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Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…

This PhD thesis focuses on local conformal nets of von Neumann algebras on the circle. For a more detailed description of its content and of the results published within, see its preface.

Cherednik's quantum affine Knizhnik-Zamolodchikov equations associated to an affine Hecke algebra module M form a holonomic system of q-difference equations acting on M-valued functions on a complex torus T. In this paper the quantum affine…

We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…

This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.

This paper has been withdrawn, as it has been merged into arXiv:1009.6144

This paper reviews advances in the understanding of quantum gravity based on field theory calculations in the AdS/CFT correspondence.

We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…

We define inclusive scattering matrix in the framework of geometric approach to quantum field theory . We review the definitions of scattering theory in the algebraic approach and relate them to the definitions in geometric approach.

Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…

In this note, we study possible $\mathcal{R}$-matrix constructions in the context of quiver Yangians and Yang-Baxter algebras. For generalized conifolds, we also discuss the relations between the quiver Yangians and some other Yangian…

We review the structures imposed on perturbative QFT by the fact that its Feynman diagrams provide Hopf and Lie algebras. We emphasize the role which the Hopf algebra plays in renormalization by providing the forest formulas. We exhibit how…

The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one…

By analyzing the decategorification of bordered sutured Heegaard Floer homology, we reinterpret and generalize the classical Frohman-Nicas TQFT for the Alexander polynomial in the setting of 3d sutured cobordisms between sutured surfaces.…

The quadratic embedding property of graphs consisting of three paths (theta graphs) is fully characterised. For this aim, a theorem by Winkler (1985) is utilized. An alternative proof of that result using the RKHS technique is presented.

This bundle contains the paper "Hermitian Morita Theory: a Matrix Approach", published in Irish Math. Soc. Bulletin 62 (2008), pp. 37-41 (reproduced with permission of the Irish Mathematical Society), and with abstract "In this note an…

We show that the inclusion of an affine Hecke algebra in its Schwartz completion induces an isomorphism on periodic cyclic homology.

Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.

The goal of this work is twofold: (i) to provide a detailed analysis of some categories of inductive graded ring - a concept introduced in [DM98] in order to provide a solution of Marshall's signature conjecture in the algebraic theory of…

We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version…