


Speaker: Prof. Umesh Dubey: HRI
Title: A functorial construction of moduli of parabolic sheaves.
Abstract:
The moduli construction for vector bundle over smooth projective curves due
to Mumford and Seshadri was extended to moduli of torsionfree 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.
AlvarezConsul 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.
Commutative algebra seminar Tuesday, 11 October 2022 Time: 3.30 pm4.45 pm Venue: Ramanujan Hall Speaker: H. Ananthnarayan Title: BoijSoderberg Conjectures and the Multiplicity ConjectureII Abstract: 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. EisenbudSchreyer (2009) show that the BoijSoderberg conjectures are true. In these talks, we will introduce the multiplicity conjectures, indicate their connection to the BoijSoderberg conjectures, and give an idea of how EisenbudSchreyer resolve the latter conjectures. We explore similar results over other standard graded rings.
This is a reminder for the upcoming talk on Thursday 13 October. https://sites.google.com/math.iitb.ac.in/geometricanalysis/home Speaker: Luca Martinazzi (Sapienza University of Rome) Time: October 13, Thursday, 4 pm (Indian Standard Time) Title: Critical points of the MoserTrudinger functional on closed surfaces Abstract: Given a 2dimensional closed surface, we will show that the MoserTrudinger functional has critical points of arbitrarily high energy. Since the functional is too critical to directly apply to it the known variational methods (in particular the Struwe monotonicity trick), we will approximate it by subcritical ones, which in fact interpolate it to a Liouvilletype functional from conformal geometry. Hence our result will also unify and give common results for these two apparently unrelated problems. This is a joint work with F. De Marchis, A. Malchiodi and PD. Thizy. Google Meet joining info Video call link: https://meet.google.com/cputchrnvu Or dial: (US) +1 2408121225 PIN: 262 484 324#
Prof. Nitin Nitsure will continue his lecture series on 'Algebraic Stacks and Moduli Theory' tomorrow (13th Oct) at 5:00 pm. The talk will be in Ramanujan Hall and of 75 minutes duration.
Speaker: Ramya Dutta (TIFRCAM) Time: October 14, Friday, 11:30 am Venue: Room 216 Title: Apriori decay estimates for HardySobolevMaz'ya equations and application to a BrezisNirenberg problem. Abstract: In this talk we will discuss some qualitative properties and sharp decay estimates of solutions to the EulerLagrange equation corresponding to HardySobolevMazya inequality with cylindrical weight. Using these sharp asymptotics we will establish a BrezisNirenberg type existence result for class of $C^1$ sublinear perturbations of the pHardySobolev equation with cylindrical weight in a bounded domain in dimensions $n > p^2$ and an appropriate notion of positivity for these perturbations.
Virtual Commutative Algebra Seminar Speaker: Parnashree Ghosh, Indian Statistical Institute Kolkata, India Date/Time: 14 October 2022, 5:30pm IST/ 12:00pm GMT /8:00am ET (joining time 5:20 pm IST) Gmeet link: meet.google.com/eapqswgxvg [1] Title: On the triviality of a family of linear hyperplanes Abstract: Let k be a field, m a positive integer, V an affine subvariety of $A^{m+3}$ defined by a linear relation of the form $x_1^{ r_1} · · · x_r^{r_m} y = F(x_1, . . . , x_m, z, t),$ A the coordinate ring of V and $G = X_1^{ r_1} · · · X_r^{r_m} Y  F(X_1, . . . , X_m, Z, T).$ We exhibit several necessary and sufficient conditions for V to be isomorphic $A^{m+2}$ and G to be a coordinate in $k[X_1, . . . , X_m, Y, Z, T],$ under a certain hypothesis on F. Our main result immediately yields a family of higherdimensional linear hyperplanes for which the AbhyankarSathaye Conjecture holds. We also describe the isomorphism classes and automorphisms of integral domains of type A under certain conditions. These results show that for each integer d ⩾ 3, there is a family of infinitely many pairwise nonisomorphic rings which are counterexamples to the Zariski Cancellation Problem for dimension d in positive characteristic. This is joint work with Neena Gupta. For more information and links to previous seminars, visit the website of VCAS: https://sites.google.com/view/virtualcommalgebraseminar [2] Links:  [1] http://meet.google.com/eapqswgxvg [2] https://sites.google.com/view/virtualcommalgebraseminar