The second Summer School of the RTG will be the Simons School on Moduli of curves, abelian varieties and K3 surfaces, held at the Erdös Center in Budapest from August 24 to August 28. It will consist of four minicourses by Lucia Caporaso, Phil Engel, Rahul Pandharipande and Aaron Pixton, as well as some short presentations and/or poster session by the PhD students of the RTG.

More details will be added in due time.

• Daniel Litt: Local systems on algebraic varieties

The representation theory of the fundamental group of a smooth quasi-projective variety carries a great deal of geometric information about that variety. I'll survey some questions about representations of such fundamental groups, focusing on the interplay between Hodge theory, topology, and arithmetic. Already there are many interesting deep results and open questions in case of (punctured) curves of genus zero, which will be a running theme throughout.

• Isabel Vogt: The normal bundle and restricted tangent bundle of curves in projective space and applications to moduli

In this mini-course we will study the geometry of curves and their moduli spaces by considering maps from the curve to projective space.  Deformation theory relates the local structure of relevant moduli spaces to natural vector bundles on curves. Two key players in this story are the restricted tangent bundle and the normal bundle of a curve in projective space. We will use embedded degeneration to reducible nodal curves to understand these bundles.

• Olivier Wittenberg: Rationality of algebraic varieties over non-closed fields

Determining which algebraic varieties are rational and which are irrational is one of the central problems of algebraic geometry.  In this mini-course we will explore this question with a focus on ground fields that are non-algebraically closed.  Existing tools include: unramified cohomology, birational rigidity, intermediate Jacobians.

Monday 15:

09:30-10:30: Vogt

10:30-11:00: Coffee Break

11:00-12:00: Litt

12:00-14:30: Lunch Break

14:30-15:45: 5 Short PhD Talks

15:45-16:15: Pause

16:15-17:15: 4 Short PhD Talks

17:30-dinner: PIs meeting (only PIs and coordinator)

Tuesday 16:

09:30-10:30: Vogt

10:30-11:00: Coffee Break

11:00-12:00: Wittenberg

12:00-14:30: Lunch Break

14:30-15:30: Litt

15:30-15:45: Pause

15:45-17:00: Panel/Discussion: How to listen to a talk + How to write and publish a paper.

17:00-: Meetings with Coadvisors / Working time

Wednesday 17:

09:30-10:30: Vogt

10:30-11:00: Coffee Break

11:00-12:00: Wittenberg

Free afternoon

Thursday 18:

09:30-10:30: Vogt

10:30-11:00: Coffee Break

11:00-12:00: Wittenberg

12:00-14:30: Lunch Break

14:30-15:30: Litt

15:30-15:45: Pause

15:45-17:00: General Assembly (also for PhD students and associated)

17:00-: Working time

Friday 19:

09:30-10:30: Wittenberg

10:30-11:00: Coffee Break

11:00-12:00: Litt

The summer school will take place in the building "Torre Archimede" of the Math Department. Via Trieste, 63 - 35121 Padova.

• The talks are in room 1AD 100, first floor, access via staircase A or staircase D.

• The coffee breaks will be on the ground floor.

The participants will stay at the following hotels/residences:

• Hotel Igea

• Camplus Padova Turazza

• Foresteria "La Nave"

• Job Campus - Collegio Mazza

Remke Kloosterman and Orsola Tommasi