- Time:
- 3:30pm-5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra seminar.

Speaker: R V Gurjar.

Affiliation: IIT Bombay.

Date and Time: Monday 19 August, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Ramification in Commutative Algebra and Algebraic Geometry.

Abstract: We will consider mainly the following situation. Let R,S be

complete normal local domains over an alg. closed field k of char. 0 such

that S is integral over R. Our aim is to describe three ideals in S; I_N,

I_D, I_K (Noether, Dedekind, Kahler differents resp.) each of which

capture the ramified prime ideals in S over R. In general these three

ideals are not equal. An important special case when all are equal is when

S is flat over R. We will prove many of these statements.

The case when there is a finite group G of k-automorphisms of S such that

R is the ring of invariants is already very interesting. Then many nice

results are proved.

These include works of Auslander-Buchsbaum, Chevalley-Shephard-Todd,

Balwant Singh, L. Avramov, P. Roberts, P. Griffith, P. Samuel,....

I will try to discuss all these results.

I believe that these results and ideas involved in them will be very

valuable to students and faculty both.

Prerequisites. Basic knowledge of Commutative Algebra and language of

Algebraic Geometry (no sheaf theory!). I will

- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium
Speaker: Karthik Adimurthi.
Affiliation: TIFR CAM, Bangalore.
Date and Time: Monday 19 August, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Uniform boundedness and Lipschitz estimates for quasilinear
parabolic equations.
Abstract: In this talk, we will discuss some well known regularity issues
concerning equations of the form $u_t - div |\nabla u|^{p-2} \nabla u = 0$
for $1
2$) and the singular case ($p<2$) separately. Moreover in several instances, the estimates are not even stable as $p\rightarrow 2$. In this talk, I shall discuss two regularity estimates and give an overview on how to obtain uniform $L^{\infty}$ and $C^{0,1}$ estimates in the full range $\frac{2N}{N+2}

- Time:
- 2:45pm-3:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium

Speaker: Rahul Gupta.

Affiliation: University of Freiburg, Germany.

Date and Time: Wednesday 21 August, 2:45 pm - 3:45 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Milnor $K$-theory and Chow groups.

Abstract: In this talk, we shall define Milnor $K$-groups and Chow groups.

We study various properties of these and also theorems relating both

groups. In particular, we talk about Bloch's formula and Totaro's map.

Towards the end, I shall state my results in this direction, which are

joint work with Prof A. Krishna.

- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Popular talk in Mathematics.

Speaker: Debraj Chakrabarti.

Affiliation: Central Michigan University, USA.

Date and Time: Wednesday 21 August, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: The flat-earth society: conformal mapping from Claudius Ptolemy to

Louis Nirenberg.

Abstract: The problem of constructing flat representations of spherical

surfaces arises naturally in geography and astronomy while making maps. We

look at a mathematical formulation of this problem using the notion of

conformal mapping, and discuss its relation with complex analysis. After

reviewing the contributions of Gauss, Riemann, and Poincaré to this

problem, we end with some glimpses of 20th century developments. This will

be an expository talk accessible to undergraduate and postgraduate

students.

- Time:
- 11:30am-12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Number theory seminar.

Speaker: Aprameyo Pal.

Affiliation: University of Duisburg-Essen, Germany.

Date and Time: Thursday 22 August, 11:30 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: A central value formula of degree 6 complex L-series and arithmetic

applications.

Abstract: We prove an explicit central value formula for a family of

complex L-series of degree 6 for GL2 × GL3 which arise as factors of

certain Garret--Rankin triple product L-series associated with modular

forms. Our result generalizes a previous formula of Ichino involving

Saito--Kurokawa lifts, and as an application, we prove Deligne's

conjecture about the algebraicity of the central values of the considered

L-series up to the relevant periods. I would also include some other

arithmetic applications towards subconvexity problem, construction of

associated p-adic L function etc. This is joint work with Carlos de Vera

Piquero.

- Time:
- 2:00pm-3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics seminar.

Speaker: Deepanshu Kush.

Affiliation: IIT Bombay.

Date and Time: Tuesday 22August, 2:00 pm - 3:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Normalized Matching Property in Random & Pseudorandom Graphs.

Abstract: Normalized Matching Property (NMP) is a simple and natural

generalization of the famous Hall's marriage condition for bipartite

graphs, to the setting when the sizes of the two vertex classes are

distinct. It is a well-studied notion in the context of graded posets and

several well-known ones are known to have it (for instance the boolean

lattice or the poset of subspaces of a finite dimensional vector space).

However, in this talk, we will consider NMP with a 'random twist': if for

every possible edge in a bipartite graph, we toss a coin in order to

decide if we keep it or not, how biased must the coin be to expect to have

NMP in the graph with high probability? We shall arrive at a sharp

threshold for this event. Next, what can we say about explicit graphs that

are known to behave 'random-like'? One of the earliest notions of a

pseudorandom graph was given by Thomason in the 80s. We shall prove an

'almost' vertex decomposition theorem: every Thomason pseudorandom

bipartite graph admits - except for a negligible portion of its vertex set

- a partition of its vertex set into trees that have NMP and which arise

organically through the Euclidean GCD algorithm.

- Time:
- 3:45pm-4:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Dr. P. V. Sukhatme Memorial Lecture.

Speaker: Rajeeva Karandikar.

Affiliation: Chennai Mathematical Institute.

Date and Time: Thursday 22 August, 3:45 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: On Connections between Partial Differential Equations and Diffusion

Processes.

Abstract: In this talk we will describe connections between second order

partial differential equations and Markov processes associated with them.

This connection had been an active area of research for several decades.

The talk is aimed at Analysts and does not assume familiarity with

probability theory.

- Time:
- 4:30pm-5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Number theory seminar II.

Speaker: Anuj Jakhar.

Affiliation: Institute of Mathematical Sciences, Chennai.

Date and Time: Friday 23 August, 4:30 pm - 5:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: On discriminant and integral basis of pure number fields.

Abstract:

By a pure number field we mean an algebraic number field of the type Q(

√n a)

where the polynomial x

n − a with integer coefficients is irreducible over the field

Q of rationals. In this talk our aim is to provide a formula for the discriminant

of pure number fields K = Q(

√n a) where for each prime p dividing n, p does not

divide the gcd of a and vp(a); vp(a) stands for the highest power of p dividing a.

We also describe explicitly an integral basis of such fields. This takes care of all

pure fields K = Q(

√n a), where either a, n are coprime or a is squarefree.