Related papers: Sparse Modular Forms, Lattices, and Codes
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
Scale invariance (SI) can in principle be realized in the elastic response of solid materials. There are two basic options: that SI is a manifest symmetry or that it is spontaneously broken. The manifest case corresponds physically to the…
A recently introduced one-dimensional two-particle Bose-Hubbard model with a single impurity is studied on finite lattices. The model possesses a discrete reflection symmetry and we demonstrate that all eigenstates odd under this symmetry…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…
Lattices and Z-modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar images according to their indices for certain 4D examples that are…
Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly…
We present a coherent and effective theoretical framework to systematically construct numerically exact nonlinear solitary waves from their respective linear limits. First, all possible linear degenerate sets are classified for a harmonic…
We define a new construct in quantum field theory - the causal density matrix - obtained from the singularity structure of correlators of local operators. This object provides a necessary and sufficient condition for a quantum field theory…
Motivated by recent experimental and theoretical results on optical X-waves, we propose a new type of waveforms in 2D and 3D discrete media -- multi-legged extended nonlinear structures (ENS), built as arrays of lattice solitons (tiles or…
We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We…
In this thesis, we investigate the low-energy expansion of scattering amplitudes of closed strings at one-loop level (i.e. at genus one) in a ten-dimensional Minkowski background using a special class of functions called modular graph…
We describe odd-length-cube tilings of the n-dimensional q-ary torus what includes q-periodic integer lattice tilings of R^n. In the language of coding theory these tilings correspond to perfect codes with respect to the maximum metric. A…
In this paper we deal with Drinfeld modular forms, defined and taking values in complete fields of positive characteristic. Our aim is to study a sequence of families of Drinfeld modular forms depending on a parameter t that produces, for…
We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms…
A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…
Studies of strong gravitational lensing in current and upcoming wide and deep photometric surveys, and of stellar kinematics from (integral-field) spectroscopy at increasing redshifts, promise to provide valuable constraints on galaxy…
In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC…
We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions…
By the theory of Eisenstein series, generating functions of various divisor functions arise as modular forms. It is natural to ask whether further divisor functions arise systematically in the theory of mock modular forms. We establish,…
We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces $F \sim r^{-\beta}$. The inverse-cube case corresponds to Calogero-Moser systems, which are well known to be…