Bombay)

Title: Spectral theory of automorphic forms seminar

Time, day and date: 11:30:00 AM - 1:00:00 PM, Wednesday, October 9, 2024

Venue: Room No .215, Department of Mathematics

Colloquium:
Speaker: Jugal K. Verma (IIT Gandhinagar)

Title: Real roots of real polynomials, real nullstellensatz, and a solution to Hilbert's 17th problem

Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, October 9, 2024

Venue: Ramanujan Hall, Department of Mathematics

Complex Algebraic Surfaces
Speaker: Ronnie Sebastian (Department of Mathematics, IIT Bombay)

Title: Complex Algebraic Surfaces

Time, day and date: 3:30:00 PM - 5:00:00 PM, Thursday, October 10, 2024

Venue: Room No .114, Department of Mathematics

Algebraic groups seminar
Speaker: Chayan Karmakar (Department of Mathematics, IIT Bombay)

Title: Nilpotent Conjugacy Classes

Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, October 11, 2024

Venue: Room No .215

Number theory seminar
Speaker: Keshav Aggarwal (IIT Bombay)
Title: Tate's thesis learning seminar
Time, day and date: 11:30:00 AM - 1:00:00 PM, Monday, October 14, 2024
Venue: Room 215

Algebraic groups seminar
Speaker: Deep Makadiya (IIT Bombay)
Title: Two Dimensional root systems
Time, day and date: 4:00:00 PM - 6:00:00 PM, Tuesday, October 15, 2024
Venue: Ramanujan Hall, Department of Mathematics

Number theory seminar
Speaker: K. Mallesham (IIT Bombay)
Title: Spectral theory of automorphic forms
Time, day and date: 11:30:00 AM - 1:00:00 PM, Wednesday, October 16, 2024
Venue: Room 215

Combinatorics seminar
Speaker: Rogers Mathew (IIT Hyderabad)
Title: Extremal results on conflict-free coloring
Time, day and date: 11:30:00 AM - 1:00:00 PM, Wednesday, October 16, 2024
Venue: Ramanujan Hall, Department of Mathematics

Abstract
A conflict-free open neighborhood coloring of a graph is an assignment of colors to the vertices such that for every vertex there is a color that appears exactly once in its open neighborhood. For a graph $G$, the smallest number of colors required for such a coloring is called the conflict-free open neighborhood (CFON) chromatic number and is denoted by $\chi_{ON}(G)$. By considering closed neighborhood instead of open neighborhood, we obtain the analogous notions of conflict-free closed neighborhood
(CFCN) coloring, and CFCN chromatic number (denoted by $\chi_{CN}(G)$). The notion of conflict-free coloring was introduced in 2002, and has since received considerable attention. In this talk, we explore some extremal questions on CFON and CFCN colorings. This talk is based on a joint work with Sriram Bhyravarapu, Shiwali Gupta, and Subrahmanyam Kalyanasundaram.

Complex Algebraic Surfaces
Speaker: Ronnie Sebastian (IIT Bombay)
Title: Complex Algebraic Surfaces
Time, day and date: 3:30:00 PM - 5:00:00 PM, Thursday, October 17, 2024
Venue: Room 114
 

Commutative Algebra seminar
Speaker: Om Prakash (IIT Bombay)
Title: Affine semigroups and semigroup rings
Time, day and date: 4:00:00 PM - 5:30:00 PM, Thursday, October 17, 2024
Venue: Room 215

Algebraic groups seminar
Speaker: Deep Makadiya (IIT Bombay)
Title: The structure constants
Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, October 18, 2024
Venue: Room 215

Expository lectures on the Ricci flow
Speaker: Pradip Kumar Maity (IIT Bombay)
Title: Talk 1
Time, day and date: 4:00:00 PM - 5:00:00 PM, Friday, October 18, 2024
Venue: Ramanujan Hall, Department of Mathematics
 

Commutative Algebra seminar
Speaker: Prof. J. K. Verma (IIT Gandhinagar)
Title: Hilbert-Kunz multiplicity of powers of an ideal
Time, day and date: 5:30:00 PM - 6:30:00 PM, Friday, October 18, 2024
Venue: Ramanujan Hall, Department of Mathematics

1. Number theory seminar

Time, Day, Date: 21st October, Monday  11:30 am

Venue : Room 215

Speaker: Aratrika Pandey

Title :  Tate's thesis learning seminar

Abstract : We will finish calculating certain local zeta integrals by
carefully choosing test functions in the unramified vs ramified cases.
This finishes section 2.3 of Goldfeld and Hundley's book. If time allows,
we will start the discussion of section 2.4.
 

2. Algebraic groups seminar

Time, Day, Date: 22nd October, Tuesday, 4:00 pm

Venue: Ramanujan Hall

Speaker: Shripad Garge

Title: Structure constants

Abstract : We are progressing towards understanding the structure of
reductive groups. Understanding the structure constants in the Chevalley
commutator formula is a step in that direction.

