Research
Research
Research
Research
1,281+ open-access research outputs.
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a p…
Koll\'{a}r showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K…
In this paper, we study the almost everywhere convergence of the cubic nonlinear Schr\"odinger flow to the initial data on $\mathbb S^2$, \begin{equation*} iu_t + \Delta_g u = |u|^2u, \quad (t,x)\…
Discrete quantum groups were introduced as duals of compact quantum groups by Podle\'s and Woronowicz in 1990. They have been studied intrinsically by Effros and Ruan (1994) and by the author (1996). …
We prove a law of large numbers and a functional central limit theorem for the empirical density of a Marcus-Lushnikov model. The limiting density turns out to be the solution of a Smoluchowski equati…
We extend the theory of complex cells introduced by Binyamini and Novikov to the sharply o-minimal setting, obtaining cellular preparation and parameterization theorems which are polynomially effectiv…
In this paper, a three-dimensional competitive Lotka-Volterra system with four limit cycles is constructed for class 28 in Zeeman's classification. Combined with existing results -- from Gyllenberg an…
This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformul…
The aim of these notes is to explain various enumerative results about $K3$ surfaces without assuming familiarity with Gromov--Witten theory. The enumerative results in question are due to Beauville, …
The $i$-dimensional Potts lattice Higgs model is a random assignment of spins in $\mathbb{Z}_q$ to the $i$-dimensional cells of a cell complex induced by a Hamiltonian with a Potts interaction on the …
We consider the (compact) abelian lattice Higgs model with charge \( k \geq 1 \) and show, using charged Wilson~loop observables and charged versions of the Marcu--Fredenhagen ratio, that this model e…
Income-based poverty indicators are insufficient to fully explain the multifaceted socio-economic issue of energy poverty. The ability of households to obtain and use energy services sustainably is si…
This paper introduces a number of new techniques in the study of the famous question from numerical linear algebra: what is the largest possible growth factor when performing Gaussian elimination with…
Let $\mathbb{Z}$ be the additive group of all integers and $\mathbb{N}$ the sub-monoid of $\mathbb{Z}$ of all non-negative integers. For a finite subset $X$ of $\mathbb{Z}$, we denote by ${\rm max}\ X…
In this paper we construct, for given any small positive number $\epsilon$ and given natural number $n$, and given any closed hyperbolic surface $M$, a closed hyperbolic covering surface $\widetilde{M…
We generalize the sparsification algorithm of Batson, Spielman and Srivastava, making one part of the result dimension-independent. In particular, we recover discretization inequalities in $L_2$- and …
We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined…
Spectral analysis has long been recognized as a fundamental tool for studying the existence, uniqueness, and qualitative behavior of solutions to semilinear elliptic and parabolic equations, as well a…
We study subvarieties of very general complete intersections $X\subset \mathbb{P}^n$ of multidegree $(d_1,\dots,d_c)$, when $d:= d_1+\dots +d_c$ is sufficiently large. In a seminal paper Ein proved th…
In this paper, we are concerned with the Cauchy problem for the generalized KdV equation with random data and rough data. Firstly, when $s\in\mathbf{R}$, by using the initial value randomization techn…
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