Prime Fano threefolds in positive characteristic
We prove that every prime Fano threefold of genus $\geq 7$ in positive characteristic is a linear section of a Mukai variety.
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Mathematics
arXiv preprints from January 1, 2026 through September 5, 2026 — 13:08:02 EST
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Mukai bundles and Brill-Noether generality for prime Fano threefolds in positive characteristic
Let $X$ be a prime Fano threefold of genus $g\geq 8$ in positive characteristic. For every nontrivial decomposition $g =rs$, we prove that there exists a unique Mukai bundle on $X$ of type $(r, s)$. To this end, we show that every smooth hyperplane section of $X$ is Brill-Noether general.
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Coincidence of dimensions for stratifiable spaces
In this paper we prove the equality of the dimensions IndX and dimX for any stratifiable spaces. As a consequence, we obtain the equality of the dimensions IndX, indX and dimX for stratifiable spaces with a countable network. It has been proven that every stratifiable space is an S-space (possesses an S-network).
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Laws of the iterated logarithm for random Dirichlet series with general weights
For each $s>0$, we consider a random Dirichlet series $X(s)=\sum_{k\geq 1}k^{-1/2-s}a_kη_k$, where $η_1$, $η_2,\ldots$ are independent and identically distributed random variables with mean zero and finite positive variance, and $(a_k)_{k\geq 1}$ is a deterministic sequence of real numbers satisfying $\sum_{k\geq...
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The spin-1/2 Heisenberg XXZ chain and the Lorentz mirror model with loop weight 2
We prove that for the spin-1/2 Heisenberg XXZ chain in the range $Δ\in[-1,1/2]$, the ground state on the torus of length $L$ converges to an infinite volume ground state $\langle\cdot\rangle$ as $L\to\infty$, and that the spin-spin correlation $\langle S_0^{(1)}S_x^{(1)}\rangle$ decays polynomially fast in $x$. In the range...
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Primal Acceleration of Newton's Method
We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian. The algorithm uses only primal variables and performs just one linear solve per iteration. With a simple predetermined choice of parameters, it achieves the global convergence rate of $O(1/k^3)$ in terms of the...
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Almost sure upper bound for sums of random multiplicative functions and critical chaos
Let $f$ be a Steinhaus or Rademacher random multiplicative function. We use methods from the theory of critical chaos to improve on the best known upper bound for partial sums of random multiplicative functions. In particular, our results imply that for any $\varepsilon>0$, almost surely $$ \Big|\sum_{n\le x}f(n)\Big| ...
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Cohomological Reduction for Fiber-Contracting Extensions:From Subcohomology to Thermodynamic Formalism
We develop a reduction and transfer framework for cohomological, variational, and thermodynamic problems in fiber-contracting extensions of local homeomorphisms. Under uniform contraction along the fibers and the existence of a continuous global section, every Hölder potential admits the explicit decomposition \[...
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Pattern avoidance in canon permutations
A canon permutation is a $k$-regular word over $[n]$ in which, for each $j$, the $j$-th copies of the letters form the same permutation $σ$. These were introduced by Elizalde as a generalization of nonnesting multipermutations, which are the case $k = 2$. We study classical pattern avoidance in them for arbitrary $k$. We show that...
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Sums of products of Kloosterman sums to prime power moduli
We prove new bounds on complete sums of products of k additively shifted Kloosterman sums to odd high prime power moduli q=p^n, which feature substantially stronger power savings (about q^(-1/ceil(k/2)) in generic configurations) and a novel quantification of the alignment among the shifts. We prove our bounds by developing a method...
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Exact Minimum $d$-Degree Thresholds for Hypergraph Perfect Matchings
For fixed integers $k\ge3$ and $1\le d\le k-1$ and sufficiently large $n\in k\mathbb N$, we establish the sharp minimum $d$-degree thresholds that forces perfect matching in every $n$-vertex $k$-uniform hypergraphs. This was conjectued by Treglown and Zhao, and the $d=1$ case was conjectued by Kühn, Osthus and Treglown.
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Stable $s$-minimal cones in $\mathbb{R}^3$ are flat for $s$ close to zero
We prove that stable nonlocal minimal cones in three dimensions are flat, for $s$ sufficiently close to zero. Our approach develops new structural properties of stable $s$-minimal surfaces in every dimension as $s \downarrow 0$, notably a compactness theory and pinching theorems near a half-space.
