Mathematics

We study when an equidimensional toric morphism is forced to be a projective-space bundle. Our main result is an affine rigidity theorem: if the base space is affine, the toric relative canonical divisor is $\mathbb Q$-Cartier, and its…

We study the exterior Dirichlet problem for the mixed Hessian quotient equation \[ \frac{\sigma_k(\eta(D^2 u))}{\sigma_l(\eta(D^2 u))} = 1, \] where $\eta(M) = (\operatorname{tr} M)I - M$. We establish existence and uniqueness of smooth…

Electroporoelasticity equations couple Maxwell's equations with Biot's poroelasticity model and admit severe Poisson locking in standard conforming finite element discretizations when the Lam\'e constant is large. In this paper, we provide…

In this paper, we give an explicit construction of surface measures on a class of surfaces with arbitrary, possibly infinite, codimension in $\ell^2$. These measures are constructed from local representations associated with a fixed…

In the published paper [T10], K. Trim\`eche presented a proof of the statement that for suitable nonnegative multiplicities and regular arguments, the representing measures of Dunkl's intertwining operator and its dual are absolutely…

We show how to extend Makdisi's algorithms to compute explicitly with the Poincar\'e torsor on the Jacobian of an algebraic curve.

We give a detailed proof of interior $W^{2,p}$ regularity for uniformly elliptic equations in nondivergence form \[ a^{ij}(x)D_{ij}u+b^i(x)D_i u=f. \] The leading matrix is assumed to have sufficiently small mean oscillation on the balls…

For a number field $K$, a prime $p$ and a finite set of tame places $S$ we consider the groups $G_{K,S}$ - the Galois groups of the maximal pro-$p$ extension of $K$ unramified outside $S$. The tame Fontaine--Mazur Conjecture predicts that…

We prove Sobolev space well-posedness of the decoupled potential integral equations. Using basic pseudo-differential techniques, discrete stability is obtained for the standard $L^2$-pairing, and we deduce spectral convergence for a…

We introduce the notion of moderate and rapid decay nearby cycles relative to a holomorphic function $f$ for an arbitrary holonomic $\mathcal{D}$-module. They are proved to be $\mathbb{R}$-constructible complexes on the product of the…

We study necessary and sufficient conditions on $\gamma$ for several classes of polynomials of the form $X+\gamma \operatorname{Tr}_{q}^{q^n}(h(X))$ to be permutation polynomials over finite field $\mathbb{F}_{q^n}$, where $q$ is a prime…

In recent years, integrable hierarchies have been used to great advantage for the enumeration of combinatorial maps. They have led to recurrence formulas with respect to the size and genus of the maps, e.g. for triangulations, bipartite…

We prove the Weinstock inequality for the first Steklov eigenvalue of convex domains in hyperbolic space $\mathbb{H}^{n}$, resolving Open Question 4.27 of Colbois-Girouard-Gordon-Sher(2024) for the remaining case $n=3$. Our argument…

Anatomical image registration commonly relies on a sequential pipeline where an affine alignment is estimated first and then held fixed while a non-rigid diffeomorphic deformation is applied. This two-step process often leads to suboptimal…

We study spatial decay properties of solutions to the dispersion generalized Benjamin-Ono equation. We first establish persistence properties in weighted Sobolev spaces under a sharp condition between decay and regularity, improving…

Many approximation methods enlarge a trial space by adjoining function blocks generated by different operators. Exact redundancy and strong cross-level interaction can make coefficients nonunique and render pairwise or diagonal-dominance…

We introduce fully nonlinear curvature flows of horo-convex hypersurfaces in the sphere that preserve an arbitrarily prescribed spherical quermassintegral. The non-local normalization is defined relative to a fixed ambient origin, and we…

We compute the stability degree of curves of genus g and show that it is equal to the classical Minkowsky bound. We also compute the stability degree of semi-abelian varieties with prescribed toric and abelian ranks. The proof uses a…

We study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet, Neumann or Robin boundary condition at the fixed boundary $x=0$. In the case of…

We introduce a Hybrid High-Order framework for differential forms on general polyhedral meshes. For each form degree $k\in\{0,\ldots,n-1\}$, the discrete space combines polynomial differential forms on mesh cells with polynomial trace…