Research
Research
Research
Research
6,773+ open-access research outputs.
We study the moduli spaces of rational curves on cubic hypersurfaces in characteristic $\neq2,3$. As a result, we prove that for every integer $d\geq1$ the Kontsevich moduli space of stable maps on a …
We prove that over a generic Poncelet triangle family, the locus of the circumcenter of an inversive triangle is a conic. Additionally, we prove an earlier conjecture: over generic Poncelet triangles,…
The three-dimensional cubic conformal field theory governs the critical behaviour of Heisenberg magnets with cubic anisotropy. Studying this theory non-perturbatively is challenging, because its most …
This work investigates the role of the $U(N) \times U(\tilde{N})$ global symmetry in tree-level scattering amplitudes of the bi-adjoint $\phi^3$ theory from three perspectives: combinatorics, correlat…
Let $\pi$ be an irreducible, cuspidal automorphic representation of $GL_n(\mathbb{A}_\mathbb{Q})$ ($n\geq 3$), which is tempered only for $n=3$. Let $s$ be a complex number such that $\Re(s)\notin \le…
Noisy labels are a pervasive challenge in medical image classification, where annotation errors arise from inter-observer variability and diagnostic ambiguity. Although several noise-robust learning m…
A microbubble is, in essence, a fully enclosed thin-walled microcavity. Unlike spherical microbubbles formed by expansions, 3D printing enables the free definition of their geometry, allowing precise …
Classical ReLU-based Input Convex Neural Networks (ICNNs) are equivalent to the optimal value functions of Linear Programming (LP). This intrinsic structural equivalence restricts their representation…
We produce infinitely many local systems on (level covers of) the moduli space of smooth cubic threefolds, with algebraic monodromy group equal to the exceptional group $E_6$. These local systems aris…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric a…
We study cubic realizations of posets compatible with projection maps, meaning that the projection is represented by deletion of the last coordinate. For cylindrical projections, we introduce the pre-…
The Chabauty--Coleman--Kim method, under favourable circumstances, describes the set of integral points of a hyperelliptic curve inside the $p$-adic zeroes of certain transcendental functions. For an …
We classify pairs $(X,G)$ consisting of a (possibly singular) cubic threefold $X\subset\mathbb{P}^4$ and a finite subgroup $G\subset\mathrm{Aut}(X)$ such that $X$ is $G$-birationally rigid, i.e., $X$ …
We consider the cubic nonlinear Schr\"{o}dinger system with Rashba type Spin-Orbit coupling (SOC) on $\mathbb{R}^2$, which is also called the Gross--Pitaevskii equation with SOC. The system describes …
We study the three classical integrable generalized cubic H\'enon--Heiles systems -- Kaup--Kupershmidt, KdV$_5$, and Sawada--Kotera -- from the viewpoint of bi-Hamiltonian geometry and separation of v…
We show how the circle method can be used to study rational points on a certain cubic fourfold, going beyond the square-root barrier.…
The expected meeting time of two random walkers on an undirected graph of size $N$, where at each time step one walker moves and the process stops when they collide, satisfies a system of $\binom{N}{2…
Generalized Additive Models (GAMs) can be used to create non-linear glass-box (i.e. explicitly interpretable) models, where the predictive function is fully observable over the complete input space. H…
In this work we develop and analyze a semi-smooth Newton method for the general nonlinear conic programming problem. In particular, we study the problem with a generalized simplicial cone, i.e., the i…
$\gamma$-${\rm Ba}_{3}{\rm CoNb}_{2}{\rm O}_{9}$ realizes a disordered simple-cubic spin-$1/2$ lattice in which Co$^{2+}$ ions randomly occupy one third of the sites, placing the system close to the s…
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