Mathematics colloquium

15 January, 2023, 4 pm

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Venue: Ramanujan Hall

Host: Jugal Verma

Speaker: Sujatha Ramadorai

Affiliation: University of British Columbia, Vancouver, Canada

Title:  Asymptotics of Rational Points of Elliptic curves

and Krull dimension

Abstract: Modules over power series rings occur naturally in 

Number Theory and in concrete cases, certain asymptotics

arising from the study of such modules encode arithmetic information 

related to the Krull dimension of the modules. We will discuss this

phenomena specifically for elliptic curves.

Algebraic geometry seminar

Tuesday, 16 January, 11.30 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR, Mumbai (retd)

Title:  Separated Morphisms and Proper Morphisms.

Abstract: Separated morphisms and proper morphisms are two very important classes of morphisms in algebraic geometry. In the next few lectures, we will study these for schemes, algebraic spaces, and algebraic stacks. The basic theory of such morphisms between schemes is given in Hartshorne's `Algebraic Geometry', Chapter 2, Section 4. After recalling the basics, we will go on to consider such morphisms between algebraic spaces and then between algebraic stacks. The first few lectures should be easily accessible to beginner students in algebraic geometry.

Commutative Algebra Seminar

Tuesday, 16 Jan 2023, 3 pm-4 pm

Note the unusual time

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Host: Tony Puthenpurakal

Venue: Room 215

Speaker: Tony J. Puthenpurakal

Affiliation: IIT Bombay

Title: Modules over Weyl algebras with application to local cohomology modules over polynomial rings-2

Abstract. Let K be a field of characteristic zero. We study finitely generated modules over the Weyl algebra A_n(K). We give application to local cohomology modules of K[X_1,...., X_n]

Algebraic Groups seminar
Tuesday, 16 January 2024, 4 pm
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Venue: Ramanujan Hall
Host: Shripad M. Garge

Speaker: Shripad M. Garge
Affiliation: IIT Bombay

Title: Finite morphisms and normal varieties

Abstract: We introduce the notion of normal varieties and prove the following version of Zariski's main theorem: A bijective and birational morphism of irreducible varieties, \phi: X  Y, is an isomorphism if Y is normal. 

Number Theory seminar

Tuesday, January 16, 16:00 - 17:00

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Venue: Room 105

Host:  Ravi Raghunathan

Speaker: Surya Ramana

Affiliation: Harish-Chandra Research Institute

Title: An Improved Bound for the Additive Energy of Large Sets of Prime Numbers

Abstract: When A and B are subsets the integers, the additive energy of A and B is the quantity E(A,B) defined by  E(A,B) = | { (x_1,x_2,y_1, y_2) \in A\times A \times B \times B\, | x_1 +y_1 = x_2 +y_2 } | Additive energy is a basic notion in additive number theory and additive combinatorics. Given $\alpha$ in $(0,1)$ and $\lambda >0$ and a large enough integer $N$, we obtain an essentially optimal upper bound for the additive energy $E(A,B)$ of any subsets $A$ and $B$ of the prime numbers in the intervals $[1, N]$ and $[1, \lambda N]$ respectively, when $A$ satisfies $|A| \geq \alpha N$. This is based on work with K. Mallesham and Gyan Prakash.

Mathematics colloquium

Wednesday, 17 January, 2023, 4 pm

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Venue: Ramanujan Hall

Host: Ravi Raghunathan

Speaker: R. Balasubramanian

Affiliation: Institute of Mathematical Sciences, Chennai

Title:  Product of three primes in an arithmetic progression

Abstract. Linnik proved that there exists a positive constant c such that the set {p: p is a prime ≤ q c} contains all invertible residue classes mod q. The original value of c was very large. The best known is c = 5 . It is expected to be true for any c > 2. We ask an analogous question What is the value of c for which we can claim that the set {p_1p_2p_3: p_i ≤ q c for i = 1, 2, 3} covers all invertible residue classes mod q . We shall explain how additive combinatorics naturally enters into the proof. This is a joint work with Ramare and Priyamvad Srivastav.