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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Algebraic Geometry


Algebraic group actions, moduli problems, toric geometry, surfaces and higher dimensional algebraic varieties, affine geometry, secant varieties, Hilbert schemes, geometry over fields of positive characteristic, relations to algebraic topology.



  • Algebraic group actions and quotients
  • Curves on surfaces, deformations of curves singularities, connections with knot theory, lattice homology
  • Toric geometry, secant varieties, rank of tensors
  • Secantt varieties, ranks of tensors and polynomials, Hilbert schemes, actions of groups on varities, toric geometry, Mori Dream spaces and Cox rings, complex contact manifolds
  • Cox rings, resolution of singularities, hyperkaehler manifolds, combinatorial algebraic geometry
  • Finite schemes, Hilbert chemes, tropical geometry
  • Toric geometry, G-Hilbert schemes, quiver representations
  • Moduli spaces, surfaces and higher dimensional varieties, algebraic geometry over fields of positive characteristic
  • Complex algebraic geometry, non-commutative geometry
  • Topology of algebraic varieties: intersection cohomology, weight filtration, equivariant cohomology, Thom polynomials and equivariant characteristic classes of singularities
  • Fano manifolds, varieties with group actions.
  • Jacobian conjecture, connections of ODE's with algebraic geometry.