IPM Algebraic Geometry Seminar


Past 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
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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
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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
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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
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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
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