ERC Consolidator Grant · 2020
Refined invariants in combinatorics, low-dimensional topology and geometry of moduli spaces
Some invariants appearing in low-dimensional topology and algebraic geometry admit a so-called refinement: a much stronger, but more complicated invariant. For instance, in low-dimensional topology we study the Poincare polynomial of the triply-graded Khovanov-Rozansky homology of a knot, which is a refined version of the HOMFLY-PT polynomial. The usual Poincare polynomial and the E-polynomial of a character variety are refined by the full mixed Hodge polynomial. On the cohomology of a moduli space of Higgs bundles, we need an extra filtration, the so-called perverse filtration, to define the refinement. Where classical invariants produce polynomials in one variable q, and often have…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.