Related papers: Good Towers of Function Fields
We discuss the applicability of classical control theory to problems in smart grids and smart cities. We use tools from iterated function systems to identify controllers with desirable properties. In particular, controllers are identified…
We establish a general Kronecker limit formula of arbitrary rank over global function fields with Drinfeld period domains playing the role of upper-half plane. The Drinfeld-Siegel units come up as equal characteristic modular forms…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
This work is a survey of relations between Drinfeld modules and higher dimensional fields of positive characteristic. The main new result stated is the expression of vanishing orders of certain modular forms through partial zeta values.
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
In this note we study the weak topology on paired modules over a (not necessarily commutative) ground ring. Over QF rings we are able to recover most of the well known properties of this topology in the case of commutative base fields. The…
False theta functions are functions that are closely related to classical theta functions and mock theta functions. In this paper, we study their modular properties at all ranks by forming modular completions analogous to modular…
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common…
Effective field theory methods provide a convenient approach to study static observables in field theory at finite temperature. In this talk, I will outline the construction of the effective field theory that describes effective observables…
This is a survey on Anderson t-motives -- high-dimensional generalizations of Drinfeld modules. They are the functional field analogs of abelian varieties with multiplication by an imaginary quadratic field. We describe their lattices,…
The dynamical properties of the gauge theory of Born-Infeld type action, which is expected as the high-energy effective theory, are investigated by adding a complex scalar field to this gauge system. Especially the Coleman-Weinberg…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
The genus of projective curves discretely separates decidedly different two variable algebraic relations. So, we can focus on the connected moduli M_g of genus g curves. Yet, modern applications require a data variable (function) on such…
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
Non equilibrium effective field theory is presented as an inhomogeneous field theory, using a formulation which is analogous to that of a gauge theory. This formulation underlines the importance of structural aspects of non-equilibrium,…
We present novel algorithms to factor polynomials over a finite field $\F_q$ of odd characteristic using rank $2$ Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial…
In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…
We discuss the role effective field theory plays in making predictions in nuclear physics in an approach that combines both the high sophistication of the standard nuclear many-body approach and the power of systematic higher chiral-order…