Related papers: Fake Z
Baer's Criterion of injectivity implies that injectivity of a module is a factorization property w.r.t. a single monomorphism. Using the notion of a cotorsion pair, we study generalizations and dualizations of factorization properties in…
Satisfiability Modulo Theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulas. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of polynomial constraints.…
We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both…
We revisit the consistency of torus partition functions in (1+1)$d$ fermionic conformal field theories, combining traditional ingredients of modular invariance/covariance with a modernized understanding of bosonization/fermionization…
In this article, using key tools including Zhou valuations, Tian functions and a convergence result for relative types, we establish necessary and sufficient conditions for the existence of valuative interpolations on the rings of germs of…
Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, which use tools from the topology of real manifolds. Simpler proofs were discovered in the new century, of the Hilbert Nullstellensatz, and the…
The well-known modular property of the torus characters and torus partition functions of (rational) vertex operator algebras (VOAs) and 2d conformal field theories (CFTs) has been an invaluable tool for studying this class of theories. In…
Modular graph functions are $SL(2,{\mathbb Z})$-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus $\tau$. For one-loop graphs they reduce to real analytic Eisenstein series.…
An efficient randomized polynomial identity test for noncommutative polynomials given by noncommutative arithmetic circuits remains an open problem. The main bottleneck to applying known techniques is that a noncommutative circuit of size…
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory…
In this paper we consider self-dual NRT-codes, that is, self-dual codes in the metric space endowed with the Niederreiter-Rosenbloom-Tsfasman (NRT-metric). We use polynomial invariant theory to describe the shape enumerator of a binary…
We generalize a number of works on the zeros of certain level 1 modular forms to a class of weakly holomorphic modular functions whose $q$-expansions satisfy \[ f_k(A, \tau) \colon = q^{-k}(1+a(1)q+a(2)q^2+...) + O(q),\] where $a(n)$ are…
We overview numerous algorithms in computational $D$-module theory together with the theoretical background as well as the implementation in the computer algebra system \textsc{Singular}. We discuss new approaches to the computation of…
We review the physical meaning of modular invariance for unitary conformal quantum field theories in d=2. For QFT models, while T invariance is necessary for locality, S invariance is not mandatory. S invariance is a form of completeness of…
In 2007, G.E. Andrews introduced the $(n+1)$-variable combinatorial generating function $R_n(x_1,x_2,\cdots,x_n;q)$ for ranks of $n$-marked Durfee symbols, an $(n+1)$-dimensional multisum, as a vast generalization to the ordinary…
We review 2d CFT in the bootstrap approach, and sketch the known exactly solvable CFTs with no extended chiral symmetry: Liouville theory, (generalized) minimal models, limits thereof, and loop CFTs, including the $O(n)$, Potts and $PSU(n)$…
This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first consider a robust reconstruction problem for polynomials from erroneous residues when the degrees of all residue errors are assumed small, namely…
We consider a lattice $\mathcal{L}\subset \mathbb{R}^n$ and a trigonometric potential $V$ with frequencies $k\in\mathcal{L}$. We then prove a strong integrability condition on $V$, using the support of its Fourrier transform. We then use…
In this paper we study deformations of mod $p$ Galois representations $\tau$ (over an imaginary quadratic field $F$) of dimension $2$ whose semi-simplification is the direct sum of two characters $\tau_1$ and $\tau_2$. As opposed to our…
Planar functions over finite fields give rise to finite projective planes and other combinatorial objects. They exist only in odd characteristic, but recently Zhou introduced an even characteristic analogue which has similar applications.…