Termin: Freitag 14-16 Uhr in WSC-S-U-3.01.
Dozenten J. Heinloth.

Due to the special circumstances this seminar will take place online through BigBlueButton – please contact the organizer for information on how to join

In both complex and algebraic geometry it is of fundamental interest to construct and study parameter spaces of geometric objects like vector bundles, (elliptic) curves etc. Those moduli spaces are usually not complex manifolds or algebraic varieties themselves but what one calls a stack (german: Stack, french: champ). We have the following hierarchy:

(analytic/algebraic spaces) ⊂ (analytic/algebraic stacks)

Aim of the seminar is to learn what these are by studying prototypical examples of stacks like

(1) stacky curves
(2) moduli spaces of elliptic curves
(3) moduli spaces of vector bundles.

In order to attend the seminar, you should be familiar with either complex or algebraic geometry as covered by a two semester course. Depending on the background of the participants the seminar will be either more algebraic or more analytic/topoogical. The program discussion takes place in room

WSC-S-3.14 on Tuesday February 11 at 15:00.

In case you are interested but can not join the program discussion, please contact me, e.g. by email.

A preliminary program

Termin Vortragender Titel
24.4.2020 Jochen Heinloth Two Examples: Elliptic curves and Vector bundles
8.5.2020 Suraj Dash Moduli spaces I: Definition and Examples
15.5.2020 Jochen Heinloth Moduli spaces II: Gluing and Descent
22.5.2020 Anneloes Viergever Stacks: Fibered categories or pseudo functors
29.5.2020 Suraj Dash The 2-Yoneda lemma and representable morphisms
5.6.2020 Alexander Kutzim Differentiable/Algebraic stacks: Properties and examples
12.6.2020 Paulina Fust Groupoids and Quotients
26.6.2020 Anneloes Viergever fpqc-Descent
3.7.2020 Dhruva Kelkar Vector bundles on curves I
10.7.2020 Dario Weißmann Vector bundles on curves II