Geometry and Quantum Theory (GQT)

School

The academic program consists of a 3-day graduate school and a 2-day conference.

Graduate School (January 24 to 26, 2022)

The idea behind the GQT school is that participants will get a basic understanding of some central topics in GQT-research, including many important themes which may lie outside one’s own research specialization. Hence, we strongly encourage Ph.D. students to participate in all three days as a way to broaden their mathematical formation and increase awareness regarding the research carried out within the cluster.
Another important aspect of the event is that it will provide the opportunity for graduate students within the GQT cluster to get to know and socialize with each other as well as have academic interactions.
The school will consist of three days of lectures and exercise sessions; the topics and speakers are as follows:

Schedule
During the school days the lectures and exercise classes will be arranged roughly as follows:

 

Mon Tue Wed

 

Course description and prerequisites

Johan Commelin – TBA
Course description: TBA.

Exercises: TBA.

Pre-requisites: TBA.

Reading material: TBA

Magdalena Kedziorek – TBA
Course description: TBA.

Exercises: TBA.

Pre-requisites: TBA.

Reading material: TBA

Adrien Sauvaget – Application of the virtual localization formula in Gromov-Witten theory
Course description: Let X be a complex scheme (or a symplectic manifold). The moduli space M(X) of stable maps to X is a geometric object that classifies maps from complex curves to X. The Gromov-Witten invariants are numbers defined as integrals of cohomology classes over M(X). Unfortunately, the geometric description of these cohomology classes is notoriously difficult in general as the moduli space M(X) is highly singular. If X admits a torus action, Graber and Pandharipande proved a «  virtual localization formula »  which allows to compute the GW invariants of X, going around the technical difficulty of describing M(X).

   The purpose of the lectures is to state the virtual localization formula and to present some of its concrete applications e.g.: computation of Hodge integrals, computation of GW invariants of local Calabi-Yau 3-folds, the proof of the DR-cycle formula and of the ELSV formula if the time allows. The lectures are meant to be self-contained for a student with a course in Algebraic geometry or complex analytic geometry.

Exercises: TBA.

Pre-requisites: TBA.

Reading material: TBA