Fabian Haiden Room: 1.107 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 spaces of quadratic differentials? Based on arxiv:1409.8611, 1808.06364, 2104.06018, 2410.08028.

Martin Möller Room: 1.107 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

Carlos Matheus Room: 1.107 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 mathematical objects such as quasi-modular forms, Lyapunov exponents, slopes of holomorphic bundles, intersection numbers, ... In this talk, we shall explain how a precise control of the monodromy actions of the orbifold fundamental group of connected components of strata of Abelian differentials on relative cohomology groups allow to compute (and get some surprising phenomena about) the Siegel-Veech constants of loci of cyclic covers of translation surfaces. This is based on a joint work with D. Aulicino, A. Calderon, N. Salter and M. Schmoll.

Ivan Yakovlev Room: 1.107 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.

Gregorio Baldi Room: 1.107 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 Urbanik). I will aim to highlight a unifying theme throughout: atypical intersections.

Anja Randecker Room: 1.107 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 in distribution to a Poisson distributed random variable. In the talk, I will introduce the geometric aspects of the topic and connect it to Siegel-Veech constants. This is based on joint work with Howard Masur and Kasra Rafi.

David Urbanik Room: 1.107 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 orbit closures. If we have time, we explain how this finiteness can be made effective. Joint work with Greg Baldi.

Matteo Costantini Room: 1.107 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.

Samuel Grushevsky Room: 1.107 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.

Jarod Alper Room: 1.013

Tim Browning Room: 1.013

Soheyla Feyzbakhsh Room: 1.013

Rahul Pandharipande Room: 1.013