(PQ) MATHEMATICS

The research activities of the Group focus on:

- Regularity properties for the solutions of Partial Differential Equations and for the minimizers of some integral functionals of the Calculus of Variations;

- Functional Spaces and their applications in Probability and Statistics;

- Interpolation spaces and applications of the interpolation theory to PDE’s;

- Integral operators. 

• Graph theory and its applications
• Extreme graph theory
• Combinatorics
• Algorithms and data structures
• Computational complexity
• Discrete optimization (task scheduling)
• Discrete and computational geometry
• The theory of concurrency
• Stochastic networks and their reliability

APPLICATIONS OF ALGEBRO-GEOMETRIC TECHNIQUES: K-THEORY  IN REGULAR RINGS, C * -ALGEBRAS AND  LEAVITT PATH ALGEBRAS, THEORY OF LIE; ALGEBRAIC GEOMETRY, HOLOMORPHIC FOLIATIONS AND MODULAR CURVES.
FACTORIZATIONS IN NUMERICAL SEMIGROUPS AND AFFINE SEMIGROUPS.

-          new estimates of Shannon's entropy obtained from the known properties of superquadratic functions,

-          new estimates of the relative entropy derived from Jensen's inequality for superquadratic functions,

Central focus of the research of this group includes graph theory (with emphasis on extremal graph theory), complex networks (with emphasis on multiplexes, curriculum networks and network descriptors), mathematical chemistry (with emphasis on molecular descriptors, nanotechnology, peptide antibiotics), and discrete mathematics in general. Our goal is to obtain purely mathematical results and multidisciplinary applications.

Vertex operator algebras, infinite-dimensional Lie algebras and superalgebras, W-algebras, conformal field theory