Research
Research
Research
Research
921+ open-access research outputs.
The impossibility of eliminating hallucination, understood here as incorrect definite answers, in sufficiently expressive yes-or-no formal domains is an immediate consequence of classical undecidabili…
We compute the dimension of the motivic Galois group of a 1-motive M defined over the field of complex numbers, expressing it explicitly in terms of the rank of the multiplicative group generated by t…
The concept of context-free grammar in Combinatorics was first introduced by Chen in 1993. In 1996, Dumont significantly extended the theory of context-free grammars to a variety of other combinatoria…
We consider the spectrum of the Almost Mathieu operator (AMO) and show that the moments of the restriction of the Lebesgue measure to the intersection spectrum $\text{Leb}|_{\Sigma_{\alpha,\lambda}}$ …
The authors previously formulated the hybrid conjecture, unifying Andr\'e-Pink-Zannier and Andr\'e-Oort conjectures, and proved it in Shimura varieties of abelian type. We study its analogue for mixed…
Let $\xi$ be a value, at an algebraic point, of a Siegel $E$-function. As a special case of a very general interpolation result, we prove that there exists an $E$-function $f$ such that $f(1)=\xi$, an…
We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals…
Given a Nori motivic local system over a smooth, connected complex algebraic variety, we define its exceptional locus as a way to measure the variation in the motivic complexity of its stalks. The def…
In this paper, we investigate the asymptotic distribution of the normalized error for the Mittag--Leffler Euler (MLE) method applied to a class of multidimensional fractional stochastic differential e…
Based on the work of Dundas, Lindenstrauss and Richter we compute the topological Andr\'e-Quillen homology with reduced coefficients for Eilenberg-MacLane spectra such as $H\mathbb{Z}$ and $H\mathbb{Z…
Let S be a connected and smooth scheme of finite type over the complex numbers. We construct functorially the Hodge realization of a 1-motive over S as a torsion-free, polarizable and admissible varia…
McMullen's compact Kobayashi-geodesic curve $V \subset X_L$, arising from the hyperbolic triangle group $\Delta(14,21,42)$ via a modular embedding into the Hilbert modular sixfold $X_L = \mathbb{H}^6/…
This paper investigates the long-time asymptotics and the existence of stationary solutions for a class of stochastic Volterra equations (SVEs). To address the non-Markovian nature of SVEs, we employ …
That Dirichlet processes are discrete with probability 1 is demonstrated once more. And yes, these two pages spent fifty years in Norwegian.…
Simone Weil is one of the most prominent 20th century French philosophers. She is the sister of Andr{\'e} Weil, the renowned mathematician, the father of modern algebraic geometry and the initiator of…
We survey the construction of a range of function spaces used in harmonic analysis of PDE, including classical results as well as recent developments. We frame these constructions in a common conceptu…
The universal property for the B\'enabou bicategory of distributors (although we call them "modules") presented here is somewhat implicitly spread over a series of papers and yet, to my knowledge, doe…
Probabilities is the English translation of the book Probabilit\'es Tome 1 and Tome 2. The mathematic content is authored by Prof. Jean-Yves Ouvrard. The English version has been done by his eldest so…
The principal aim of this paper is to establish a purity theorem for Mahler functions that is reminiscent of famous purity theorems for G-functions by D. and G. Chudnovsky and for E-functions (and, mo…
We establish the following strengthening of the celebrated Andr{\'a}sfai--Erd\H{o}s--S\'{o}s theorem: If $G$ is an $n$-vertex $K_{r+1}$-free graph whose minimum degree $\delta(G)$ and maximum degree $…
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