Related papers: Equidistribution theorems for holomorphic Siegel m…

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms,…

We consider a special theta lift $\theta(f)$ from cuspidal Siegel modular forms $f$ on $\mathrm{Sp}_4$ to "modular forms" $\theta(f)$ on $\mathrm{SO}(4,4)$. This lift can be considered an analogue of the Saito-Kurokawa lift, where now the…

We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer…

We prove a strong induction theorem for graded Hecke algebras and we classify the tempered and square integrable representations of such algebras using methods of equivariant homology.

We show that the systems of Hecke eigenvalues that appear in the coherent cohomology with coefficients in automorphic line bundles of any mod $p$ abelian type compact Shimura variety at hyperspecial level are the same as those appearing in…

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky group acting on $ {\mathbb H}^{n+1}$: in strips parallel to the imaginary axis the zeta function is bounded by $ \exp (C |s|^\delta) $ where $ \delta $…

We introduce a new class of higgs type complex-valued scalar fields $U$ with Feynman propagator $\sim 1/p^4$ and consider the matching to the traditional fields with propagator $\sim 1/p^2$ in the viewpoint of effective potentials at tree…

We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of non-holomorphic automorphic forms for GSp(4), contributing to coherent cohomology of Siegel threefolds in positive degrees. We…

We construct an Euler system attached to general-type cohomological cuspidal automorphic representations of $\mathrm{GSp}(4)$ twisted by a Groessencharacter of an imaginary quadratic field. We then use this to bound strict Selmer groups…

We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks $G$-Zip$^{\mu}$. Restricting to zip data of Hodge type, we obtain a group-theoretical Hasse invariant on every Ekedahl-Oort stratum…

We establish uniform bounds for the sup-norms of modular forms of arbitrary real weight $k$ with respect to a finite index subgroup $\Gamma$ of $\mathrm{SL}_2(\mathbb{Z})$. We also prove corresponding bounds for the supremum over a compact…

We derive explicit formulae for the subalgebra zeta functions of all higher Heisenberg Lie algebras over an arbitrary compact discrete valuation ring $\mathfrak{o}$. To this end, we develop Hecke-theoretic techniques for the enumeration, by…

For a paramodular group of any degree and square free level we study the Hecke algebra and the boundary components. We define paramodular theta series and show that for square free level and large enough weight they generate the space of…

We prove that one hundred percent of the closed geodesic periods of a Hecke--Maa{\ss} cusp form for the modular group are non-vanishing when ordered by length. We present applications to the non-vanishing of central values of…

Let $G$ be a split reductive group over a finite field $k$. In this note we study the space $V$ of finitely supported functions on the set of isomorphism classes $G$-bundles on the projective line ${\mathbb P}^1$ endowed with a…

We prove the weight part of Serre's conjecture for Galois representations valued in $\mathrm{GSp}_4$ that are tamely ramified with explicit genericity at places above $p$ as conjectured by Herzig--Tilouine and Gee--Herzig--Savitt. This…

In this paper we present an algorithm for computing Hecke eigensystems of Hilbert-Siegel cusp forms over real quadratic fields of narrow class number one. We give some illustrative examples using the quadratic field $\Q(\sqrt{5})$. In those…

In this technical note, we complete the PhD work of A. Esterle about determining the image of any Artin group of finite Coxeter type inside the associated Hecke algebra over a finite field, when the latter is semisimple. The only remaining…

We study the equivariant oriented cohomology ring $h_T(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott-Samelson classes in…

Let $K/F$ be a finite Galois extension of number fields. It is well known that the Tchebotarev density theorem implies that an irreducible, finitely ramified $p$-adic representation $\rho$ of the absolute Galois group of $K$ is determined…