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Two-year research plan (2016-2018) Department of Mathematics

 

Two-year research plan (2016-2018) / Department of Mathematics

Abstract harmonic analysis

Amenability of groups and semigroups; Fourier and Fourier-Stieltjes algebras

Algebraic geometry

Semigroup (Toric) algebras; Homology theory; Topology of algebraic plane curves; Combinatorial algebraic geometry (excess number of ideals)

Algebraic hyperstructures

Hypergroups, hyperrings, hypermodules, with application in geometry, graph theory, combinatorics, and fuzzy set theory

Algebraic topology

Stable and unstable homotopy theory; Homotopy theory of Madsen-Tillman spectra; Curtis-Madsen conjecture on the type of spherical classes in homology of QS0; Hit problem over Steenrod algebra

Analysis and topological dynamics

Ergodic theory; Transformation groups; Dynamical systems (topological); General topology; Chaos; Generalized shifts; Interaction between algebras of continuous maps and continuous group actions

Combinatorics

Alexander duality for multigraded modules; Associated radical ideals of monomial ideals; Characterization of Cohen-Macaulay simplicial complexes; Combinatorics of graphs, designs and codes; Geometric combinatorics and commutative algebra

Commutative algebra

Combinatorial and computational commutative algebra; Algebraic statistics; Cellularity of transversal monomial ideals; Algebraic K-theory; Representation theory of algebras

Differential Geometry

Riemannian, semi- and sub-Riemannian geometries; Applications to: game theory, economics, geometric mechanics and control

Dynamical systems and control theory

Bifurcation; Partial stabilization and applications

Functional analysis

Amenability of Banach algebras; - and -algebras; Hilbert -modules

Group theory and generalizations

Finite groups, their characters and numerical characterization; Finite fields and their applications on simple groups of Lie type

Linear and multilinear algebra; matrix theory

Numerical linear algebra; Applications of functional analysis to matrix theory (numerical ranges)

Number theory

Effective methods for solving Diophantine equations, e.g. Thue equations; Integral points on elliptic curves

Numerical analysis

Neurodynamical optimization; Numerical methods in linear algebra

Operations research and optimization (ORO), mathematical programming

Vector optimization; Nonsmooth optimization; Linear and nonlinear programming; Applied ORO

Operator theory

Operator algebras and frame theory