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

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

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

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

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

| Stable and unstable homotopy theory; Homotopy theory of Madsen-Tillman spectra; Curtis-Madsen conjecture on the type of spherical classes in homology of |

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

| 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 |

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

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

| Bifurcation; Partial stabilization and applications |

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

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

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

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

| Neurodynamical optimization; Numerical methods in linear algebra |

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

| Operator algebras and frame theory |