数学

The Kohayakawa--Nagle--R\"odl--Schacht conjecture predicts that locally dense graphs contain, asymptotically, at least as many homomorphic copies of any fixed graph as the random graph of the same edge density. We prove that every graph…

We say that a hypersurface $\Sigma \subset\mathbb{R}^{n+1}$ is $\alpha$-stationary if it is a critical point of the Euler-Dierkes-Huisken functional $\mathcal{E}_\alpha(\Sigma)=\int_\Sigma|X|^\alpha\, d\mathcal{H}^n$, introduced by Dierkes…

In joint work with Lacini and Sheridan, we proved that the first and second secant varieties of a smooth projective complex variety embedded by the complete linear system of a sufficiently positive line bundle are projectively normal. The…

We consider nonparametric estimation of the regression function in a model where individuals share a common noise component and repeated measurements are available for each individual. We propose a projection estimator which minimizes a…

We are interested in conducting political polls sequentially, so that one can stop acquiring data as soon as possible while safely yielding statistically significant results. Building off e-values, which have recently become a useful tool…

We prove Strichartz estimates for the space-time density $\rho$ of solutions to the free Liouville equation on flat tori. In dimension one, we obtain the optimal range of estimates for the density $\rho \in L^p_{t,x}$ in terms of $f_0 \in…

We consider two coupled linear heat equations on different spatial domains that interact through a lower dimensional interface. This models conjugate heat transfer. The problem is solved using Dirichlet-Neumann waveform relaxation. This…

The Schatten-$q$ quasi-norm is a widely used nonconvex rank surrogate and matrix factorization is an effective approach to reduce computational cost. In this paper, we consider the equivalent group-sparse factorized reformulation of…

We study composition operators induced by a smooth symbol between weighted Bergman spaces of the polydisc. We first prove a compactness criterion that only requires knowing what happens on the distinguished boundary. Then we prove simple…

We introduce a Delsarte linear programming approach to the finite field Erd\H{o}s--Falconer distance problem. Let \(q\) be an odd prime power, let \(n\) be even, and let \(Q\) be a non-degenerate quadratic form on \(\mathbb{F}_q^n\). For…

For cellular automata over finite alphabets, bijectivity already implies reversibility. Over infinite alphabets this implication may fail, and the remaining obstruction in the periodic case was recorded by Ceccherini-Silberstein and…

We prove the first boundedness and pointwise decay result for the scalar wave equation on rotating extremal black holes without any symmetry assumptions. The result applies to slowly rotating (equivalently, strongly charged) extremal…

Fundamental logic is a non-classical logic based only on the introduction and elimination rules for conjunction, disjunction, negation, and the quantifiers in a Fitch-style natural deduction system. In this paper, we attempt to obtain a…

Let $p\ge 3$ be a prime and $b\ge 2$ an integer such that $p$ does not divide $b$. Then $1/p$ has a periodic digit expansion with respect to the basis $b$. The length $l$ of the period is the (multiplicative) order of $b$ mod $p$. In the…

This research reviews several crucial aspects of the universal model for the Lorenz curve proposed by Sitthiyot and Holasut (2023) (hereafter, SH (2023)). A first issue concerns the mathematical definition of the proposed curves. The four…

Laguerre tessellations offer an efficient way to parameterize a large class of convex partitions of Euclidean space using only a set of points and scalar weights. For this reason, they have become popular in computational geometry, imaging…

We develop a nonlinear potential theory for elliptic equations with Orlicz growth under general monotonicity and growth conditions, without any homogeneity or scaling assumptions. The lack of scaling invariance prevents the use of many…

We establish the global-in-time existence of a codimension $1$ canonical multi-phase free boundary Brakke flow in the upper halfspace which is integer rectifiable up boundary, starting from a countably $n$-rectifiable set. Under a suitable…

In this paper, we upgrade the instanton TQFT from ordinary categories to a functor $CI$ from an $\infty$-cobordism category $\mathrm{BI}$ for instantons to an $\infty$-derived category $\mathsf{D}$ of $2$-periodic chain complexes and sums…

We exhibit a simple deterministic one-dimensional convex composite optimization problem for which AdaGrad scheme does not achieve the classical convergence rate $\mathcal{O}(n^{-(1+\nu)/2})$ associated with H\"older-smooth objectives. The…