IPM Algebraic Geometry Seminar

IPM is holding a biweekly zoom Algebraic Geometry seminar for Fall 2023.


When: Wednesdays
Where: Zoom
Meeting ID: 908 611 6889
Passcode: 13440 × the number of lines on a cubic surface
Seminar mailing list: google group
Poster: here


Speaker: Jean Fasel, Universit´e Grenoble Alpes (France)
Title: Vector bundles on threefolds
Abstract: In this talk, I will survey classification results for vector bundles on smooth threefolds over an algebraically closed field. I will start with classical results in the affine case, and then show how to complete the classification in that case. Then, I will pass to quasi-projective threefolds, focusing on the case of complex varieties.
Date: December 13, 2023
Video link
Passcode: @P4Mp0Qj

Speaker: Claudio Fontanari, University of Trento (Italy)
Title: Generalized Abundance and Nonvanishing: remarks and open questions
Abstract: The Nonvanishing Conjecture and the Abundance Conjecture are longstanding open problems in the Minimal Model Program. I am going to present some unexpected generalizations which appeared in the literature in the last few years and to discuss a few variants of them.
Date: November 29, 2023
Video link
Passcode: u9=H54sM

Speaker: Ivan Cheltsov, University of Edinburgh (UK)
Title: Equivariant geometry of singular cubic threefolds
Abstract: I will report on a joint work with Yuri Tschinkel (Simons Foundation) and Zhijia Zhang (New York University) on linearizability of actions of finite groups on singular cubic threefolds.
Date: November 15, 2023
Video link
Passcode: 8yXxM.1X

Speaker: Steven Dale Cutkosky, University of Missouri (US)
Title: Generating sequences of valuations
Abstract:Suppose that $(K,v_0)$ is a valued field, $f(x)\in K[x]$ is a monic and irreducible polynomial and $(L,v)$ is an extension of valued fields, where $L=K[x]/(f(x))$. Let $A$ be a local domain with quotient field $K$ dominated by the valuation ring of $v_0$ and such that $f(x)$ is in $A[x]$. The study of these extensions is a classical subject. In this talk, we discuss the history of this subject, connections with resolution of singularities, and recent progress. We will discuss our recent work with Razieh Ahmadian on the problem of describing the structure of the associated graded ring ${\rm gr}_v A[x]/(f(x))$ of $A[x]/(f(x))$ for the filtration defined by $v$ as an extension of the associated graded ring of $A$ for the filtration defined by $v_0$. We give a complete simple description of this algebra when there is unique extension of $v_0$ to $L$ and the residue characteristic of $A$ does not divide the degree of $f$. To do this, we show that the sequence of key polynomials constructed by MacLane's algorithm can be taken to lie inside $A[x]$. This result was proven using a different method in the more restrictive case that the residue fields of $A$ and of the valuation ring of $v$ are equal and algebraically closed in a recent paper by Cutkosky, Mourtada and Teissier.
Date: November 1, 2023
Video link
Passcode: 9qB7n@^L

Speaker: Bernd Sturmfels, Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany); University of California, Berkeley (US)
Title: Algebraic Varieties in Quantum Chemistry
Abstract:We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.
Date: October 18, 2023
Video link
Passcode: 5yt2b%*s

Speaker: Elham Izadi, University of California, San Diego (US)
Title: Hyperkahler manifolds and Lagrangian fibrations
Abstract: This is mostly an introduction to and short survey of hyperkahler manifolds and Lagrangian fibrations, including some known results and some open problems.
Date: Octopber 4, 2023
Video link
Passcode: jkpT0?5*