Tue, October 11, 2022
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11:00am [11:30am] Prof. Umesh Dubey: HRI

Speaker: Prof. Umesh Dubey: HRI

Title: A functorial construction of moduli of parabolic sheaves.

The moduli construction for vector bundle over smooth projective curves due
to Mumford and Seshadri was extended to moduli of torsion-free sheaves over
higher dimensional varieties by Gieseker and Maruyama. Simpson later
generalized it to the moduli of pure sheaves on higher dimension projective
schemes and Langer extended it to mixed characteristics.
   Alvarez-Consul and King used embedding of the category of regular
sheaves to the category of Kronecker representations to get a functorial
moduli construction of pure sheaves.
 In this talk, we will briefly describe the construction of the Consul and
King. If time permits, we will also mention the related results obtained
jointly with Sanjay Amrutiya for parabolic sheaves using the moduli of
filtered Kronecker representations.

3:00pm [3:30pm] H. Ananthnarayan, IIT Bombay
Commutative algebra seminar

Tuesday, 11 October 2022

Time: 3.30 pm-4.45 pm

Venue: Ramanujan Hall

Speaker: H. Ananthnarayan

Title: Boij-Soderberg Conjectures and the Multiplicity Conjecture-II

In an article published in 2008, Boij and Soderberg introduced the 
notion of a cone related to the graded Betti numbers of a graded
module over the polynomial ring over a field, and stated a couple of 
conjectures related to the extremal rays of this cone. They also showed
that a positive answer to these conjectures resolves the Multiplicity 
conjecture. Eisenbud-Schreyer (2009) show that the Boij-Soderberg
conjectures are true.

In these talks, we will introduce the multiplicity conjectures, indicate 
their connection to the Boij-Soderberg conjectures, and give an idea of
how Eisenbud-Schreyer resolve the latter conjectures. We explore similar 
results over other standard graded rings.