Related papers: Polyfold and Fredholm Theory
Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman…
A cohomology theory for lambda-rings is developed. This is then applied to study deformations of lambda-rings.
This is a series of lecture notes explaining topos theory and its application in physics.
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
A (biased and incomplete) review of the status of the theory of symplectic connections on supermanifolds is presented. Also, some comments regarding Fedosov's technique of quantization are made.
A review of the inverse scattering transform is given, and an introduction to solitons is provided.
This is a copy of the article published in Math Res. Letters 5, (1998) 497-516.
Works on the Dyadosphere are reviewed.
This is a series of lectures on M Theory for cosmologists. After summarizing some of the main properties of M Theory and its dualities I show how it can be used to address various fundamental and phenomenological issues in cosmology.
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static…
The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of products of two simplices. Applications…
This paper focuses on determining the volumes of permutation polytopes associated to cyclic groups, dihedral groups, groups of automorphisms of tree graphs, and Frobenius groups. We do this through the use of triangulations and the…
This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem…
This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…
In this report I discuss the relations between systoles and volumes of hyperbolic manifolds and a conjecture of Lehmer about the Mahler measure of non-cyclotomic polynomials.