Related papers: Singularities and vanishing cycles in number theor…

The classification of simple biset functors is known, but the evaluation of a simple biset functor at a finite group G may be zero. We investigate various situations where this happens, as well as cases where this does not occur. We also…

We continue our study of the Hodge theory of degenerations, Part I of which covered consequences of the Decomposition Theorem and Part II of which concerned geometric applications in the isolated singularity case. The focus here in Part III…

Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…

We prove the Kawamata-Viehweg vanishing theorem for a large class of divisors on surfaces in positive characteristic. By using this vanishing theorem, Reider-type theorems and extension theorems of morphisms for normal surfaces are…

The effective field theory approach to high temperature field theory can be used to study the phase transition in theories with spontaneously broken symmetry. I construct a sequence of two effective three--dimensional field theories which…

Using the dilaton theorem, we show that the classical action of closed string field theory vanishes on-shell.

The theory of nucleation with depletion zones is discussed. The approach of stochastic effects of solitary droplet is analyzed. The negative features of a solution with fixed boundary are outlined. A new solution with effective fixed…

There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave…

We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient…

We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.

We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to two-loop integrals involving several mass…

A method of constructing an entire function with given zeros and estimates of growth is suggested. It gives a possibility to describe zero sets of certain classes of entire functions of one and several variables in terms of growth of volume…

It is discussed how a limiting procedure of (super)conformal field theories may result in logarithmic (super)conformal field theories. The construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field…

We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…

This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…

Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…

We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic…

The theory of quadratic forms and class numbers has connections to many classical problems in number theory. Recently, class numbers have appeared in the study of black holes in string theory. We describe this connection and raise questions…

The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one…

After a brief overview of the so-called silent models and their present status, we consider the subclass of Bianchi Type--I models with a magnetic field source. Due to the presence of the magnetic field, the initial singularity shows…