Related papers: A relative trace formula identity for non-tempered…

We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild homology) of a dualizable object in the…

This paper establishes trace-formulae for a class of operators defined in terms of the functional calculus for the Laplace operator on divergence-free vector fields with relative and absolute boundary conditions on Lipschitz domains in…

For $E/F$ quadratic extension of local fields and $G$ a reductive algebraic group over $F$, the paper formulates a conjecture classifying irreducible admissible representations of $G(E)$ which carry a $G(F)$ invariant linear form, and the…

We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this…

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the…

This is the first of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of relative trace…

We consider time periodic Hamiltonians with complex potentials on the lattice and determine trace formulas. As a corollary we estimate eigenvalues of the quasienergy operator in terms of the norm of potentials.

We introduce the relativistic version of the well-known Henon's isochrone spherical models: static spherically symmetrical spacetimes in which all bounded trajectories are isochrone in Henon's sense, i.e., their radial periods do not depend…

In this paper we prove a version of Connes' trace theorem for noncommutative tori of any dimension~$n\geq 2$. This allows us to recover and improve earlier versions of this result in dimension $n=2$ and $n=4$ by Fathizadeh-Khalkhali. We…

Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a…

Using the heat kernel method, we compute nonrelativistic trace anomalies for Schr\"odinger theories in flat spacetime, with a generic background gauge field for the particle number symmetry, both for a free scalar and a free fermion. The…

We introduce and study fractional variable exponents Sobolev trace spaces on any open set in the Euclidean space equipped with the Lebesgue measure. We show that every equivalence class of Sobolev functions has a quasicontinuous…

We consider the case of scattering by several obstacles in $\mathbb{R}^d$ for $d \geq 2$. We establish a relative trace formula for Neumann and transmission boundary conditions analogous to the one obtained in arXiv:2002.07291 for Dirichlet…

For a smooth map between noetherian schemes, Verdier relates the top relative differentials of the map with the twisted inverse image functor `upper shriek'. We show that the associated traces for smooth proper maps can be rendered concrete…

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the…

The local non-tempered Gan-Gross-Prasad conjecture suggests that, for a pair of irreducible Arthur type representations of two successive general linear groups, they have a non-zero Rankin-Selberg period if and only if they are "relevant".…

We give an exposition of central value formulas for twisted L-functions for GL(2) in terms of compact periods, with a focus on explaining an approach via the relative trace formula and joint work of the author with David Whitehouse.

We propose a path integral formulation of noncommutative generalizations of spacetime manifold in even dimensions, characterized by a length scale $\lambda_P$. The commutative case is obtained in the limit $\lambda_P=0$.

In this paper, we focus on qualitative temporal sequences of topological information. We firstly consider the context of topological temporal sequences of length greater than 3 describing the evolution of regions at consecutive time points.…

We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov index of boundary data, and a Morse index theorem, equating…