Let $X$ be an algebraic variety and let $S$ be a tropical variety associated to $X$. We study the tropicalization map from the moduli space of stable maps into $X$ to the moduli space of tropical curves in $S$. We prove that it is a continuous map an...
In this paper, we present a unified study of the moduli space of tropical curves and Outer space which we link via period maps to the moduli space of tropical abelian varieties and the space of positive definite quadratic forms. Our work is a first s...
We give a survey of our previous work on relatively minimal isotrivial fibrations $α\colon X \to C$, where $X$ is a smooth, projective surface and $C$ is a curve. In particular, we consider two inequalities involving the numerical invariants $K_X^2$...
This article is a revised version of the talk I gave at the conference ``Beauville Surfaces and groups'' held in Newcastle in June 2012. It presents some group theoretical methods to give bounds on the number of connected components of the moduli spa...
The national flag of Brazil is a blue disc depicting a starry sky (which includes the Southern Cross) spanned by a curved band inscribed with the national
We construct an elliptic generalization of the Schlesinger system (ESS) with positions of marked points on an elliptic curve and its modular parameter as independent variables (the parameters in the moduli space of the complex structure). ESS is a...
We give the complete solution to the local diffeomorphism classification problem of generic singularities which appear in tangent surfaces, in as wider situations as possible. We interpret tangent geodesics as tangent lines whenever a (semi-)Riemanni...
To measure the column densities of interstellar and intergalactic gas clouds using absorption line spectroscopy, the apparent optical depth technique (AOD) of Savage & Sembach (1991) can be used instead of a curve-of-growth analysis or profile fit....
A banana manifold is a compact Calabi-Yau threefold, fibered by Abelian surfaces, whose singular fibers have a singular locus given by a "banana configuration of curves". A basic example is given by $X_{ban}$, the blowup along the diagonal of the fib...
In this paper, we study the modeling and the classification of functional data presenting regime changes over time. We propose a new model-based functional mixture discriminant analysis approach based on a specific hidden process regression model tha...
The meaning of CURVY is having curves; often : having an attractively curved feminine figure : curvaceous. How to use curvy in a sentence.
OUT 100 VOICES From 'Drag Race' to Broadway and beyond, Peppermint is owning her spotlight The bisexual comedy queen who is unfiltered, unstoppable, and always ahead of the curve
This note compares the usual (absolute) Gromov-Witten invariants of a symplectic manifold with the invariants that count the curves relative to a (symplectic) divisor D. We give explicit examples where these invariants differ even though it seems a...
We use the well established duality of topological gravity to a double scaled matrix model with the Airy spectral curve to define what we refer to as topological gravity with arbitrary Dyson index $\upbeta$ ($\upbeta$ topological gravity). On the mat...
In the paper we formulate and derive the family blowup formula of family Seiberg-Witten invariants. The formula has been used in the enumerative application of counting singular curves on algebraic surfaces. We first give a topological derivation o...
The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our pro...
For a smooth algebraic curve defined over a number field, one can associate a bipartite graph known as a dessin d'enfant. In this paper, we investigate the regularity and automorphism groups of dessins d'enfants with uniform passports, that is, those...
We present optical photometric and spectroscopic observations, and an analysis of archival X-ray data of three polars: RX J0859.1+0537, RX J0749.1-0549, and RX J0649.8-0737. Optical light curves of these three polars reveal eclipse features that are...
Our understanding of large amplitude pulsating stars and their status in stellar evolution is briefly reviewed. The paper then describes the near-infrared light curves of various asymptotic giant branch stars, concentrating on possible evidence for...
This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this conjecture i...