Geometry and Quantum Theory (GQT)

School

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

Graduate School (3 to 5/Jul)

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 side to the event is that it will provide the opportunity for graduate students within the GQT to get to know and socialize with each other as well as have some academic interaction.
The school will consist of three days of lectures and exercise sessions; the topics and speakers are as follows:

  • 3/Jul — Ana Ros Camacho: Topological field theories
  • 4/Jul — Roland van der Veen: Knot theory
  • 5/Jul — TBA: TBA

Besides the three minicourses, there will be one or two Ph.D. talks (given by Ph.D. students to Ph.D. students) on Tuesday and Wednesday morning before the beginning of the minicourse.

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

 

Mon Tue Wed
9:00 – 10:00 Arrival Speaker 1 Speaker 2
10:00 – 11:00 Lecture Lecture Lecture
11:00 – 12:00 Lecture Lecture Lecture
12:00 – 12:30 Discussion Discussion Discussion
12:30 – 14:00 Lunch Lunch Lunch
14:00 – 15:00 Lecture Lecture Lecture
15:00 – 16:00 Lecture Lecture Lecture
16:00 – 17:00 Exercises Exercises Exercises
17:00 – 18:00 Exercises Exercises Exercises
18:00 – 19:00 Solution of exercises Solution of exercises Solution of exercises
19:00 Dinner Dinner Dinner

Course description and prerequisites
Topological field theories — Ros Camacho
Course description: We will present several algebraic and categorical notions concerning the functorial definition of topological field theories and then explore several examples in lower dimensions (like e.g. the two dimensional case and its relation with Frobenius algebras, Turaev-Viro and Reshetikhin-Turaev).
Pre-requisites: Familiarity with the basics of category theory should be enough.
Reading material:
– J. Kock, “Frobenius algebras and 2D topological quantum field theories
– M. Atiyah, “Topological quantum field theories”, Publ. Math. IHE ́S68 (1988) 175-186
– R. Dijkgraaf and E. Witten, “Topological gauge theory and group cohomology”, Comm. Math. Phys. 129 (1990)
– J. Lurie, “On the classification of topological field theories”, Current Developments in Mathematics, Volume 2008 (2009), 129-280.

Knot theory — Van der Veen
Course description: TBA
Pre-requisites: TBA.
Reading material: TBA.

TBA — TBA
Course description: TBA
Pre-requisites: TBA
Reading material: TBA

Ph.D. talks
TBA