相关论文: Relative character identities and theta correspond…

In this paper, we investigate three-term linear relations among theta series of positive-definite integral binary quadratic forms. We extend Schiemann's methods to characterize all possible three-term linear relations among theta series of…

Scattering transform is a well known powerful tool for quantisation of field theories in (1+1) dimensions. Conventionally only those models whose classical counterparts admit a Lax pair (origin of which is always mysterious) have been…

We verify the relative Langlands duality conjecture proposed by Ben-Zvi, Sakellaridis, Venkatesh for the hyperspherical Hamiltonian variety $T^*(\operatorname{Sp}_{2n}\backslash \operatorname{GL}_{2n+1})$. We provide numerical (over number…

The goal of this article and its precursor is to demonstrate, by example, the existence of "transfer operators" betweeen relative trace formulas, which generalize the scalar transfer factors of endoscopy. These transfer operators have all…

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. We generalize the Kudla-Millson relation between intersection numbers of cycles and Fourier coefficients of Siegel…

We investigate the Gross-Prasad conjecture and its refinement for the Bessel periods in the case of $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$. In particular, by combining several theta correspondences, we prove the…

We find identities between theta constants with rational characteristics evaluated at period matrix of $R,$ a cyclic 3 sheeted cover of the sphere with $3k$ branch points $\lambda_1...\lambda_{3k}.$ These identities follow from Thomae…

We check Sakellaridis-Venkatesh conjectures giving a description of the discrete spectrum of a spherical variety $\mathscr{X}=G/H$ in the Langlands-Arthur formalism when $G$ is a classical real group and $\mathscr{X}$ is a symmetric space.…

We study period relations of Jacobi forms. It turns out that the relations satisfied by Mordell integral coming from Lerch or Appell sums are the special case of those. The existence of Jacobi integral associated to given period function…

We describe the construction of vector valued modular forms transforming under a given congruence representation of the modular group SL(2,Z) in terms of theta series. We apply this general setup to obtain closed and easily computable…

We consider the time-dependent Hamiltonian $H(t)= {1 \over 2} p^2 -E(t) \cdot x + V(t,x)$ on $L^2(R^n)$, where the external electric field $E(t)$ and the short-range electric potential $V(t,x)$ are time-periodic with the same period. It is…

We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT) . To do this, we first study…

Transfer operators are conjectural "operators of functoriality," which transfer test measures and (relative) characters from one homogeneous space to another. In previous work, I computed transfer operators associated to spherical varieties…

The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint $\gamma$-factor of its $L$-parameter. In this paper, we…

The theory of almost characters which is closely related to character sheaves is proposed by Lusztig to study the representation theory of finite reductive groups. In this article we show that the decomposition of the Weil character for…

In this paper, we give a method for characterizing the local Langlands conjectures in the vein of Scholze's alternate proof of the local Langlands conjecture for $\mathrm{GL}_n$. More specifically, we show that if a local Langlands…

We give a new integral representation of the $\wedge^2 \otimes \mathrm{std}_2$ $L$-function of generic cusp forms on $\mathbf{GL}_4 \times \mathbf{GL}_2$ and $\mathbf{GU}_{2,2}\times \mathbf{GL}_2$. In the former case, we use it to prove a…

The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. The input in this construction is not a classical Lagrangian, but rather a prescribed…

The delay experienced by a probe due to interactions with a scattering media is highly related to the internal dynamics inside that media. This property is well captured by the Wigner delay time and the resonance widths. By the use of the…

We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…