Topology and Related Topics Seminar

Thursday, 26 Oct. 2:30 pm - 3:45 pm

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Venue: Room 215

Host: Rekha Santhanam

Speaker: Omkar Javadekar 

Affiliation: IIT Bombay

Title: A review of derived category and related topics-2

Abstract: We will continue the discussion on derived categories and the Hopkins-Neeman theorem for small R-complexes.

Online Number Theory Seminar 

Thursday, 26 October, 3.15 pm

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Venue:  https://meet.google.com/zrc-owyg-ukt

Host: Ravi Raghunathan

Speaker: Aditi Savalia

Affiliation: IIT Gandhinagar

Title: Limitations to equidistribution in arithmetic progressions

Abstract: It is well known that prime numbers are equidistributed in arithmetic progressions. Such a phenomenon is also observed more generally for a class of arithmetic functions. A key result in this context is the Bombieri-Vinogradov theorem which establishes that the primes are equidistributed in arithmetic progressions “on average” for moduli $q$ in the range $q ≤ x^{1/2−\epsilon}$ for any $\epsilon > 0$. Building on the idea of Maier, Friedlander and Granville showed that such equidistribution results fail if the range of the moduli $q$ is extended to $q ≤ x/(log x)^B$ for any $B > 1$. We discuss variants of this result and give some applications. This is joint work with Akshaa Vatwani.

Commutative Algebra seminar

Thursday, 26 Oct. 4.00-5.30 pm

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Venue: Ramanujan Hall

Host: Tony Puthenpurakal

Speaker: Jugal Verma, IIT Bombay

Title: The Grothendieck-Serre formula for Hilbert functions

Abstract: We will prove the Grothendieck-Serre formula for Hilbert functions of finite graded modules over graded Noetherian rings.