arXiv preprints from January 1, 2026 through July 20, 2026 — 20:29:08 EST
Let $E$ be an elliptic curve defined over $\mathbb{Q}$ which has good supersingular reduction at the odd prime $p$. We study the variation of Iwasawa invariants and the $\mathfrak{M}_H(G)$-property for signed Selmer groups over $\mathbb{Z}_p$-extensions of an imaginary quadratic number field $K$ that lie inside the...
This Ph.D. thesis reports on progress in rigorously establishing hydrodynamic principles from the microscopic Hamiltonian dynamics of quantum many-body systems in a general, non-model-specific manner. Using the C*-algebra framework of statistical mechanics, we treat systems directly in the thermodynamic limit, primarily focusing on...
We study the free energy for pure and mixed spherical $p$-spin models with i.i.d.\ disorder. In the mixed case, each $p$-interaction layer is assumed either to have regularly varying tails with exponent $α_p$ or to satisfy a finite $2p$-th moment condition. For the pure spherical $p$-spin model with regularly varying disorder of...
We study the behavior of slope-stability of reflexive twisted sheaves over a normal projective variety $X$ under pullback along a cover. Slope-stability is always preserved if the cover does not factor via a quasi-étale cover. Fixing the rank, there is one quasi-étale cover that checks whether a twisted sheaf remains slope-stable on...
Let $\mathcal{H}=(V, E)$ be an $r$-uniform hypergraph on $n$ vertices. The signless Laplacian spectral radius of $\mathcal{H}$ is defined as the maximum modulus of the eigenvalues of the tensor $\mathcal{Q}(\mathcal{H})=\mathcal{D}(\mathcal{H})+\mathcal{A}(\mathcal{H})$, where $\mathcal{D}(\mathcal{H})$ and $\mathcal{A}(\mathcal{H})$...
Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric coefficients, computing financial Greeks, or optimizing neural networks. These sensitivities are...
De la Llave's examples are Anosov diffeomorphisms on the four-torus $\mathbb{T}^4$ with constant Lyapunov spectrum, yet they are not $C^{1}$-conjugate to the linear model or to each other. Nevertheless, we show that such examples are ``locally exceptional'': we prove deformation and local rigidity for generic diffeomorphisms in...
We investigate the ferromagnetic Ising model on the Erdős-Rényi random graph $\mathbb{G}(n,m)$ with bounded average degree $d=2m/n$. Specifically, we determine the limiting distribution of $\log Z_{\mathbb{G}(n,m)}(β,B)$, where $Z_{\mathbb{G}(n,m)}(β,B)$ is the partition function at inverse temperature $β>0$ and external field...
In this paper we compute an explicit closed formula for the total Tjurina number $τ(C)$ of a reduced projective plane curve $C$ in terms of the graded Betti numbers of the corresponding Jacobian algebra. This formula allows a completely new view point on the classical upper bounds for the total Tjurina number $τ(C)$ of a plane curve...
In this article, we develop what are, to the best of our knowledge, the first negative results for scalar conservation laws. We begin with explicit examples where bounded initial data leads to $L^{\infty}$ blow-up despite flux regularity. More strikingly, we demonstrate that Kružkov's entropy equalities alone fail to ensure uniqueness...
We prove that constant minimum degree already forces cycles with almost linearly many chords. Specifically, every graph $G$ with $δ(G)\ge C$ contains a cycle of length $\ell\ge 4$ with $Ω(\ell/\log^{C}\ell)$ chords for some absolute constant $C>0$. This is the first result showing that a constant-degree condition yields an unbounded...
Attaching a Casson handle to a slice disk complement yields a smooth 4-manifold that is homeomorphic to $\mathbb{R}^4$. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic $\mathbb{R}^4$'s made using the simplest positive Casson handle are not diffeomorphic, giving us a countably...
Consider $M_n$ the maximal position at generation $n$ of a supercritical branching random walk. Aïdékon (2013) obtained and described the convergence in law, as time $n$ goes to infinity, of $M_n-m_n$, where $m_n$ is an explicit function. Equivalently, he identified the limit of $\mathbb{P}(M_n > m_n + x)$, for any $x \in \mathbb{R}$....
We develop and analyse an adaptive fully mixed finite element method for stationary generalized bioconvective flows, where the Navier--Stokes equations with concentration-dependent viscosity are coupled with a conservation law for swimming microorganisms. The formulation introduces auxiliary variables including the trace-free velocity...
We study a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation within a prescribed constraining set. Existence, variational representability, and regularity of solutions to the growth...
This article describes Boy's surface in a nice way that does not make many demands on three-dimensional visualization. The article includes a kit that you can print out onto card stock and assemble with scissors and tape.
The rapid growth of urban populations and the increasing need for sustainable transportation solutions have prompted a shift towards electric buses in public transit systems. However, the effective management of mixed fleets consisting of both electric and diesel buses poses significant operational challenges. One major challenge is...
Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions over the years calls for computationally cheap DFRO algorithms, that is, algorithms requiring as...
We show how the robustness of gamma hedging can be understood without using rough-path theory. Instead, we use the concepts of $p^{th}$ variation along a partition sequence and Taylor's theorem directly, rather than defining an integral and proving a version of Itô's lemma. The same approach allows classical results on delta-hedging...
We show Shelah's original creature forcing from 1984 strongly preserves tight mad families. In particular, answering questions of Fischer and Friedman and Friedman and Zdomskyy, we show the constellation $\aleph_1 = \mathfrak{a} < \mathfrak{s} = \aleph_2$ is consistent with the existence of a $Δ_3^1$ wellorder of the reals and tight...
Portfolio optimization (PO) is a core tool in financial and operational decision-making, typically balancing expected profit and risk. In real-world applications, particularly in the energy sector, decision variables can be expressed as physical quantities (e.g., production volumes), and nonlinear performance metrics such as Return on...
Let us denote elements of the symmetric group $S_n$ using square brackets for the one-line notation. Cycles will be represented using parentheses, following the standard cycle notation. Under this convention, the full reversal of the identity element $()$ is the element $s = [n\ n-1 \dots 1]$. In the present work, we obtain a lower...
A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the domain-decomposition-inspired additive architecture of FBPINNs, in which local neural networks are defined on...
We compute the Chow quotient of the complete flag variety of isotropic subspaces of a four dimensional complex vector space with respect to a skew/symmetric form, and show that it is a singular del Pezzo surface of degree four.
This paper investigates a class of generalized inverse mixed variational inequality problems (GIMVIPs), which consist in finding a vector $\overline{w}\in \R^d$ such that \[ F(\bar w)\in Ω\quad \text{and} \quad \langle h(\bar w), v-F(\bar w) \rangle + g(v)-g(F(\bar w)) \ge 0, \quad \forall v\in Ω, \] where \(h,F:\R^d\to\R^d\) are...