Mathematics Colloquiumm

Date and time: Thursday, 24 November 2022, 2.30 pm

Venue: Ramanujan Hall

Speaker: Parimala Raman, Emory University, Atlanta, GA, USA

Title: Quadratic forms over function fields

Abstract: A classical theorem of Hasse-Minkowski leads to the fact that 
every quadratic form in at least five variables over a totally imaginary 
number field represents zero nontrivially. One is naturally led to 
similar questions concerning function fields of curves over totally 
imaginary number fields. Do quadratic forms in a sufficiently large 
number of variables represent zero nontrivially over these fields? This 
is a big open question even for the rational function field in one 
variable over a totally imaginary number field. The expectation is that 
every quadratic form in at least nine variables over such a field 
represents zero nontrivially; over function fields of p-adic curves, 
every form in nine variables admits a nontrivial zero. We shall explain 
some recent progress in this direction.

Speaker: Jérôme Vétois (McGill University)
Time: November 24, Thursday, 4 pm (Indian Standard Time)

Title: Sign-changing blowing-up solutions to the Yamabe equation on a
closed Riemannian manifold

Abstract: In this talk, I will discuss the question of existence of
families of sign-changing solutions to the Yamabe equation, which blow up
in the sense that their maximum values tend to infinity. It is known that
in the case of positive solutions, there does not exist any blowing-up
families of solutions to this problem in dimensions less than 25, except
in the case of manifolds conformally equivalent to the round sphere
(Khuri, Marques and Schoen, 2009). I will present a construction showing
the existence of a non-round metric on spherical space forms of dimensions
greater than 10 for which there exist families of sign-changing blowing-up
solutions to this problem. Moreover, the solutions we construct have the
lowest possible limit energy level. As a counterpart, we will see that
such solutions do not exist at this energy level in dimensions less than
10. This is a joint work with Bruno Premoselli (Université Libre de
Bruxelles).


Google Meet joining info:
Video call link: https://meet.google.com/rmq-ijfz-edh
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Algebraic geometry seminar

Date and time: Thursday, 24 Nov. 2022, 5 pm

Venue: Ramanujan Hall

Speaker: Nitin Nitsure

Title: Stacks and moduli