The talks take place in the room W01 0-015 at Campus Wechloy. The registration is in front of this room. There are signposts leading you from the bus station directly in front of the main entrance to the lecture room. 

Please be aware that the Oldenburg University has two campuses: Campus Wechloy and Campus Haarentor. The conference takes place at Campus Wechloy (Carl von Ossietzky Straße). The line 306 (direction: Universität) is the preferred way to reach the Campus Wechloy from Oldenburg central station.

Toric singularities (Andrea Petracci (Bologna))
Toric resolutions of singularities (Eleonore Faber (Leeds))
Valuative Methods in Singularity Theory (Harold Blum (Utah))

The online live stream via BBB (big blue button) https://meeting.uol.de/b/mil-usw-dc0-f48 continues with the workshop.

Florin Ambro: On toric Fano fibrations

We discuss the classification of germs of toric Fano fibrations, extending work of A. Borisov in the case of \(\mathbb{Q}\)-factorial toric singularities. As an application, we verify in the toric case a conjecture of V. Shokurov on the existence of complements with bounded index and prescribed singularities.

Ana Maria Botero: Equivariant Chern Classes of Toric Vector Bundles over a DVR and Bruhat-Tits Buildings

We define equivariant Chern classes of a toric vector bundle over a toric scheme over a DVR and provide a combinatorial description of these in terms of piecewise polynomial functions on a polyhedral complex. We use the characterization of toric vector bundles in terms of  piecewise affine maps to the extended Bruhat--Tits building $\GL(r)$ given by K. Kaveh, C. Manon and B. Tsvelikhovskiy. We further discuss potential applications in the arithmetic intersection theory of toric varieties. This is joint work with C. Manon and K. Kaveh.

Lukas Braun: Log terminal singularities and group actions

In this talk, I will present a result about quotients by reductive groups obtained together with Daniel Greb, Kevin Langlois, and Joaquin Moraga. In particular, I will show that quotients of smooth points by reductive groups produce Kawamata log terminal singularities, and this class is preserved by (further) quotients. This generalizes an
analogous result by Boutot about rational singularities. The result is obtained by decomposing the reductive group into its (finite) group of components, the derived subgroup (which is semisimple) and a torus, and analyzing each case separately.

Maria Donten-Bury: Kazhdan-Lusztig varieties and torus actions

We investigate a naturally defined torus action on the class of Kazhdan-Lusztig (KL) varieties. We look at two permutations, $v$ and $w$, which determine a KL variety, and at the associated combinatorial objects: Rothe diagrams and directed graphs. Our aim is to describe properties of the torus action, in particular its complexity, in terms of these objects. We also introduce a combinatorial operation on the Rothe diagram on $w$ which, under certain assumptions on $v$, almost always leaves the complexity of associated KL varieties unchanged. This is a joint project with Laura Escobar and Irem Portakal.

Matej Filip: Mutations and smoothing of affine toric Gorenstein varieties

We give a correspondence between mutations of a polytope and one-parameter deformations of the corresponding affine Gorenstein toric variety X. Moreover, we describe conditions under which these one-parameter deformations are unobstructed and produce a smoothing of X.

Jürgen Hausen: Log del Pezzo surfaces with torus action

After a short introduction to the subject, we discuss recent classification results and applications to geometric questions.

Milena Hering: The F-splitting ratio of a toric variety

The Frobenius morphism is a useful tool in the study of commutative rings and algebraic varieties. One of its uses is to give a measurement of how bad the singularities of a ring are. This measurement is called the the F-splitting ratio, which agrees with the  F-signature for normal rings. The F-signature of a normal toric ring was computed by Von Korff. I will give give an introduction to these notions and present the computation of the F-splitting ratio of a seminormal toric ring. This is joint work with Kevin Tucker.

Alex Küronya: Lattice polygons and finite generation of certain valuation
semigroups

The central theme of the talk is the combinatorics of lattice polygons and its relationship to the geometry of the associated toric surfaces. We will focus on geometric  finiteness properties such as the polyhedrality of the cone of curves and the finite generation of valuation semigroups. This is an account of joint work with Klaus Altmann, Christian Haase, Karin Schaller, and Lena Walter.

Hussein Mourtada: A geometric approach to resolution of singularities

I will begin by explaining an approach to resolution of singularities (via toric morphisms) which is based on the geometry of jet schemes, arc spaces and re-embedding in "higher dimension" affine spaces.
I will then report on a joint work with Ana Belen de Felipe and Pedro Gonzalez-Perez, where we apply this approach to find an embedded resolution of a reduced curve singularity by one toric morphism.

Špela Špenko: Noncommutative crepant resolutions of 3-dimensional affine toric varieties

Noncommutative crepant resolutions are a natural algebraic analogue of (geometric) crepant resolutions. They exist for many classes of quotient singularities for reductive groups. In particular, using the theory of dimer models Broomhead proved that every 3-dimensional Gorenstein affine toric variety Spec R admits a (toric) non-commutative crepant resolution (NCCR). We give an alternative proof of this result by constructing a tilting bundle on a (stacky) crepant resolution of Spec R using standard toric methods.This is a joint work with Michel Van den Bergh.

We will organize a poster session on Wednesday Afternoon. If you want to participate, please send an email with the title of your poster to milena.wrobel@uol.de.

Please register via email with Milena Wrobel <milena.wrobel@uni-oldenburg.de> and let us know which part(s) of the event you are planning to attend.

We would like to also bring the following conference to your attention:
https://www.math.uni-kiel.de/geometrie/de/essig/conferences/charclasses2023conf