Mon, October 26, 2020
Public Access

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October 2020
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11:00am [11:30am] Omkar Javadekar
Date and Time: Monday 26 October, 11.30am Speaker: Omkar Javadekar Google Meet link: Title: Serre’s conjecture for projective modules Abstract: Also known as Quillen-Suslin theorem, Serre's conjecture is a result concerning the relationship between free and projective modules over polynomial rings. It states that every finitely generated projective module over a polynomial ring over a field is free. The statement was conjectured by Serre in 1955, and the first proofs were given independently by Quillen and Suslin in 1976. In this talk we will see a proof of Serre's conjecture. We begin by defining unimodular extension property. We then show that polynomial rings have unimodular extension property. Finally, appealing to the result that finitely generated projective modules over polynomial rings are stably free, we conclude the proof of Serre's conjecture by showing that stably free modules over a ring having unimodular extension property are free.

4:00pm [4:00pm] Praveen Roy, TIFR
Speaker: Praveen Roy, TIFR Time: Monday 26th October 4 to 5pm (joining time 3.50pm IST) Google Meet Link: Title: Seshadri Constant on Surfaces. Abstract: Seshadri constant is a tool to study/quantify the positivity of a line bundle on a projective variety. It was defined by Demailly in late 80s to study the Fujita conjecture, but afterwards it arose as an independent area or research with computing and bounding the constant as some of the main topics of research. In this talk we will see some of such results obtained on Hyperelliptic surfaces and on surfaces of general type.