


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 pm4 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 rings2
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: HarishChandra 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.