Joint ICMS & IMSA Seminar
Kyoung-Seog Lee
University of Miami & IMSA
Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations
Friday, March 11, 2022, 9:30am
Hybrid
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Abstract: Logarithmic transformation is an important operation introduced by Kodaira in the 1960s. One can obtain an elliptic surface with multiple fibers by performing logarithmic transformations of an elliptic surface without multiple fibers. On the other hand, vector bundles on elliptic surfaces are important objects in many branches of mathematics, e.g., algebraic geometry, gauge theory, mathematical physics, etc. In this talk, I will discuss how certain Higgs bundles on elliptic surfaces are changed via logarithmic transformations. This talk is based on a joint work with Ludmil Katzarkov.
Joint ICMS & IMSA Seminar
Erik Paemurru
University of Miami & IMSA
Birational Geometry of Sextic Double Solids with a Compound An Singularity
Friday, February 18, 2022, 9:30am
Hybrid
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Abstract: Sextic double solids, double covers of ℙ3 branched along a sextic surface, are the lowest degree Gorenstein Fano 3-folds, hence are expected to behave very rigidly in terms of birational geometry. Smooth sextic double solids, and those which are ℚ-factorial with ordinary double points, are known to be birationally rigid. In this talk, we discuss birational geometry of sextic double solids with an isolated compound An singularity. I have shown that n is at most 8, and that rigidity fails for n > 3.
Joint ICMS & IMSA Seminar
Rene Mboro
University of Miami & IMSA
On the Geometry of Cubics
Wednesday, February 9, 2022, 5:00pm
Hybrid
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Abstract: We will start by recalling some classical results on geometry of three and four dimensional cubics. Some new results on 5 dimensions cubics will be discussed as well.
Joint ICMS & IMSA Seminar
Sebastian Torres
University of Miami & IMSA
Windows and Geometric Invariant Theory
Friday, February 4, 2022, 9:30am
Online
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Abstract: The theory of windows was introduced relatively recently by both Halpern-Leistner and Ballard, Favero and Katzarkov, and is a great tool to study derived categories of algebraic varieties that appear as GIT constructions, as well as their behavior at wall crossings as we vary the stability conditions. We will discuss this theory and explore different applications, from cohomology computations to semi-orthogonal decompositions.
Joint ICMS & IMSA Seminar
Rodolfo Aguilar
University of Miami & IMSA
Quantum Representations and Bogomolov-Katzarkov Surfaces
Friday, January 28, 2022, 9:30am
Online
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Abstract: We will present some results of Eyssidieux-Funar as in arXiv:2112.06726, they are related to the so-called Shafarevich conjecture on holomorphic convexity.
There, they used quantum representations of the fundamental group of Riemann surfaces to show that most of the algebraic surfaces proposed by Bogomolov and Katzarkov in the late 90's are not counterexamples to this conjecture.
Joint ICMS & IMSA Seminar
Tokio Sasaki
ICMS & IMSA
Degeneration of Cubic Threefolds with Nodes
Friday, January 21, 2022, 9:30am
Online
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Abstract: For a general smooth cubic threefolds $X$ in $\mathbb{P}^4$, its intermediate Jacobian and the fano variety of lines play the main role in the proof of the irrationality of $X$. When $X$ is a cubic with finitely many nodes, each node determines a sextic curve and a double covering of plane quintic curve similarly as smooth cubics. Since the Jacobian of the former curve is isomorphic to the Prym variety of the latter covering, by applying the theory of degeneration of Prym varieties and unimodular systems of vectors as matroids, one can observe the limiting behavior of the Jacobian of the sextic curve from the configuration of nodes. This is a survey talk mainly based on results by A. Collino, J. P. Murre, V. Alexeev, and T. Gwena.
