Research
Research
Research
Research
4,955+ open-access research outputs.
In this paper we provide a geometric condition satisfied by certain closed subsets of the Riemann sphere which implies that their hyperbolic convex hulls in $\mathbb{H}^3$ have infinite volume. As a c…
Reusing verification artefacts requires identifying structural and semantic similarities across programs and their specifications. In this paper, we focus on graph construction as a foundational step …
Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations,…
In this paper, we introduce GET-2D-1.0, a fast grasp planner for the GET asymmetrical gripper that operates from a single-view RGB-D image, using the Ferrari-Canny metric and a novel sampling strategy…
We introduce a framework within which a large class of joint equidistribution problems can be studied and resolved with effective error terms. This involves proving a higher dimensional and $\mu$-anal…
Genomic Schur functions were introduced by Pechenik and Yong in connection with the $K$-theory of Grassmannians. Pechenik proved that genomic Schur functions admit a positive expansion in the basis of…
Large Language Models (LLMs) show promise in automated software engineering, yet their guarantee of correctness is frequently undermined by erroneous or hallucinated code. To enforce model honesty, fo…
Let $f$ be the Hecke eigenform for the modular group $SL_2(\mathbb{Z})$, and $L(s, \text{sym}^2 f)$ be the symmetric square $L$-function associated with $f$. For $\frac{1}{2}<\sigma<1$, define $m(…
We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of stan…
Monitoring frying oil degradation is critical for food safety, yet current practice relies on destructive wet-chemistry assays that provide no spatial information and are unsuitable for real-time use.…
Let $F$ be a finite extension of $\mathbb{Q}_p$. The so-called supersingular representations are the basic building blocks in the theory of mod $p$ representations of ${\rm GL}_2(F)$. The space of pro…
In this paper, we study the Littlewood theory associated with the quantum super immanants and supersymmetric polynomials, including both the super case and the quantum generalization. In the setting o…
We study sums of absolute values of Hecke eigenvalues of $\textrm{GL}(2)$ representations that are tempered at all finite places. We show that these sums exhibit logarithmic savings over the trivial b…
We describe a conjectural approach to obtaining canonical bases of the Hecke algebra at $q=1$ via continuous quadratic optimization. We focus on Specht modules $S^\lambda$ and proper cones inside $S^\…
Diffusion-based image synthesis has emerged as a promising source of synthetic training data for AI-based object detection and classification. In this work, we investigate whether images generated wit…
Certified program synthesis (aka vericoding) is the process of automatically generating a program, its formal specification, and a machine-checkable proof of their alignment from a natural-language de…
We introduce two 2-categories which categorify the monodromic Hecke algebra. The first is algebraic in nature and generalizes Abe's theory of Soergel bimodules. The second is a diagrammatic category d…
Let $\mathrm{HK}_{\Theta}$ denote the Hecke-Kiselman monoid associated to a finite simple oriented graph $\Theta$. We reduce the problem of describing the endomorphism monoid $\mathrm{End}(\mathrm{HK}…
Under standard assumptions, we compute the GK-dimension of Hecke eigenspaces in the mod $p$ cohomology of an inner form $D^\times$ of $\mathrm{GL}_2$ over a totally real field unramified at $p$, allow…
On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and th…
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