98 citations · 336 across the 20 of their papers we have counts for
22 papers
Spectral decomposition and Siegel-Veech transforms for strata: The case of marked tori
Jayadev Athreya, Jean Lagacé, Martin Möller +1
Generalizing the well-known construction of Eisenstein series on the modular curves, Siegel-Veech transforms provide a natural construction of square-integrable functions on strata…
A smooth compactification of spaces of stability conditions: the case of the -quiver
Anna Barbieri, Martin Möller, Jeonghoon So
We propose a notion of multi-scale stability conditions with the goal of providing a smooth compactification of the quotient of the space of projectivized Bridgeland stability cond…
Teichmüller curves in hyperelliptic components of meromorphic strata
Martin Möller, Scott Mullane
We provide a complete classification of Teichmüller curves occurring in hyperelliptic components of the meromorphic strata of differentials. Using a non-existence criterion based o…
Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients
Matteo Costantini, Martin Möller, Johannes Schwab
We provide formulas for the Chern classes of linear submanifolds of the moduli spaces of Abelian differentials and hence for their Euler characteristic. This includes as special ca…
Quadratic differentials as stability conditions: collapsing subsurfaces
Anna Barbieri, Martin Möller, Yu Qiu +1
We introduce a new class of triangulated categories, which are Verdier quotients of three-Calabi-Yau categories from (decorated) marked surfaces, and show that its spaces of stabil…
Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
D. Chen, M. Möller, A. Sauvaget +3
We describe a conjectural formula via intersection numbers for the Masur-Veech volumes of strata of quadratic differentials with prescribed zero orders, and we prove the formula fo…
The area is a good enough metric
Matteo Costantini, Martin Möller, Jonathan Zachhuber
In the first part we extend the construction of the smooth normal-crossing divisors compactification of projectivized strata of abelian differentials given by Bainbridge, Chen, Gen…
The moduli space of multi-scale differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space o…
Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials
Dawei Chen, Martin Möller, Adrien Sauvaget +1
We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained by intersection numbers on the strata of Abelian differentials with prescribed orders of zeros.…
Non-existence and finiteness results for Teichmueller curves in Prym loci
Erwan Lanneau, Martin Moeller
The minimal stratum in Prym loci have been the first source of infinitely many primitive, but not algebraically primitive Teichmueller curves. We show that the stratum Prym(2,1,1)…
Strata of -differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
A -differential on a Riemann surface is a section of the -th power of the canonical line bundle. Loci of -differentials with prescribed number and multiplicities of zeros…
Counting Feynman-like graphs: Quasimodularity and Siegel-Veech weight
Elise Goujard, Martin Moeller
We prove the quasimodularity of generating functions for counting torus covers, with and without Siegel-Veech weight. Our proof is based on analyzing decompositions of flat surface…
Lower bounds for Lyapunov exponents of flat bundles on curves
Alex Eskin, Maxim Kontsevich, Martin Moeller +1
Consider a flat bundle over a complex curve. We prove a conjecture of Fei Yu that the sum of the top k Lyapunov exponents of the flat bundle is always greater or equal to the degre…
Quasimodularity and large genus limits of Siegel-Veech constants
Dawei Chen, Martin Moeller, Don Zagier
Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides qu…
Compactification of strata of abelian differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of s…
Modular embeddings of Teichmueller curves
Martin Moeller, Don Zagier
Fuchsian groups with a modular embedding have the richest arithmetic properties among non-arithmetic Fuchsian groups. But they are very rare, all known examples being related eithe…
Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces
Martin Moeller, Domingo Toledo
Shimura curves on Shimura surfaces have been a candidate for counterexamples to the bounded negativity conjecture. We prove that they do not serve this purpose: there are only fini…
A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces
Carlos Matheus, Martin Moeller, Jean-Christophe Yoccoz
We present a Galois-theoretical criterion for the simplicity of the Lyapunov spectrum of the Kontsevich-Zorich cocycle over the Teichmueller flow on the -orbit of a square…
Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle
Artur Avila, Alex Eskin, Martin Moeller
Suppose N is an affine SL(2,R)-invariant submanfold of the moduli space of pairs (M,w) where M is a curve, and w is a holomorphic 1-form on M. We show that the Forni bundle of N (i…
Prym covers, theta functions and Kobayashi curves in Hilbert modular surfaces
Martin Moeller
Algebraic curves in Hilbert modular surfaces that are totally geodesic for the Kobayashi metric have very interesting geometric and arithmetic properties, e.g. they are rigid. Ther…
Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant
M. Möller, A. D. Pohl
We characterize Maass cusp forms for any cofinite Hecke triangle group as 1-eigenfunctions of appropriate regularity of a transfer operator family. This transfer operator family is…
Differential equations associated with nonarithmetic Fuchsian groups
Irene Bouw, Martin Moeller
We describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential…