Joint ICMS & IMSA Seminar

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 on 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

Sextic double solids, double covers of ℙ^3 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 A_n singularity. I have shown that n is at most 8, and that rigidity fails for n > 3.

The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) [...]

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 behaviour at wall crossings as we vary the stability conditions.

Speaker: Rodolfo Aguilar (University of Miami & IMSA) Time: January 28th, 09:30 AM Eastern Time (US and Canada) Title: Quantum representations and Bogomolov-Katzarkov surfaces

The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) [...]

In this talk, I will briefly introduce homological mirror symmetry for certain hypersurface singularities. I will introduce basic definitions, Berglund-Hubsch duality of invertible polynomials, and some known results. Then I will discuss several examples in detail.

Now that we have set up the Frobenius Manifold of a singularity, we can see 2 more places where the steenbrink spectrum of a singularity appears in its singularity category. Namely, the non-commutative mixed hodge structure of a singularity and the dimensional properties of the category. The former appearance being somehow natural, and the latter somewhat mysterious. In this talk we'll conduct a surface level investigation of these appearances.

On August 20, 2021, Prof. Rene Mboro gave the talk "On determinantal cubic hypersurfaces" and prof. Rodolfo Aguilar gave the talk "Quantum representations of fundamental groups of curves with infinite image."