Seminars this semester


   Series:


Oct 17 Tue Alexander Vishik (Nottingham)
14:00 J11 Subtle Stiefel-Whitney classes
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Oct 18 Wed Thomas Prince (Imperial)
15:00 J11 From period integrals to toric degenerations of Fano manifolds
 
  Abstract:
Given a Fano manifold we will consider two ways of attaching a (usually infinite) collection of polytopes, and a certain combinatorial transformation relating them, to it. The first is via Mirror Symmetry, following a proposal of Coates-Corti-Kasprzyk-Galkin-Golyshev. The second is via symplectic topology, and comes from considering degenerating Lagrangian torus fibrations. We then relate these two collections using the Gross--Siebert program. I will also comment on the situation in higher dimensions, noting particularly that by 'inverting' the second method (degenerating Lagrangian fibrations) we can produce topological constructions of Fano threefolds.
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Oct 24 Tue Pierrick Bousseau (Imperial)
14:00 J11 Quantum mirrors of log Calabi-Yau surfaces
 
  Abstract:
I will start describing the Gross-Hacking-Keel realization of mirror symmetry for log Calabi-Yau surfaces: the mirror variety is constructed by gluing elementary pieces together according to some gluing functions determined by counting rational curves in the original variety. I will then explain how to construct non-commutative deformations of these mirrors by including contributions of counts of higher genus curves in the original variety.
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Nov 7 Tue Soheyla Feyzbakhsh (Edinburgh)
14:00 J11 Reconstructing a K3 surface from a curve via wall-crossing
 
  Abstract:
In 1997, Mukai introduced a geometric program to reconstruct a K3 surface from a curve on that surface. The idea is to first consider a Brill-Noether locus of vector bundles on the curve. Then the K3 surface containing the curve can be obtained uniquely as a Fourier-Mukai partner of the Brill-Noether locus. Mukai carried out this program for curves of genus 11. I will explain how wall-crossing with respect to Bridgeland stability conditions implies that the Mukai's strategy works for curves of higher genera.
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Nov 21 Tue Davide Masoero (Lisbon)
14:00 J11 The isomonodromic deformation method for Painleve I and meromorphic functions with 5 transcendental singularities
 
  Abstract:
I will introduce the isomonodromic deformation method for Painleve I and the corresponding Riemann-Hilbert problem in term of Stokes multipliers. I will then use a theory due to R. Nevanlinna, [Ueber Riemannsche Flaechen mit endlich vielen Windungspunkten, Acta Math 1932] to give an alternative construction of the monodromy manifold, and a proof of the surjectivity of the monodromy map. Finally, I will comment on some applications of the same method to other Painleve equations: in particular, I will show how to compute the numer of real roots of the rational solutions of the fourth Painleve equations.
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Nov 28 Tue Emilie Dufresne (Nottingham)
14:00 J11 TBA
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Dec 5 Tue Gregory Stevenson (Glasgow)
14:00 J11 A^1-homotopy invariants of singularity categories
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Dec 12 Tue Marta Mazzocco (Loughborough)
14:00 J11 TBA
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