Research
Research
Research
Research
196+ open-access research outputs.
In 1998, Bremner conjectured that elliptic curves over the rationals having long sequences of different rational points whose $x$-coordinates are in arithmetic progression, have large rank. This conje…
In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constants in the uniform Mo…
We introduce a class of proper differential graded algebras which we call Serre cyclotomic. They generalize fractionally Calabi-Yau algebras and categorify de la Pe\~na's algebras of cyclotomic type. …
We produce a family of bodies in $\mathbb R^3$ parameterized by $\varepsilon > 0$, each bounded by a smooth topological sphere with principal curvatures in $[-1, 1]$, and having volume arbitrarily clo…
We compute the second order asymptotics of the maximum of the absolute value of the log-characteristic polynomial of random Jacobi matrices whose coefficients satisfy some exponential integrability co…
We give an expansion in $1/N$ and $\beta$ of the cumulants of power sums of the particles of the $\beta$-ensemble. This new expansion is obtained using the tridiagonal model of Dumitriu and Edelman. T…
We propose Dimitra++, a novel framework for audio-driven talking head generation, streamlined to learn lip motion, facial expression, as well as head pose motion. Specifically, we propose a conditiona…
In a previous work, B\'ona and Pantone studied permutations that avoided all but one pattern of length $k$ that began with a length $k-1$ increasing subsequence. We draw the connection between that id…
This work pose an example of a smooth closed surface in $\mathbb{R}^3$ which has genus $0$, normal curvatures at most $1$ in absolute value and encloses a volume smaller than the volume of a unit ball…
Let $X\subseteq \mathbb{P}^3$ be a smooth projective surface of degree $d\ge 4$ defined over a number field $K$, and let $N_{X^{\prime}}(B)$ be the number of rational points of $X$ of height at most $…
Partially ordered patterns (POPs) generalize the classical notion of permutation patterns within the framework of pattern avoidance. Building on recent work by Burstein, Han, Kitaev, and Zhang, which …
We derive the hot-electron-limit (HEL) closure for the moment hierarchy used to solve the gyrokinetic equations, known as the gyromoment (GM) approach. By expanding the gyroaveraging kernels in the sm…
We consider polynomials which take integer values on the integers (IVPs), and satisfy an additional growth condition on the natural numbers. Elkies and Speyer, answering a question by Dimitrov, showed…
The aim of this paper is to calculate entropy in the sense of Dimitrov-Haiden-Katzarkov-Kontsevich and polynomial entropy as defined by Fan-Fu-Ouchi of derived autoequivalences of derived discrete alg…
Consider the random bipartite Erd\H{o}s-R\'{e}nyi graph $\mathbb{G}(n, m, p)$, where each edge with one vertex in $V_{1}=[n]$ and the other vertex in $V_{2} =[m]$ is connected with probability $p$, an…
We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for $2 \times 2$ random matrix ensembles. For GUE matrices, we resolve a previously reported discrepancy between the…
For each $\alpha \in \mathbb{R}$, $t \geq 1$, we show that there exists a unique $\mathbb{N}$-indexed line ensemble of random continuous curves $\mathbb{R}_{\le 0} \to \mathbb{R}$ with the following p…
In a spirit of Ap\'ery's proof of the irrationality of $\zeta(3)$, we construct a sequence $p_n/q_n$ of rational approximations to the $2$-adic zeta value $\zeta_2(5)$ which satisfy $0 < |\zeta_2(5)-p…
We present a symplectic electromagnetic fully-kinetic particle-in-cell simulation of microinstabilities in plasma, using parameters from the Cyclone Base Case [Dimits, et al., Physics of Plasmas 7, 96…
In this paper, I pay tribute to my exceptional colleagues and friends Dmitri Diakonov, Victor Petrov, and Maxim Polyakov by examining the experimental progress and current status of the searches of th…
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