Mathematik in den Naturwissenschaften Leipzig Witten ’ s Volume Formula , Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions

für Mathematik in den Naturwissenschaften Leipzig Duality versus Dual Flatness in Quantum Information

We investigate questions in quantum information geometry which concern the existence and non-existence of dual and dually flat structures on stratified sets of density operators on finite-dimensional Hilbert spaces. We show that the set of density operators of a given rank admits dually flat connections for which one connection is complete if and only if this rank is maximal. We prove moreover ...

für Mathematik in den Naturwissenschaften Leipzig Dually Flat Manifolds and Global Information Geometry

Dually flat manifolds constitute fundamental mathematical objects of information geometry. This note establishes some facts on the global properties and topology of dually flat manifolds which, in particular, provide answers to questions and problems in global information geometry posed by Amari and Amari-Nagaoka.

Max - Planck - Institut für Mathematik in den Naturwissenschaften Leipzig Immunity space generated by a non trivial genetic - antigenic relation

für Mathematik in den Naturwissenschaften Leipzig Mathematics of CLIFFORD - A Maple package for

CLIFFORD performs various computations in Graßmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in C (B) the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. Two user-selectable algorithms for the Clifford product are implemented: cmulNUM based on Chevalley’s recursive formula, and cmulRS based on a non-recursive Rot...

MICHÈLE VERGNE Multiple Bernoulli Series and Volumes of Moduli Spaces of Flat Bundles over Surfaces

Using Szenes formula for multiple Bernoulli series, we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also multiple zeta values.