10:30-11:30 | Francesca Acquistapace | C-semianalytic sets | We propose a class of semianalytic sets smaller than the usual class defined by Lojasiewicz, namely the class of those semianalytic sets that can be locally described using only global analytic functions on a C-analytic set. This class is stable under boolean and topological operations and verifies a "direct image property". As a main application we prove that the set of points where a C-analytic set is not coherent is C-semianalytic. |

Tea/Coffee | |||

12:00-13:00 | Fabrizio Broglia | Nullstellensätze | We prove a Nullstellensatz for ideals in the ring O(X) of global real analytic functions on a C-analytic space. We use the Lojasiewicz radical instead of the real radical because Hilbert's 17-th Problem did not get a general solution in rings of analytic functions. The same radical works for rings of smooth functions or quasi-analytic functions. |

Lunch | |||

14:30-15:30 | John Michael Burns | Subroot systems, flag manifolds and numerical invariants | Subroot systems (of a Lie algebra root system) provide a natural setting for ‘geometric induction’ and also lead to many interesting homogeneous spaces, such as flag manifolds. In the study of related geometric objects, such as homogeneous vector bundles, it seems natural to seek relations with the geometric data of the parent root system. We will consider the role of simple numerical invariants such as the Coxeter number, the dual Coxeter number and exponents in this context. In particular we relate them to Chern classes, ampleness, Nef values and the defect of dual varieties. |

Tea/Coffee | |||

16:00-17:00 | Benjamin McKay | Affine connections on complex manifolds | We will see why a compact complex manifold with finite fundamental group and algebraic dimension zero admits no holomorphic affine connection. We will learn something about the rigid geometric structures a la Gromov on such manifolds. |

17:10-18:10 | Andrei Mustata | Varieties with C\* actions and their invariants | For every variety X with a C\* action there exists a moduli space parameterizing the broken flow lines of the C\* action. Part of the homology of this space forms a ring which can be computed in terms of the data of the C* action. Moreover this ring can be used to describe the intersection ring of X, the equivarint cohomology of X and the Gromov-Witten invariants of X. This is joint work with Anca Mustata. |

Conference dinner at 7 pm |

##### Saturday, May 14

9:30-10:30 | Gwyn Bellamy | Symplectic resolutions of quiver varieties. | Quiver varieties, as introduced by Nakaijma, play a key role in representation theory. They give a very large class of symplectic singularities and, in many cases, their symplectic resolutions too. However, there seems to be no general criterion in the literature for when a quiver variety admits a symplectic resolution. In this talk I will give necessary and sufficient conditions for a quiver variety to admit a symplectic resolution. This result is based on work of Crawley-Bouvey and of Kaledin, Lehn and Sorger. The talk is based on joint work with T. Schedler. |

Tea/Coffee | |||

11:00-12:00 | Bernd Kreussler | Zariski decomposition on rational surfaces and algebraic dimension of twistor spaces | In the calculation of the algebraic dimension of compact, simply connected 3-dimensional twistor spaces the anti-Kodaira dimension of certain rational surfaces play an essential role. A powerful tool to study the anti-Kodaira dimension of rational surfaces is the Zariski decomposition of an anti-canonical divisor on such a surface. In this talk, which reports on joint work with N. Honda, our results on the Zariski decomposition of an anti-canonical divisor on a rational surface will be explained. The main application of these results is a proof that a certain type of twistor space cannot exist. |

12:10-13:10 | Norbert Hoffmann | Line bundles on noncommutative algebraic surfaces | Let X be a complex algebraic surface. Let A be a (noncommutative) coherent O_X-algebra whose generic stalk is a central division algebra. Then the pair (X,A) can be thought of as a noncommutative algebraic surface. This talk deals with the moduli space of line bundles on (X,A), i.e., of locally free A-modules of rank one, in some cases where the pair (X,A) is Calabi-Yau or Fano. It turns out that the moduli space is dense in its compactification by torsion-free A-modules, and that this compactification is smooth and, in the Calabi-Yau case, holomorphically symplectic. This is joint work with U. Stuhler and with F. Reede. |

[printable version](IGC 2016.pdf) #### Travel and Accomodation * [TCD Campus Map](https://www.tcd.ie/Maps/assets/pdf/tcd-campus.pdf) * [Interactive map](http://www.tcd.ie/Maps/map.php?b=195) #### Organisers * [Sergey Mozgovoy](http://www.maths.tcd.ie/~mozgovoy/) (TCD) * [Andreea Nicoara](https://www.maths.tcd.ie/people/Andreea_Nicoara.php) (TCD) #### Support IGC 2016 is generously supported by * School of Mathematics, Trinity College Dublin. * Irish Mathematical Society. ---- Please send your queries to [IGC2016org@gmail.com](mailto:IGC2016org@gmail.com)