Date: 24  27 Aug 2015
Venue: Western Gateway Building, UCC
Theme 6 talks will take place in room G04 of Western Gateway Building. All plenary talks will be in room 107. Talks by Theme 4 invited speakers will take place in room G02.
Monday 24th August:
08:5009:00  Opening 
09:00  10:00 room G04 
Alessio Corti  Mirror Symmetry and Fano Orbifolds Abstract: I discuss results and conjectures on mirror symmetry for Fano orbifolds and applications to the classification of Fano orbifolds, with special emphasis on the case of surfaces. 
10:00  10:30  Coffee & Tea 
10:30  11:30 room G04 
Ionuț CiocanFontanine Wallcrossing in quasimap theory
Abstract: Quasimap theory is concerned with curve counting on certain GIT quotients. In fact, one has a family of curve counting theories, depending on the linearization in the GIT problem. It may be viewed as one possible mathematical incarnation of the GLSM in the geometric phases  the linearization is the FI parameter of the GLSM. I will present a wallcrossing formula at the level of virtual classes (in all genera) as the size of the linearization changes, as well as some of its numerical consequences. This is joint work with Bumsig Kim.

11:30  12:30 room G04 
Andrew Morrison  Motivic classes of generalized Kummer schemes via relative power structures Abstract: We describe the cohomology of moduli spaces of points on schemes over Abelian varieties and give explicit calculations for schemes in dimensions less that three. The construction of Gulbrandsen allows one to consider virtual motives in dimension three. In particular we see a new proof of his conjectures on the Euler numbers of generalized Kummer schemes recently proven by Shen. Joint work with Junliang Shen. 
12.30  14.00  Lunch 
14.00  15.00 room G04 
Sven Meinhardt 
About the nature of DonaldsonThomas invariants for quivers with potential Abstract: The aim of the talk is to show how DonaldsonThomas sheaves are related to intersection complexes of quiver moduli spaces and vanishing cycle functors. In particular, DonaldsonThomas theory can be used to provide an easy (recursive) algorithm to compute the intersection cohomology of quiver moduli spaces. This result has been obtained in a joint work with Ben Davison and Markus Reineke. 
15.00  16.00 room G04 
Gregory Sankaran 
Homotopy invariants of toroidal compactifications Abstract: I will describe recent and less recent work of several people (mostly other people) on the behaviour of basic topological invariants, such as cohomology and the fundamental group, for moduli spaces compactified by toroidal methods.

