IPM Algebraic Geometry Seminar
IPM is holding a biweekly zoom Algebraic Geometry seminar for the Spring 2022.
Where: Zoom
Meeting ID: 908 611 6889
Passcode: 362880
Seminar mailing list: google group
Poster: here
Talks
Speaker: Hossein Movasati, IMPA (Brazil)
Title: Hodge conjecture
Abstract: Hodge conjecture is one of the major conjectures in complex algebraic geometry which is
still unsolved. In this talk I will tell my own experience with this conjecture, why it is hard even in very
special cases and what are the implications of this conjecture. The talk is mainly based on my book:
A Course in Hodge Theory: With Emphasis on Multiple Integrals, Somerville, MA: International Press Boston, 2021.
Date: June 7, 2022
Video link
Passcode: WqBT6@J=
Speaker: Luca Chiantini, University of Siena (Italy)
Title: Configurations of points and tensor analysis
Abstract: I will make an overview on the theory of secant varieties to projective varieties,
starting with fundamental motivations and basic tools, and focusing on
some recent developments of the theory. The general pattern shows that properties of secant varieties
to X are intimately related with the geometry of its configurations of points, thus
with the intrinsic geometry of the variety X. The recent awareness of strong connections
between the theory of secant varieties and multilinear algebra
suggests several lines of investigations which involve highly sophisticated geometric tools,
and poses questions on projective loci that represent a challenge for the
development of Algebraic Geometry.
Date: May 24, 2022
Video link
Passcode: 2swENF7^
Speaker: Ciro Ciliberto, University of Rome Tor Vergata (Italy)
Title: Enumeration in geometry
Abstract: Enumeration of geometric objects verifying some specific properties is an old and venerable subject.
In this talk I will start by briefly reviewing some of its history and problems. In the last decades, enumerative
geometry saw the flourishing of new problems and underwent a tremendous change of perspective and a spectacular
progress, with the introduction of extremely refined new mathematical ideas and tools which launched unexpected
bridges between different parts of mathematics. This has been due also, sometimes mainly, to the input of
questions coming from physics. New insights have also been provided by discretization methods in algebraic
geometry introduced by the so--called tropical mathematics, which, by the way, has quite interesting
applications in phylogenetics. Being impossible to present all this material in a one hour talk,
I will limit myself to give general information on some aspects of these topics, the ones which
are closer to my own research and (limited) knowledge.
Date: May 10, 2022
Video link
Passcode: N$Qe@8Z2
Speaker: Hamid Abban, Loughborough University (UK)
Title: What is K-stability?
Abstract: K-stability is an algebraic notion introduced by Tian and Donaldson to characterise which Fano manifolds admit
a Kähler-Einstein metric. There are various equivalent definitions for K-stability, amongst them the more recent ones are
based on valuative criteria and are more useful from a birational point of view. In this talk, I will give an introduction to
the subject, from a birational viewpoint, and explain some key questions and developments in the field, mostly around methods
of verifying K-stability. This is based on joint work with Ziquan Zhuang.
Date: April 26, 2022
Video link
Passcode: j^Ks1G9m
Speaker: Takuya Murata, IPM (Iran)
Title: A map to a toric variety and construction of a toric degeneration
Abstract: In the first part of the talk, I consider a map to a toric
variety, a generalization of a map to a projective space (also known
as a linear system). A torus embedding is a special case of such a map
and thus the notion can be thought of as a generalization of a torus
embedding or, when the map is flat, a generalization of a vector
bundle on or a covering map of a toric variety. The work on this part
is a joint work with Lara Bossinger.
In the second part, I consider a toric degeneration (= degeneration to
a toric variety) with the focus on a construction of it. Instead of a
general construction, I will discuss illustrative examples. Depending
on time, I will also discuss some applications of toric degenerations.
Date: April 12, 2022
Video link
Passcode: 1^dV6ANS