Research Interests (as at April 2019)

Primary MSC

• 15A45 - Miscellaneous inequalities involving matrices
• 15A60 - Applications of functional analysis to matrix theory
• 15A63 - Quadratic and bilinear forms, inner products
• 15B48 - Positive matrices and their generalizations; cones of matrices
• 33C20 - Generalized hypergeometric series, pFq
• 33C45 - Orthogonal polynomials and functions of hypergeometric type
• 33C60 - Hypergeometric integrals and functions defined by them
• 33E20 - Functions defined by series and integrals
• 44A05 - General integral transforms
• 46N10 - Applications of functional analysis in optimization and programming
• 46N50 - Applications of functional analysis in quantum physics
• 47D07 - Markov semigroups of linear operators and applications to diffusion processes
• 52A20 - Convex sets in n dimensions (including convex hypersurfaces)
• 52A40 - Inequalities and extremum problems (convex geometry)
• 52B12 - Special polytopes (linear programming, centrally symmetric, etc.)
• 60A10 - Probabilistic measure theory
• 60E05 - General theory of probability distributions
• 60E10 - Transforms of probability distributions
• 60G07 - General theory of stochastic processes
• 60H05 - Stochastic integrals
• 60H30 - Applications of stochastic analysis (to PDE, etc.)
• 60G44 - Martingales with continuous parameter
• 60G46 - Martingales and classical analysis
• 60G48 - Generalizations of martingales
• 60G51 - Processes with independent increments; Lévy processes
• 60G57 - Random measures
• 62E10 - Characterization and structure theory of statistical distributions
• 62E15 - Exact distribution theory in statistics
• 62H05 - Characterization and structure theory (multivariate analysis)
• 62H10 - Multivariate distributions of statistics
• 62H99 - Multivariate analysis
• 81P05 - General and philosophical topics in quantum theory
• 81P15 - Quantum measurement theory
• 81P40 - Quantum coherence, entanglement, quantum correlations
• 81P45 - Quantum information, communication, networks
• 90C09 - Boolean programming
• 90C20 - Quadratic programming
• 90C22 - Semidefinite programming
• 90C25 - Convex programming
• 90C27 - Combinatorial optimization
• 94C10 - Switching theory, application of Boolean algebra; Boolean functions

Secondary MSC

• 05D40 - Probabilistic methods in combinatorics
• 42A61 - Probabilistic methods in Fourier analysis
• 46B07 - Local theory of Banach spaces
• 46B28 - Spaces of operators; tensor products; approximation properties
• 46G10 - Vector-valued measures and integration
• 46G12 - Measures and integration on abstract linear spaces
• 46L07 - Operator spaces and completely bounded maps
• 47L20 - Operator ideals
• 52A07 - Convex sets in topological vector spaces (convex geometry)
• 60C05 - Combinatorial probability
• 60E07 - Infinitely divisible distributions; stable distributions
• 60H07 - Stochastic calculus of variations and the Malliavin calculus
• 60J65 - Brownian motion
• 62A01 - Foundations and philosophical topics in statistics
• 68Q25 - Analysis of algorithms and problem complexity
• 81P68 - Quantum computation
• 90C35 - Programming involving graphs or networks
• 91G20 - Derivative securities
• 91G30 - Interest rates (stochastic models)
• 91G40 - Credit risk

Keywords Primary: Analysis of Boolean functions; Bell’s inequality; Bell’s theorem; CHSH inequality; elliptope; foundations of quantum mechanics; Gaussian measure; Grothendieck’s inequality; Grothendieck constant; Hadamard matrix; quantum information; measure theory; MAX-CUT; positive semidefinite; Schoenberg; SDP; semimartingales; special functions

Keywords Secondary: Geometry of Banach spaces; Malliavin calculus; mathematical finance; mathematical foundations of machine learning; operator algebras; operator ideals; operator spaces; POVMs; statistics of machine learning; stochastic volatility models; tensor norms; vector measures

Membership in Research Networks

• ResearchGate

Most Recent Research Related Activities

• Reviewer and External Specialist Editor for zbMath -> [Login]

Online Databases for Mathematical Research

• Zentralblatt MATH Database zbMath

• MathSciNet

• arXiv

• Numdam, the French digital mathematics library

• Table of contents for issues of Annales de l'Institut Henri Poincaré. Nouvelle série. Section B. Calcul des Probabilités et Statistique

Further Interests

• Differential Geometry
• Number Theory
• Cryptology (i.e., Cryptography and Cryptoanalysis)
[Many thanks to Peter Wagner for pointing this highly fascinating subject out to me!]