webcal

Time:

11:30am

Description:

Date and Time: Monday, 3 Aug 2020 at 11.30 am

Speaker: Arvind Kumar, IIT Madras.

Google Meet link: http://meet.google.com/eti-dnnm-dts

Title: Regularity of binomial edge ideals.

Abstract: This talk is going to be about the regularity of binomial edge
ideals. There are two regularity upper bound conjectures for binomial edge
ideals. We will be discussing these two conjectures. Saeedi Madani and
Kiani conjectured that the regularity of the binomial edge ideal of a
graph is bounded above by the number of cliques of that graph. Hibi and
Matsuda conjectured that the regularity of the binomial edge ideal of a
graph is bounded above by the degree of h polynomial of that graph. We
will also be discussing the regularity of binomial edge ideals of
Cohen-Macaulay bipartite graphs.

Time:

4:00pm - 5:00pm

Description:

Speaker: Sumit Roy

Time: Monday 3rd August 4 to 5pm (joining time 3.50pm)

Google Meet Link: https://meet.google.com/qiw-njvi-unn

Title: Hitchin fibration on moduli of symplectic and orthogonal parabolic
Higgs bundles

Abstract: We shall first introduce parabolic Higgs bundles and describe
the fibers of the corresponding Hitchin map. Later, we shall discuss the
notions related to symplectic and orthogonal parabolic Higgs bundles and
their moduli space, and study the spectral data and describe the Hitchin
fibration in terms of spectral data.

Time:

6:30pm

Description:

Date and Time: Tuesday 4 August 2020, 6:30 pm IST / 01:00pm GMT / 09:00am
EDT (joining time : 6:15 pm IST - 6:30 pm IST)

Google Meet link: https://meet.google.com/pbv-ejez-eac

Speaker: Linquan Ma, Purdue university

Title: The deformation problem for $F$-injective singularities.

Abstract: A local ring $(R,\mathfrak{m})$ is called $F$-injective if the
Frobenius actions on all the local cohomology modules of $R$ supported at
$m$ are injective. The deformation problem asks if $R/xR$ is $F$-injective
for a regular element $x$ in $R,$ then whether $R$ is $F$-injective. I
will survey this question and prove some special cases.

Time:

7:00pm

Description:

Time: 7pm (Gate opens 6:45 pm), Thursday, August 6, 2020.

Google meet link: meet.google.com/fxz-cxqe-rrs.

Speaker: Gunnar Fløystad, University of Bergen.

Phone: (US) +1 541-714-3865‬ PIN: ‪750 178 024‬#.

Title: Stanley-Reisner ideals from poset partitions.

Abstract: We show how one to classes of order preserving
maps P -> N, where P is a finite poset, and N the natural numbers
may associate wide classes of Stanley-Reisner ideals. These ideals
have very good and interesting properties with respect to:

1. Free resolutions

2. Associated simplicial complexes which are balls and spheres.

3. Their deformation theory to varieties.

Time:

5:30pm

Description:

Date and Time: 7 August 2020, 5:30 pm IST/12:00GMT / 08:00am EDT (joining
time : 5:15 pm IST - 5:30 pm IST)

Google Meet link: https://meet.google.com/pys-ujdd-dnk

Speaker: Shreedevi Masuti, IIT Dharwad.

Title: Normal Hilbert coefficients and blow-up algebras.

Abstract: The normal Hilbert coefficients are important numerical
invariants associated with an ideal in an analytically unramified local
ring. They play an important role in determining the homological
properties of the blow-up algebras. This will be an expository talk on the
normal Hilbert coefficients, and its relation with blow-up algebras. We
will also discuss recent developments on this topic.

Time:

4:00pm - 5:00pm

Description:

Speaker: Poorna Narayanan

Time: Monday 10th August 4 to 5pm (joining time 3.50pm)

Google Meet Link: https://meet.google.com/ute-oxyh-xjm

Title: Ulrich bundles on double planes

Abstract: Ulrich bundles are vector bundles on a smooth projective variety
whose twists satisfy a set of vanishing conditions. It has been
conjectured that every smooth projective variety carries an Ulrich bundle.
The answer to this is not known in general but is known in the case of
certain projective varieties. In this talk, I will give an introduction to
Ulrich bundles. I will also discuss the existence of Ulrich line bundles
over double covers of the projective plane. This is based on joint work
with A.J. Parameswaran.

Time:

5:30pm

Description:

Date and Time: 11 August 2020, 5:30 pm IST /12:00 GMT / 08:00am EDT
(joining time : 5:15 pm IST - 5:30 pm IST)

Google Meet link: https://meet.google.com/zmi-ingb-dyg

Speaker:A De Stefani, University of Genoa.

Title: Deformation and stability of F-injective singularities

Abstract: Picking up from the talk given by Linquan Ma, I will discuss
some more cases where deformation of F-injectivity is known to hold, and I
will discuss the related notion of m-adic stability. The talk will be
based on joint projects with Linquan Ma (deformation) and Ilya Smirnov
(stability).

Time:

6:30pm

Description:

Date and Time: 14 August 2020, 6:30 pm IST / 01:00pm GMT / 09:00am EDT
(joining time : 6:15 pm IST - 6:30 pm IST)

Google Meet link: https://meet.google.com/xpn-pbur-dhz

Speaker: Luis Núñez Betancourt, CIMAT, Mexico

Title: Splittings and symbolic powers of Ideals

Abstract: Splittings of Frobenius have been employed to study the
singularities and cohomology of rings. In this talk we will employ ideas
inspired by this technique to obtain results of symbolic powers of
monomial and determinantal ideals.

Time:

4:00pm - 5:00pm

Description:

Speaker: Sukhendu Mehrotra

Time: Monday 17th August 4 to 5pm (joining time 3.50pm)

Google Meet Link: https://meet.google.com/wnf-ywcy-ozi

Title: Stability conditions on K3 surfaces

Abstract: This is the first of two expository talks on stability
conditions. We give a leisurely introduction to Bridgeland stability
conditions, followed by a description of the space of stability conditions
on a K3 surface. An application to calculating the group of
autoequivalences of a K3 surface is outlined. The talk is based on a paper
of Bridgeland of the same title.

Time:

5:30pm - 6:30pm

Description:

Date and Time: 18 August 2020, 5:30 pm IST - 6:30 pm IST (joining time :
5:15 pm IST - 5:30 pm IST)

Google Meet link: https://meet.google.com/krh-mgar-qip

Speaker: Pham Hung Quy, FPT University, Hanoi

Title: Frobenius closure of parameter ideals

Abstract: We discuss recent results about Frobenius closure of parameter
ideals and $F$-singularities as well as the Frobenius test exponent of
parameter ideals.

Time:

5:30pm - 6:30pm

Description:

Date and Time: 21 August 2020, 5:30 pm IST - 6:30 pm IST (joining time :
5:15 pm IST - 5:30 pm IST)

Google Meet link: https://meet.google.com/uuk-zzum-czm

Speaker: Arindam Banerjee, RKM Vivekananda Institute, Belur

Title: Lyubeznik numbers

Abstract: Lyubeznik numbers are certain Bass numbers of local cohomology
modules associated with local rings containing a field. These numerical
invariants are known to have many interesting homological, geometric, and
topological properties and have been an active area of research. In this
talk, we plan to give a brief overview of these.

Time:

5:30pm

Description:

Date and Time: 25 August 2020, 5:30 pm IST / 12:00GMT/ 08:00am EDT
(joining time : 5:15 pm IST - 5:30 pm IST)

Google Meet link: https://meet.google.com/wxq-droj-bii

Speaker: Vivek Mukundan, IIT Delhi

Title: Reduction to characteristic $p$ - Part 1

Abstract: This is an expository talk introducing the methods of reducing
to characteristic $p$. The main tools and general notions necessary to
reduce a problem to characteristic $p$ will be discussed in this talk. It
is based on chapter 2 of the excellent resource "Tight Closures in
Characterisitic zero" by Hochster and Huneke. We will be restricting
ourselves to the case of affine algebras since it is more accessible.

Time:

5:30pm

Description:

Date and Time: 28 August 2020, 5:30 pm IST / 12:00GMT/ 08:00am EDT
(joining time : 5:15 pm IST - 5:30 pm IST)

Google Meet Link: https://meet.google.com/wxq-droj-bii

Speaker: Vivek Mukundan, IIT Delhi

Title: Reduction to characteristic $p$ - Part 2

Abstract: This talk presents problems solved by using the method of
reduction to characteristic $p.$ Mainly, we present two nice problems
which have been solved using the reduction to characteristic $p$ methods.
We also present a recent result in the field of symbolic power which uses
the reduction to characteristic $p.$

Time:

4:00pm - 5:00pm

Description:

Speaker: Chetan Balwe, IISER Mohali

Time: Monday 31st August 4 to 5pm (joining time 3.50pm)

Google Meet Link: https://meet.google.com/wnf-ywcy-ozi

Title: Geometric approach for the sheaf of A^1-connected components

Abstract: The $\mathbb{A}^1$-homotopy theory of Morel-Voevodsky attempts
to use
homotopical methods in algebraic geometry by having the affine line play
the role of the unit interval. Analogous to the set of connected
components of a topological space, one associates the sheaf of
$\mathbb{A}^1$-connected components to any variety. However, this sheaf is
extremely difficult to compute since its definition is mired in abstract
machinery. We will discuss how this sheaf may be studied by means using
purely algebro-geometric methods, via the sheaf of ``naively"
$\mathbb{A}^1$-connected components. This approach has been successful in
proving some results about the sheaf of $\mathbb{A}^1$-connected
components by very elementary techniques. We will look at some of these
results and briefly describe the techniques used to prove them. This talk
is based on joint work with Amit Hogadi and Anand Sawant.