Colloquium 1:

Time, Day, Date: 23rd October, Wednesday 4:00 pm

Venue ; Ramanujan Hall

Speaker: S.K. Roushon

Title :  On the affine Artin group of type \tilde B_n

Abstract : We give a positive answer to a question of Bestvina by showing
that the group in the title is virtually poly-free. Our method also gives
another solution to the K(\pi, 1) problem in this case. This is a joint
work with Li Li.

Colloquium 2:

Time, Day, Date: 24rd October, Thursday 4:00 pm

Venue ; Ramanujan Hall

Speaker: S. Ramanan

Title : Hyperelliptic curves and Geometry of quadrics

Abstract : There is a deep relationship between hyper-elliptic curves of
genus $g$ and quadric geometry in a projective space of dimension $2g +1$.
When $g = 2$,  this was investigated by Klein in the 19th century.
Narasimhan and I related this to the moduli of vector bundles. Usha and I
generalised the results to arbitrary genus. Recently I modified and
formulated the proofs in such a way that it would work over a number
field. This was used by Parimala Raman and Jaya Iyer to get
number-theoretic consequences. I propose to give a summary of my methods
which yield some additional consequences as well.
 

4. Commutative Algebra Seminar

Time, Day and Date : 24th October, Thursday, 4:00 pm

Venue : Room 215

Speaker : Samarendra Sahoo

Title : Primes associated to multigraded rings.

Abstract :  Let A be a Noetherian ring, I be an ideal, and M be a finitely
generated A-module. Brodmann(1979) proved that the set Ass(I^nM/I^{n+1}M)
and Ass(M/I^nM) are stable for large n. McAdam and Eakin(1979) proved that
if R is a standard graded Noetherian ring with R_0=A and M is a finitely
generated graded R-module then the set Ass_A(M_n) is stable for all large
n. In this series of talks, we will discuss a multigraded version of the
above result and its applications.
 

5. Analysis Seminar (Ricci flows)

Time, Day and Date: 24th October, Thursday, 5:30 pm

Venue : Ramanujan Hall

Speaker: Pradip Kumar Maity

Title : 2nd expository talk on Ricci flows

Abstract : We will continue with Ricci solitons. Then we shall move to
variation formulas. Next we will discuss briefly short time existence of
Ricci flow. After that  we will move to Maximum principal and its
consequences.
 

3. Complex Algebraic Surfaces

Time, Day and Date: 25th October, Friday, 2.00pm to  3:30 pm

Venue : Room 215

Speaker : Ronnie Sabastian

Abstract : We will prove Castelnuovo's Theorem, which says that if q=0 and
P_2=0 then the surface is rational.
 

6. Algebraic Groups seminar

Time, Day and Date : 25th October, Friday 4:00 pm

Venue : Room 215

Speaker :  Dibyendu Biswas

Title : Nilpotent Conjugacy Classes

Abstract : We continue the analysis of nilpotent conjugacy classes from
the book of Collingwood and McGovern.
 

Colloquium:

Speaker: Santosha Pattanayak (IIT Kanpur)

Title: Commuting matrices and a higher dimensional Chevalley restriction theorem

Time, day and date: 16:00 - 17:00, Monday, October 28

Venue: Ramanujan Hall

Abstract:

The variety of d-tuples of commuting n x n matrices is an object of great interest in Mathematics. It has applications in algebraic geometry, representation theory, symplectic geometry and complexity theory. However, its geometry is complicated and surprisingly many simple looking conjectures are still open. We will discuss the geometry of the commuting variety via a higher dimensional Chevalley restriction theorem. A large part of the talk will be accessible to undergraduates.

Partial Differential Equations Seminar

Speaker: Tuhin Ghosh (HRI, Allahabad)

Title: Inverse homogenization of Maxwell equations and H-measure

Time, day and date: 16:00 - 17:00, Monday, October 28

Venue: Room 114

1. Thesis defence

Speaker: Dibyendu Biswas

Title: Some Questions in Representation Theory of General Linear and Classical Groups

Time, day and date: 11:30 - 13:00, Monday, October 28

Venue: Ramanujan Hall

Commutative Algebra Seminar

Speaker: Samarendra Sahoo (IIT Bombay)

Title: Primes associated to Multigraded rings II

Time, day and date: 12:30 - 14:00, Tuesday, October 29

Venue: Room 215

Algebraic groups seminar

Speaker: Shripad Garge  (IIT Bombay)

Title: Structure constants

Time, day and date: 16:00 - 18:00, Tuesday, October 29

Venue: Ramanujan Hall

Time, Day, Date: Wednesday 30th October, 4:00 pm

Venue: Ramanujan Hall

Speaker : Lakshmi Priya

Host: Mayukh

Title : Almost sharp lower bound for the nodal volume of harmonic functions

Algebraic groups seminar

Speaker: Saad Qadri (IIT Bombay)

Title: Nilpotent Conjugacy Classes

Time, day and date: 16:00 - 18:00, Wednesday, October 30

Venue: Room 215