Related papers: A Monomial Basis for the Holomorphic Functions on …

Using Jack polynomials, Goulden and Jackson have introduced a one parameter deformation $\tau_b$ of the generating series of bipartite maps, which generalizes the partition function of $\beta$-ensembles of random matrices. The Matching-Jack…

We study in detail the one-variable local theory of functions holomorphic over a finite-dimensional commutative associative unital $\mathbb{C}$-algebra $\mathcal{A}$, showing that it shares a multitude of features with the classical…

We construct motives over the rational numbers associated with symmetric power moments of Kloosterman sums, and prove that their L-functions extend meromorphically to the complex plane and satisfy a functional equation conjectured by…

In this paper, we continue to develop the theory of free holomorphic functions on noncommutative regular polydomains. We find analogues of several classical results from complex analysis such as Abel theorem, Hadamard formula, Cauchy…

We construct an infinite set of conserved tensor currents of rank $2n$, $n=1,2,\dots$, in the two-dimensional theory of free massive fermions, which are bilinear in the fermionic fields. The one-point functions of these currents on the…

In this paper we consider generalized monomial functions $f, g\colon \mathbb{F}\to \mathbb{C}$ (of possibly different degree) that also fulfill \[ f(P(x))= Q(g(x)) \qquad \left(x\in \mathbb{F}\right), \] where $P\in \mathbb{F}[x]$ and $Q\in…

In this paper we further investigate the geometry of monads of order-preserving functionals and of positively homogeneous functionals. We prove that for any compactum X with $w(X) = \tau$ the map $\mu_F X$, where $F\in\{O,OH\}$, is…

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal C)$) and in $l_2(\mathbb Z)$, which are related to each other by means of the Fourier transform and the…

Over a field $K$ of characteristic $p$, let $Z$ be the incidence variety in $\mathbb{P}^d \times (\mathbb{P}^d)^*$ and let $\mathcal{L}$ be the restriction to $Z$ of the line bundle $\mathcal{O}(-n-d) \boxtimes \mathcal{O}(n)$, where $n =…

In this paper we give a new proof of the Quantum Unique Ergodicity conjecture for holomorphic integral weight modular forms on the upper half plane. The proof requires only partial results towards the Ramanujan conjecture and the shifted…

The holomorphic torsion of a hermitian locally symmetric space is expressed as a special value of a geometric zeta function.

Exploiting symmetry in Groebner basis computations is difficult when the symmetry takes the form of a group acting by automorphisms on monomials in finitely many variables. This is largely due to the fact that the group elements, being…

We show that discrete exponentials form a basis of discrete holomorphic functions. On a convex, the discrete polynomials form a basis as well.

We conjecture an evaluation of three-partition cyclic Hodge integrals in terms of loop Schur functions. Our formula implies the orbifold Gromov-Witten/Donaldson-Thomas correspondence for toric Calabi-Yau threefolds with transverse type A…

A Rota-Baxter operator defined on the polynomial algebra is called monomial if it maps each monomial to a monomial with some coefficient. We classify monomial Rota-Baxter operators defined on the algebra of polynomials in one variable…

Let $f(z,w)=(p(z),q(z,w))$ be a holomorphic skew product with a superattracting fixed point at the origin. Under one or two assumptions, we prove that $f$ is conjugate to a monomial map on an invariant open set whose closure contains the…

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal…

The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli space of stable curves. The asymptotics…

For every stable presentably symmetric monoidal $\infty$-category $\mathcal{C}$ we use the Koszul duality between the spectral Lie operad and the cocommutative cooperad to construct an enveloping Hopf algebra functor $\mathcal{U}:…

In this paper, we introduce two (anti)homomorphisms that preserve the Haar state values of monomials. Together with the modular automorphism, the three (anti)homomorphisms are used in our new algorithm to compute the Haar states of…