KMPB Workshop: Holomorphic Differentials & RTG 2965 "From geometry to numbers" : Scientific opening

Contribution List

2. Fabian Haiden

20/11/2024, 09:30

Spaces of quadratic differentials versus spaces of stability conditions

Spaces of quadratic differentials are special cases of spaces of Bridgeland stability conditions. I will recall this surprising correspondence and discuss the following questions: 1) Does this tell us something new about quadratic differentials? 2) In what way do more general spaces of stability conditions behave like...

3. Martin Möller

20/11/2024, 11:00

Siegel-Veech constants and intersection theory

We give an overview over the methods to compute characteristic quantities of strata, Siegel-Veech constants, Masur-Veech volumes and sum of Lyapunov exponents, by flat geometry and by intersection theory, with a view towards answering the same questions for linear submanifolds

4. Carlos Matheus

20/11/2024, 13:30

Siegel-Veech constants of certain cover constructions

Siegel-Veech constants are quantities describing counting problems (of saddle-connections, cylinders, etc.) on flat surfaces and, after the works of many mathematicians (including Aggarwal, Chen, Eskin, Kontsevich, Moller, Sauvaget, Zagier, Zorich just to mention a few), we know that these constants are related to several interesting...

5. Ivan Yakovlev

20/11/2024, 15:00

Counting differentials combinatorially

I will present a couple of results about asymptotic enumeration of holomorphic differentials with periods in Z+iZ (square-tiled surfaces) and meromorphic differentials with periods in Z (integral metric ribbon graphs). These results were obtained by pure combinatorics, and it might be interesting to understand their algebraic meaning.

6. Gregorio Baldi

20/11/2024, 16:00

Hodge Locus and differential geometry (Ho-Lo-Diff)

I will survey various applications of algebraic differential geometry and Galois theory of foliations to finiteness results in differential geometry. Specifically, I will discuss the study of totally geodesic submanifolds of ball quotients (joint work with Ullmo) and affine invariant submanifolds of strata of abelian differentials (with...

7. Anja Randecker

21/11/2024, 09:30

Lengths of saddle connections for large genus

For a holomorphic differential on a given surface, we can consider saddle connections, that is, geodesic segments between the zeros of the differential, and we can measure their lengths. We consider the number of saddle connections in a given length range as a random variable on a stratum and show that for genus going to infinity, this converges...

8. David Urbanik

21/11/2024, 11:00

Orbit Closures as Atypical Intersections

We review the Hodge-theoretic characterization of orbit closures due to Filip. Using this characterization, we then explain how the theory of atypical intersections from Hodge theory naturally lets us classify such orbit closures as "typical" and "atypical". This classification recovers a finiteness theorem of Eskin, Filip and Wright for atypical...

9. Matteo Costantini

21/11/2024, 13:30

Geometry of strata of differentials

The geometry of spaces of algebraic curves together with meromorphic k-forms of a fixed type is still quite mysterious. The multi-scale compactification of these strata of differentials allowed to compute some of their topological and algebraic invariants. In this talk we describe the ideas behind such computations and possible applications.

10. Samuel Grushevsky

21/11/2024, 15:00

Ends of strata of differentials

Using the multi-scale compactification, we determine the number of ends of strata of meromorphic differentials. It turns that in almost all cases all connected components of the strata of differentials have only one end. This is joint work with Ben Dozier.

12. Jarod Alper

22/11/2024, 10:00

13. Tim Browning

22/11/2024, 11:30

14. Soheyla Feyzbakhsh

22/11/2024, 14:30

15. Rahul Pandharipande

22/11/2024, 16:00