Related papers: Collar lemma for Hitchin representations

In this expository article, we present a brief introduction to the theory of Hilbert modular forms and Galois representations, and describe what it means to attach a compatible system of Galois representations to a Hilbert modular form.

We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.

We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.

We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.

In this paper, we propose non-commutative analogues of infimum and supremum with the help of algebraic orthogonality.

The goal of this paper is to give an explicit description of the integrable structure of the Hitchin moduli spaces. This is done by introducing explicit parameterisations for the different strata of the Hitchin moduli spaces, and by…

We show that the theory of Lie algebra cohomology can be recast in a topological setting and that classical results, such as the Shapiro lemma and the van Est isomorphism, carry over to this augmented context.

We give integral presentations of quantum lattice Heisenberg algebras by viewing them as Heisenberg doubles. Our presentations generalize those appearing previously in the literature.

We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation…

In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.

We prove an analogue of Clifford's inequality for tropical curves. Next we focus on the hyperelliptic case and we characterize divisors attaining equality. Finally we speculate whether inequality in tropical Clifford's Theorem does imply…

In this paper we generalize the comparison theorem of Hecht and Taylor to arbitrary parabolic subalgebras of a complex reductive Lie algebra and then apply our generalized comparison theorem to obtain results about the geometric realization…

In this paper, we study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study oscillatory type integrals…

Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is: Homotopy coherence of representations, at one time known as strong homotopy representations. We…

We give a complete description of the representation of $SL(2,\mathbb{C})$ acting in the Hilbert space of the quantum Coulomb field and a constructive consistency proof of the axioms of the quantum theory of the Coulomb field.

We prove a variation of Gronwall's lemma.

We prove that a locally bounded and differentiable in the sense of Gateaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differentiable in the sense of Lorch.

Zalcman's Lemma makes significant applications in normal families, complex dynamics and related problems in complex analysis. In the present paper, we are devoted to generalizing the classical Zalcman's lemma to complex Lie groups by means…

This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.

In this paper we show that, for a class of countable graphs, every representation of the associated graph algebra in a separable Hilbert space is unitarily equivalent to a representation obtained via branching systems.