Related papers: The MacWilliams Theorem for Four-Dimensional Modul…
Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have…
We generalize the notion of ends and coends in category theory to the realm of module categories over finite tensor categories. We call this new concept "module (co)end". This tool allows us to give different proofs to several known results…
In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.
This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of…
The classical Chevalley-Weil theorem asserts that for an \'etale covering of projective varieties over a number field K, the discriminant of the field of definition of the fiber over a K-rational point is uniformly bounded. We obtain a…
This note presents Galois theory for finite fields. It was written as a handout for the MAT401 course ``Polynomial equations and fields'' taught at the University of Toronto in Spring 2026. We use without proofs some basic properties of…
The mds (maximum distance separable) conjecture claims that a nontrivial linear mds $[n,k]$ code over the finite field $GF(q)$ satisfies $n \leq (q + 1)$, except when $q$ is even and $k = 3$ or $k = q- 1$ in which case it satisfies $n \leq…
The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and…
Here we prove that Benford's law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessary asymptotics. This implies that the…
This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost…
In this paper, we establish a version of the large sieve with square moduli for imaginary quadratic extensions of rational function fields of odd characteristics.
This paper suggests an algebraic version of the theorem on the existence of eigenvectors for linear operators in abstract idempotent spaces. Earlier, the theorem on the existence of eigenvectors was only known for the cases of a free…
The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and…
We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.
In this paper, we have proved four theorems on the degree of approximation of continuous functions by matrix means of their Fourier series which is expressed in terms of the modulus of continuity and a non-negative mediate function.
This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
Recently M. Vuletic found a two-parameter generalization of the MacMahon's formula. In this note we show that certain ingredients of her formula have a clear interpretation in terms of the geometry of the moduli space of sheaves on the…
This paper considers the equivalence problem for quasi-cyclic codes over finite fields. The results obtained are used to construct isodual quasi-cyclic codes.
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…