16.00  16.30  Coffee & Tea 
16.30  17.30 room 107 
Martin J. Lindsay  Plenary talk KMSSymmetry and quantum Markov semigroups 
Tuesday 25th August:
09.00  10.00 room G04 
Sergey Mozgovoy  Refined curve counting on some local 3CY varieties
I will discuss refined DonaldsonThomas and PandharipandeThomas invariants of the 3CY varieties associated to some surfaces. The surfaces under consideration are minimal resolutions of Kleinian singularities. I will show how the problem can be reduced to counting representations of some quivers with superpotentials or counting representations of preprojective algebras. Then I will show how the latter problem is solved. 
10.00  10.30  Coffee & Tea 
10.30  11.30 room G04 
Barbara Fantechi  On the rigidity of moduli stacks of pointed curves and of their coarse moduli spaces. Abstract: Paul Hacking proved that the moduli stacks of complex pointed stable curves are rigid. Jointly with Alex Massarenti we try and extend this result to fields of arbitrary characteristic, and apply the results to studying automorphisms groups. We also study deformations of their coarse moduli spaces. 
11.30  12.30 room G04 
YuanPin Lee  GromovWitten theory and variation of Hodge structure under conifold transitions for CalabiYau threefolds. Abstract: The moduli of CalabiYau threefolds are generally believed to be connected by a geometric process called transition, which is roughly speaking degeneration followed by small resolution. In this talk, I will explain a phenomenon of partial exchange of A model (GromovWitten theory) and B model (variation of Hodge structure) when a CalabiYau threefold undergoes a conifold transition. This suggests a possibility of an "A+B theory" which is invariant under transitions.
This talk is based on joint work with H.W. Lin and C.L. Wang. 
12.30  14.00  Lunch 
14.00  15.00 room G04 
Felix Janda A formula for the double ramification cycle
Abstract: In the cohomology of the moduli space of smooth curves it is natural to consider the class of the locus of curves admitting a map to the projective line with specified ramification at zero and infinity. The double ramification cycle is an extension of this class to the DeligneMumford compactification of stable curves. Recently, generalizing work of Hain, Pixton has given a conjectural formula for the double ramification cycle in terms of tautological generators. We will present a proof of this formula. 
15.00  16.00 room G04 
Nicola Pagani  Wallcrossing on the universal compactified Jacobian: the theta divisor Abstract: The moduli space of line bundles on a curve can be noncompact even when the worst singularities of the curve are nodes. A natural compactification is obtained by adding stable rank1 torsionfree sheaves: such compactification depends on the choice of a polarization on the nodal curve. Similarly, when compactifying the universal Jacobian over the moduli space of stable curves, one obtains a family of compact birational moduli spaces that depend on a polarization parameter. In this talk I will present a wallcrossing formula that describes how the theta divisor varies with this parameter. This is a joint work with Jesse Kass (South Carolina). 
16.00  16.30  Coffee & Tea 
16.30  17.30 room 107 
Dana Scott  Plenary talk Setoids/Modest Sets/PERs: Adding and using types with a typefree λCalculus 
19.30  Dinner at the Cornstore, Cornmarket Street 
Wednesday 26th August:
09.00  10.00 room 107 
Maciej Dunajski  Plenary talk Quartics, Sextics and Beyond 
10.00  10.30  Coffee & Tea 
10.30  11.30 room G04 
Aaron Bertram Birational Geometry of Moduli Spaces of Sheaves on the Projective Plane via Stability Conditions
Abstract: When the minimal model program is applied to a moduli space, it is natural to ask whether the resulting birational models are themselves moduli spaces. In the case of moduli spaces of stable coherent sheaves on some algebraic surfaces, the answer is an emphatic yes, with moduli of Bridgelandstable objects in the derived category arising as the birational models. In this talk I want to survey some of the known results, particularly focusing on the case of the projective plane.

11.30  12.30 room G04 
Andrew Kresch 
Conic bundles that are not stably rational A specialization technique introduced recently by C. Voisin has sparked progress on questions of stable rationality. Varieties now known not to be stably rational include very general quartic double solids (Voisin) and very general quartic threefolds (ColliotThélène and Pirutka). This talk, representing joint work with B. Hassett and Y. Tschinkel, shows how the technique may be applied to conic bundles over rational surfaces. 
12.30  14.00  Lunch 
14.00  15.00 room G04 
Jan Manschot  Sheaves on surfaces and generalized Appell functions

15.00  16.00 room G02 
Ian McIntosh (Theme 4)  Equivariant minimal surfaces in the complex hyperbolic plane and their Higgs bundles. Abstract: One approach to studying the space of irreducible representations of a surface group (fundamental group of a closed orientable surface) into the isometry group of a real or complex hyperbolic space is to parameterise these by Higgs bundles. It is wellknown that the Higgs bundle equations are equivalent to the equations for an equivariant harmonic map into the hyperbolic space. But there are "too many" Higgs bundles: there is one parameterisation for every choice of conformal structure on the surface. One way to try to rectify this is to look for the best conformal structures by focussing on minimal surfaces. I will describe progress in this direction for maps into the complex hyperbolic plane, and how minimal surfaces can tell us more about the properties of a representation. 
16.00  16.30  Coffee & Tea 
16.30  17.30 room 107 
Logarithmic GromovWitten Invariants 
Thursday 27th August:
The dinner for Theme 6 is on Tuesday 25 August, 19:30 at the Cornstore Restaurant 40A Cornmarket Street, Cork.
For all Speakers of Theme 6: The dinner is free of charge and you are already booked by default. Please let the Theme organizers know if you cannot come to the dinner so that we can adjust the booking numbers.
For all delegates of Theme 6, who are not speakers: you are very welcome to join the dinner on a selfpaying basis. Please let the Theme organizers know if you would like to come to the dinner so that we can adjust the booking numbers.
If you enjoy walking to the dinner (about 30 minutes walk), please meet up at 18:50 in the WGB atrium. Weather permitting we will leave WGB at 19:00 sharp and walk to the Cornstore Restaurant. Alternatively you can reach the restaurant by bus number 208 or by taxi.
This is event is supported by Foundation Compositio Mathematica.