Related papers: Fermionic form and Betti numbers
We review various aspects of a fermionic gauge symmetry, known as the $\kappa$--symmetry, which plays an important role in formulations of superstrings, supermembranes and higher dimensional extended objects. We also review some aspects of…
In this paper we study some algebraic properties of hypergraphs, in particula their Betti numbers. We define some different types of complete hypergraphs, which to the best of our knowledge, are not previously considered in the literature.…
We prove a conjecture due to Kimoto and Wakayama from 2006 concerning Apery-like numbers associated to a special value of a spectral zeta function. Our proof uses hypergeometric series and p-adic analysis.
We present the lattice models with exact fermionic symmetries relating fermions and link variables. The plaquettes are distributed in an Ichimatsu pattern (chequered). We explain this peculiar structure allows us to have a translation in…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
We study the connection between stringy Betti numbers of Gorenstein toric varieties and the generating functions of the Ehrhart polynomials of certain polyhedral regions. We use this point of view to give counterexamples to Hibi's…
This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out…
We use the method of Bruinier--Raum to show that symmetric formal Fourier--Jacobi series, in the cases of norm-Euclidean imaginary quadratic fields, are Hermitian modular forms. Consequently, combining a theorem of Yifeng Liu, we deduce…
This mostly expository paper centers on recently proved conjectures in two areas: A) A conjecture of A. Oppenheim on the values of real indefinite quadratic forms at integral points. B) Conjectures of Dani, Raghunathan, and Margulis on…
We prove a conjecture by Tu, Zeng, Li, and Helleseth concerning trinomials $f_{\alpha,\beta}(x)= x + \alpha x^{q(q-1)+1} + \beta x^{2(q-1)+1} \in \mathbb{F}_{q^2}[x]$, $\alpha\beta \neq 0$, $q$ even, characterizing all the pairs…
We reexamine the connection between spin and statistics through the quantization of a complex scalar field, using the formulation with the property that the hermitian conjugate of canonical momentum for a variable is just the canonical…
A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence…
We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
In [J14], a conjecture was proposed on a relation between the global Arthur parameters and the structure of Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. In this paper, we discuss the…
A gauge-invariant reformulation of QCD in three spacetime dimensions is presented within a Hamiltonian formalism, extending previous work to include fermion fields in the adjoint and fundamental representations. A priori there are several…
We prove the Mumford-Tate conjecture for those abelian varieties over number fields, whose simple factors of their adjoint Mumford-Tate groups have over $\dbR$ certain (products of) non-compact factors. In particular, we prove this…
In this paper, we present a formulation of the classical theory of Fermionic (anticommuting) fields, which fits into the general framework proposed by K.Fredenhagen, M.Duetsch and R.Brunetti. It was inspired by the recent developments in…
Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or…