Related papers: Bounded deviations in higher genus I: closed geode…

We describe the intersection complex of any perversity of a toric variety completely in terms of the associated fan. It is described by a finite complex of finite dimensional graded vector spaces which we call graded exterior modules. The…

We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a…

The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…

We study Lagrangian cobordism groups of closed symplectic surfaces of genus $g \geq 2$ whose relations are given by unobstructed, immersed Lagrangian cobordisms. Building upon work of Abouzaid and Perrier, we compute these cobordism groups…

Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which…

We prove the local convergence of uniform bipartite maps with prescribed face degrees in the high genus regime. Unlike in the previous work arxiv:2012.05813 on the subject, we do not make any assumption on the tail of the face degrees,…

We give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura variety of A_{g-1}, contained in the Prym locus. First we give such a bound for a germ passing through a Prym variety of a k-gonal…

This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…

We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…

Topological bases of behaviour of trajectories for autonomous differential systems of the second order on sphere are stated. Stereographic atlas of trajectories is constructed. Differential connections between trajectories of…

We study, for plane complex branches of genus one, the topological type of its generic polar curve, as a function of the semigroup of values and the Zariski invariant of the branch. We improve some results given by Casas-Alvero in 2023,…

This paper is Part I of a two-part series. We investigate bifurcation phenomena in Lagrangian systems with various boundary conditions and constraints, focusing on the interplay between Morse theory and the existence of multiple solutions…

We give a Morse-theoretic characterization of simple closed geodesics on Riemannian $2$-spheres. On any Riemannian $2$-sphere endowed with a generic metric, we show there exists a simple closed geodesic with Morse index $1$, $2$ and $3$. In…

The question of whether a closed Riemannian manifold has infinitely many geometrically distinct closed geodesics has a long history. Though unsolved in general, it is well understood in the case of surfaces. For surfaces of revolution…

For convex domains with $C^{1,\epsilon}$ boundary we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different closed complex faces of the boundary, then the…

Slowly divergent geodesics in the moduli space of Riemann surfaces of genus at least 2 are constructed via cyclic branched covers of the torus. Nonergodic examples (i.e. geodesics whose defining quadratic differential has nonergodic…

We construct topological recursion relations (TRR's) at higher genera $g\ge2$ for general 2-dimensional topological field theories coupled to gravity. These TRR's when combined with Virasoro conditions enable one to determine the number of…

In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by…

We prove height bounds concerning intersections of finitely generated subgroups in a torus with algebraic subvarieties, all varying in a pencil. This vastly extends the previously treated constant case and involves entirely different, and…

We classify, up to isomorphism, maximal curves covered by the Hermitian curve \mathcal H by a prime degree Galois covering. We also compute the genus of maximal curves obtained by the quotient of \mathcal H by several automorphisms groups.…