Schedule, Titles and Abstracts

Enumerative Day Thu Feb 2

Location: Arts Building Lecture Room 7 (223)

13:30 - 14:30: Cristina Manolache, Desingularisation of sheaves and reduced Gromov--Witten invariants
Given a sheaf on an irreducible scheme, I will present a classical construction by Rossi, which produces a "desingularisation" of the sheaf. I will use this construction to define reduced Gromov--Witten invariants. This is work in progress with A. Cobos-Rabano, E. Mann and R. Picciotto.

14:30 - 15:15: Coffee & Tea at Maths Learning Centre, 1st floor, Watson Building 

15:15 - 16:15: Sabrina Pauli, Quadratically Refined Enumerative Geometry
TBA 

16:30 - 17:30: Ben Davison, Nonabelian Hodge theory for stacks
The nonabelian hodge isomorphism provides a homeomorphism of underlying topological (analytic) spaces between the moduli space of semistable Higgs bundles on a smooth projective curve and the moduli space of representations of the fundamental group of the curve. In particular, whatever your favourite topological invariant is, it is the same for these two moduli spaces.

Passing to the stacks of semistable Higgs bundles and representations of the fundamental group, we no longer have such a homeomorphism.  I will explain how it is possible nonetheless to show that these stacks have isomorphic Borel-Moore homology, by showing that they have isomorphic BPS cohomology, by relating this BPS cohomology to intersection cohomology of the coarse moduli spaces on both sides.

17:30: Reception at Maths Learning Centre, 1st floor, Watson Building 

Mirror Day Fri Feb 3

Location: Arts Building Lecture Room 2 (126)

10:10 - 11:10: Mark Gross, Intrinsic Mirror Symmetry
TBA 

11:30 - 12:30: Tim Gräfnitz, Mirror symmetry for (P2,E) and tropical geometry
Mirror symmetry relates curve counts (A-side) of a CY variety or log CY pair with deformations of complex structures (B-side) of the mirror. I explain how for (P2,E) both sides can be understood via tropical curves on the dual intersection complex of a toric degeneration, scattering diagrams and broken lines.

14:00 - 15:00: Michel van Garrel, The Prism of Intrinsic Mirror Symmetry
In mirror symmetry as for vinyl records, there are two sides, an A-side and a B-side. Unlike vinyl records though, both sides are supposed to be equivalent. This correspondence is usually proven through the computation of each side, which limits the scope of results. Intrinsic Mirror Symmetry by Gross and Siebert changes the game. The full enumerative invariants of the A-side construct the B-side. This is the mirror construction. Then the mirror theorem becomes a prism (period integrals) applied to the B-side in order to recover specific enumerative invariants of the A-side. In joint work with Ruddat and Siebert, we show how this works for log Calabi-Yau varieties with smooth boundary, such as Fanos with smooth anticanonical divisor.