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Combining Concurrent and Historical Functional Linear Regression
We study a function-on-function linear regression model in which the response at time $t$ depends on both the past trajectory of a predictor and its concurrent value. The model combines an $L^2$-historical effect with a point-evaluation effect, and these two coefficient functions are not automatically identifiable. We characterize the...
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Trustworthy Decisions in Reliability Set Estimation under Insufficient Model Information
Reliability set estimation identifies input regions where a response probability exceeds a target level, bridging estimation and safety-critical decisions. Practitioners typically start with a working model, an imperfect approximation of the true response surface. Relying on this imperfect model may incur decision risk, potentially...
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Backstepping-Guided Reinforcement Learning for Wide-Range Saint-Venant Canal Regulation
Backstepping control provides local stability guarantees for nonlinear Saint-Venant systems, but its regulation performance may degrade when the system operates far from the nominal equilibrium. This letter proposes a backstepping-guided soft actor-critic (SAC) controller framework that incorporates model-based control knowledge into...
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Dual Control: On Exploration-Exploitation in Linear Systems
The term "dual control" refers to the dual objective of simultaneously balancing exploration and exploitation. Problems of this kind have been studied for nearly a century. This paper is devoted to theory and methodology relevant for optimal control of linear time-invariant systems whose parameters are initially unknown and must be...
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Dynamic Portfolio Optimization under CVaR Constraints
We study continuous-time dynamic portfolio optimization under a Conditional Value-at-Risk (CVaR) constraint on the investor's terminal loss. For a general class of convex trading objectives, we exploit the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring...
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Complete Symbols of Equivariant Pseudodifferential Operators on Noncompact Symmetric Spaces
We study $G$-equivariant Hörmander pseudodifferential operators on a noncompact symmetric space $G/K$. We define a notion of a complete symbol function, called the Harish-Chandra symbol function, on the spherical tempered dual of $G$, for operators that satisfy a rapid off-diagonal decay condition on their Schwartz kernels, and we...
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The Additive Arithmetic of Linear Orders
We present a systematic development of the arithmetic of the class of linear orders under the ordered sum $(LO, +)$ and prove a number of new results. Our approach is based on a Euclidean algorithm for pairs of linear orders that almost additively commute. Among our results: (i.) We generalize and give unified proofs of the main...
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Kahn--Lovász-type inequalities for graph factors
The Kahn--Lovász theorem gives a sharp upper bound on the number of perfect matchings in a graph in terms of its degree sequence, extending the classical Brégman--Minc inequality for bipartite graphs. In this paper, we establish an asymptotically sharp extension of the Kahn--Lovász theorem to $F$-factors for every Hamiltonian graph...
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A two-point phase recovering with spherical wave reference
We consider a reference wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region. We give two-point formulas for approximate phase recovering of the radiation solution from the intensity of the total solution for the case of spherical reference wave. We show that...
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A new lower bound for the growth rate of Av(1324)
The growth rate of Av(1324) is the last unknown Stanley-Wilf limit of a length-four pattern. The best rigorous lower bound has been 10.271012 since Bevan, Brignall, Elvey Price and Pantone obtained it in 2020; we raise it to 10.617. Their scheme relaxes an interleaving rule in one direction only. Relaxing it in both is valid, and the...
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Spectral Viterbo isomorphism: complex-oriented versus framed
The Viterbo isomorphism relates the symplectic cohomology of a cotangent bundle to the homology of the free loop space of its base. We lift this to a relation of modules over (1) the complex bordism spectrum MU and (2) the sphere spectrum $\mathbb{S}$. In particular, by a result of Porcelli and the present author [BP26], it is not the...
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Robustness of random-walk Metropolis for steep potentials
In Markov chain Monte Carlo sampling, light-tailed target distributions present something of a poisoned chalice: their light tails offer good confinement, and tend to imply good mixing properties for natural continuous-time dynamics, but the steepness of their tail decay means that they often fall outside of the scope of modern...
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Optimal regularity of stable harmonic maps to spheres
In this paper, we show that the codimension of the singular set of a stable stationary harmonic map to a round $k$-sphere is at least $k+1$ when $k$ is between 3 and 6, and is at least 7 when $k$ is at least 7. The result is sharp in the sense that there exist energy minimizing 0-homogeneous maps in the aforementioned critical...