November 23, 2020 - November 27, 2020
Public Access Category: All |
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- Time:
- 4:00pm-5:00pm
- Description:
- Speaker: Gianfranco Casnati, Politecnico di Torino
Time: Monday 23rd November 4 to 5pm (joining time 3.45 pm IST)
Google Meet Link: https://meet.google.com/qvo-kduy-yco
Title: Ulrich bundles on surfaces
Abstract: An Ulrich bundle on a variety embedded in the projective space
is a vector bundle that admits a linear resolution as a sheaf on the
projective space.
Ulrich bundles have many interesting properties. E.g., the existence of
Ulrich bundles of low rank on a hypersurface $X$ is related to the problem
of finding a linear determinantal or a linear pfaffian description of the
equation of $X$.
Ulrich bundles on curves can be easily described. This is no longer true
for Ulrich bundles on a surface. In the talk we focus our attention on
this latter case. In particular we deal with surfaces $S$ such that
$q(S)=0$ and the hyperplane linear system is non-special. In this case, we
discuss some recent existence results, discussing also the case of
surfaces of degree up to $8$.
- Time:
- 6:30pm
- Description:
- Date/Time: 24 November 2020, 6:30pm IST/ 1:00pm GMT/ 8:00am EDT (joining
time: 6:15 pm IST - 6:30 pm IST)
Google meet link: meet.google.com/dhe-jsbw-jem
Speaker: Tai Huy Ha, University of Tulane
Title: The ideal containment problem and vanishing loci of homogeneous
polynomials
Abstract: We shall discuss Chudnovsky’s and Demailly’s conjectures which
provide lower bounds for the answer to the following fundamental question:
given a set of points in a projective space and a positive integer m, what
is the least degree of a homogeneous polynomial vanishing at these points
of order at least m? Particularly, we shall present main ideas of the
proofs of these conjectures for sufficiently many general points.
- Time:
- 7:30pm
- Description:
- Speaker: Alexey Garber.
Time: 7:30 pm (IST) gate opens 7:15 pm IST, 26 November, 2020
Google meet link: meet.google.com/zis-ovwc-tjy.
Title: Voronoi conjecture for five-dimensional parallelohedra.
Abstract: In this talk I am going to discuss a well-known connection
between lattices in $\mathbb{R}^d$ and convex polytopes that tile
$\mathbdd{R}^d$ with translations only.
My main topic will be the Voronoi conjecture, a century old conjecture
which is, while stated in very simple terms, is still open in general.
The conjecture states that every convex polytope that tiles
$\mathbb{R}^d$ with translations can be obtained as an affine image of
the Voronoi domain for some lattice.
I plan to survey several known results on the Voronoi conjecture and give
an insight on a recent proof of the Voronoi conjecture in the
five-dimensional case. The talk is based on a joint work with Alexander
Magazinov.
- Time:
- 5:30pm
- Description:
- Date/Time: 27 November 2020, 5:30pm IST/ 12:00 GMT/ 7:00am EDT (joining
time: 5:15 pm IST - 5:30 pm IST)
Google meet link: meet.google.com/gfz-iazq-xcc
Speaker: Ryo Takahashi, Nagoya University
Title: Getting a module from another and classifying resolving subcategories
Abstract: Let $R$ be a commutative noetherian ring. Let $M$ and $N$ be
finitely generated $R$-modules. When can we get $M$ from $N$ by taking
direct summands, extensions and syzygies? This question is closely related
to classification of resolving subcategories of finitely generated
$R$-modules. In this talk, I will explain what I have got so far on this
topic.