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