Research
Research
Research
Research
675+ open-access research outputs.
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…
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/…
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…
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 $…
Following the famous proof of Fermat's Last Theorem by Andrew Wiles using the modularity of elliptic curves over $\mathbb{Q}$, significant developments have been made in the study of Diophantine equat…
We study ordinary abelian schemes in characteristic $p$ and their moduli spaces from the perspective of char $p$ Mumford--Tate, log Ax--Lindemann, and geometric Andr\'e--Oort conjectures (abbreviated …
This is an essay on the relation of Andr{\'e} and Simone Weil with Indian culture and Sanskrit literature, especially the Bhagavad G{\=i}t{\=a}, a Hindu scripture which they knew well, which they quot…
Let $(A,\mathfrak{m})$ be an excellent local complete intersection ring and let $I = (a_1, \ldots, a_r)$ be an ideal of positive height. Let $\mathcal{R}(I) = A[It]$ be the Rees algebra of $I$. Consid…
Simsun permutations, Andr\'e I permutations and Andr\'e II permutations are three combinatorial models for Euler numbers. It's known that the descent statistic is equidistributed over the set of Andr\…
Free open-access publishing with Google Scholar indexing.
Submission Guide →