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876+ open-access research outputs.
In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.…
Let $G$ be a finite connected simple graph with a chosen orientation of its edges. For the edge potential $\psi(t)=\cosh t-1,$ we minimize $\sum_{e\in E^\to}\psi(z_e)$ over each affine class $\omega+d…
We introduce a Hybrid High-Order (HHO) method for the Schr\"odinger equation in the presence of a magnetic vector potential. In quantum mechanics, physical observables are invariant under continuous g…
We present a short proof, based on local character expansions, of the celebrated theorem of Harish-Chandra about local integrability of complex characters of $p$-adic reductive groups. The proof gives…
For the weighted Dirac eigenvalue problem, we show that the two-sided weighted spectrum depends continuously on the weight under continuous deformations within a uniformly elliptic class. Moreover, fo…
In 1970, Gelfand posed the problem of classifying the indecomposable objects in a representation category equivalent to the principal block of Harish-Chandra modules for $\mathsf{SL}_2(\mathbb{R})$; e…
In this paper, we answer the question posed by Goodwin and R\"ohrle for reductive groups and their parabolic subgroups. In addition, we consider an additive analogue of this problem. By studying this …
This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e,…
In a remarkable paper, Tatsuyuki Hikita settled a longstanding e-positivity conjecture of Stanley and Stembridge. Among many other things, he wrote down a certain formula ${\varphi}_k$, and proved tha…
We study the residual Eisenstein cohomology of semisimple groups in the context of maximal parabolic subgroups which remain maximal over $\mathbb{R}$. Under certain general hypotheses, we show that th…
The Alon-Tarsi number of a graph $ G $ is the smallest $ k $ such that there exists an orientation $ D $ of $ G $ with maximum outdegree $ k - 1 $ satisfying that the number of even Eulerian subgraphs…
For any irreducible Harish-Chandra module $V$ over the gap-$p$ Virasoro algebra, we determine the condition for $V$ to be unitary.…
Let $D(G)$ be the algebra of algebraic differential operators on a complex reductive group $G$. Denote by $\mathbb{W}$ the bi-Whittaker quantum Hamiltonian reduction of $D(G)$, also known as the quant…
We prove that the Hilbert scheme of the plane in positive characteristic admits an invertible top differential form. This implies certain integrability properties of the symmetric powers of the plan…
We prove that the character of an irreducible cuspidal representation of $GL_n(\mathbb{F}_{\ell}((t)))$ is locally bounded up to a logarithmic factor by the orbital integral of a matrix coefficient of…
The celebrated Harish-Chandra's integrability theorem states that the distributional character of an irreducible smooth representation of a p-adic group $G(F)$ is integrable, that is represented by an…
We prove dimension bounds on the jet schemes of the variety of nilpotent matrices (and of related varieties) in positive characteristic. This result has applications to the analytic properties of th…
This paper studies a flat degeneration P_n of the classical coinvariant algebra R_n, a bigraded Artinian Gorenstein algebra that arises from the coordinate ring of the Segre embedding of the n-fold se…
In this paper we prove that a recent condition of Lyons--Mart\'inez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for all finite simple gr…
The exponential equidistribution speed of iterated preimages for holomorphic endomorphisms on $\mathbb{P}^k$ was established by Drasin-Okuyama for $k=1$, and by Dinh-Sibony for arbitrary $k$. In this …
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