The description of the space of commuting elements in a compact Lie group is an interesting algebro-geometric problem with applications in Mathematical Physics, notably in Supersymmetric Yang Mills theories.

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In this talk I will discuss some problems related to the classification of some equivariant topological invariants of compact symplectic manifolds with a Hamiltonian circle action...

In a moduli space, usually, we impose a notion of stability for the objects and, when constructing the moduli space by using Geometric Invariant Theory, another notion of GIT stability appears, showing during the construction of the moduli that both notions do coincide at the stable and semistable level.

he moduli space of surfaces of general type with fixed numerical invariants is an intricate object. For most choices of invariants it has many irreducible components and it is not pure dimensional.  

I will describe a construction of symplectic manifolds diffeomorphic to T^* S^n, but with symplectic structure different from the canonical one.

There is (almost) no information available on the literature about complex algebraic surfaces of general type with geometric genus $p_g=0,$ self-intersection of the canonical divisor $K^2=3$ and with $5$-torsion.

Joint work with: Sami Dakhlia (Department of Economics and Finance, College ...

TBA