Research
Research
Research
Research
518+ open-access research outputs.
The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Bernoulli-Laplace mode…
In this paper, we study numerical multiplicities of Demazure modules in the excellent filtration of $\mathfrak{sl}_2[t]$-modules $V(\xi)$, where $V(\xi)$ denotes the fusion product associated to a par…
We study the space of K_+-fixed vectors of Iwahori-spherical representations of GL_n over a non-archimedean local field. For a generic Iwahori-spherical representation, we show that its decomposition …
Kosek, Robertson, Sabo, and Schaal studied the minimum number \(M_k(n)\) of monochromatic solutions to the strict Schur inequality system $x_1\le x_2\le x_3$ and $x_1+x_2<x_3$ in \(2\)-colorings of \(…
We use random matrix theory for the Circular Unitary Ensemble (CUE) to study moments of derivatives of the Riemann zeta function shifted a small distance from the critical line. The corresponding CUE …
Koike (2001) defined the Lipschitz--Killing curvature and established a Chern--Lashof type inequality for equiaffine immersions of arbitrary codimensions. In this paper, we study the equality case. We…
Let $\mathbf{T}_{\mathbf{a},\mathbf{b}}$ be the number of $3$-way contingency tables of size $m \times n \times p$ with two of its three plane-sum margins fixed by $\mathbf{a}=(a_1, \ldots, a_m) \in \…
We prove the convergence in probability of Wilson loops under the Yang-Mills measure on any closed, orientable surface of genus larger than two, for large unitary or special unitary groups. Our approa…
We derive an explicit formula for the ADM mass of asymptotically locally Euclidean (ALE) almost K\"ahler manifolds. The formula expresses the mass in terms of the total Hermitian scalar curvature and …
In this paper, we use the particle motion bijection introduced by Warnaar and developed by the two authors, Jouhet and Konan, to study q-series and partition identities of the Andrews--Gordon type wit…
A categorical action of a Kac--Moody algebra $\mathfrak{g}$ is built on a category $\mathcal{C}$ decomposed according to the weights $P$ of $\mathfrak{g}$, as well as biadjoint endofunctors $\mathcal{…
Some representation-theoretic multiplicities, such as the Kostka and the Littlewood-Richardson coefficients, admit a combinatorial interpretation that places their computation in the complexity class …
We study canonical basis elements in higher-level Fock spaces associated with the quantum group $U_q(\mathfrak{gl}_\infty)$, which are conjecturally related to Calogero-Moser theory for complex reflec…
We study the relation between semipositivity, nefness, and bigness of line bundles on compact K\"ahler manifolds. Every nef and big line bundle on a compact K\"ahler manifold $X$ is positive when ${\r…
Despite recent progress in 3D self-supervised learning, collecting large-scale 3D scene scans remains expensive and labor-intensive. In this work, we investigate whether 3D representations can be lear…
In 1954, following a five-year research period in the U.S., Professor Hideki Yukawa returned to Japan and visited Kochi on March 21 to attend the unveiling ceremony for the first statue of him ever bu…
We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analytic sets in the sens…
The \textit{Teleportation=Translation} conjecture posits that the recovery of information from a black hole is dual to a geometric translation in the emergent spacetime. In this paper, we establish th…
We show that the elements of the Kazhdan--Lusztig basis of the spherical Hecke algebra of type $G_2$ have an atomic decomposition. As a by-product, we obtain a new algorithm to compute generalized Kos…
We show that the parallel transport map over a reductive homogeneous space with natural torsion-free connection becomes an affine submersion with horizontal distribution. This generalizes one of the m…
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