Irish Geometry Conference 2015

Mary Immaculate College, Limerick
15 – 16 May 2015

Since 2003, the Irish Geometry Conference has taken place annually. The last three editions took place in Galway (2014), Maynooth (2013) and Cork (2012).

Registration

If you intend to participate, please fill in the registration form. There is no registration fee.

Support for Participants

There is a limited amout of funding available to contribute to travel expenses of graduate students and postdocs attending this conference.

Application is by email to the organisers. This email should include the name of the applicant, the academic or PhD advisor, the research topic or the title of PhD thesis, and the year of completion of PhD thesis or highest achieved degree to date.

Such an email must reach us on or before 23 April 2015.

Speakers

Hans-Christian Graf v. Bothmer (Hamburg)
Ulrich Derenthal (Hannover)
Brendan Guilfoyle (Tralee)
Nobuhiro Honda (Tokyo)
Daniel Huybrechts (Bonn)
Benjamin McKay (Cork)
Sergey Mozgovoy (Dublin)
Fabian Reede (Limerick)
David Wraith (Maynooth)

Schedule ⇒ printable version

All talks will take place in room T1.15, which is in the TARA building, see campus map.

Friday, 15 May
10.20 – 10.30	Michael Healy (MIC)	Opening of the Conference
10.30 – 11.20	Hans-Christian Graf v. Bothmer	Rationality of hypersurfaces I will review classical and modern results about the rationality of hypersurfaces and present our results (with Chrsitian Böhning and Pawel Sosna) regarding Kuznetsov's derived-category approach to the rationality question of cubic 4-folds.
tea/coffee
12.00 – 12.50	Daniel Huybrechts	The K3 category of a cubic fourfold The derived category of a smooth cubic hypersurface of dimension four determines the cubic. However, due to a result of Kuznetsov the category contains a full subcategory that behaves in many respects like the derived category of a K3 surface. In this talk, I will explain what is known about it from a purely categorical point of view but also from a more Hodge theoretic perspective.
lunch
14.30 – 15.20	Brendan Guilfoyle	Flowing a classical surface by its mean radius of curvature In this talk I will present joint work with Wilhelm Klingenberg on the flow of a convex surface in Euclidean 3-space by its mean radius of curvature. Under this expanding flow, it is well known that the surface runs out to infinity, becoming round as it does so. In the talk I will outline our proof that the centre of this "sphere at infinity" can be computed from the spectral data of the surface. This result can be viewed in a number of ways: convergence of the normal lines of the flowing surface or a defintion of a "centre" for an arbitrary convex surface which is conserved under mean radius of curvature flow.
tea/coffee
16.00 – 16.50	Nobuhiro Honda	Some examples of twistor spaces of algebraic dimension one It has been known that twistor spaces provide nice examples of compact complex 3-fold whose algebraic dimension takes all values from zero to three. Most compact twistor spaces are of algebraic dimension zero, and also a lot of examples are already known of twistor spaces of algebraic dimension three. Also, twistor spaces of K3 surfaces, complex tori (and also some Hopf surfaces) form a good class of twistor spaces whose algebraic dimension is one. In this talk, I will present twistor spaces of algebraic dimension one with a different flavor; namely I will present a series of simply connected twistor spaces of algebraic dimension one whose general fiber of the algebraic reduction is birational to an elliptic ruled surface. In these examples, a pair of Hopf surfaces are contained as a reducible fiber of the algebraic reduction.
17.00 – 17.50	David Wraith	Positive Ricci curvature on highly connected manifolds This talk concerns the existence of positive Ricci curvature metrics on compact (2n−2)-connected (4n−1)-manifolds. The focus will be largely topological: we will describe new constructions of these objects to which existing curvature results can be applied. The constructions are based on the technique of plumbing disc bundles. This is joint work with Diarmuid Crowley.
conference dinner at 7.00 pm
Saturday, 16 May
9.00 – 9.50	Ulrich Derenthal	Cox rings over nonclosed fields For a wide class of varieties over algebraically closed fields, Cox rings were defined and studied by Cox, Hu, Keel, Hausen, Hassett and others. We give a new definition of Cox rings for suitable varieties over arbitrary fields that is compatible with universal torsors, which were introduced by Colliot-Thélène and Sansuc. We study their existence and classification, and we make their relation to universal torsors precise. This is joint work with Marta Pieropan.
10.00 – 10.50	Sergey Mozgovoy	Counting Higgs bundles In this talk I will discuss a problem of counting semistable twisted Higgs bundles over a smooth projective curve defined over a finite field. I will also introduce the Donaldson-Thomas invariants for this problem and explain their relation to counting of indecomposable vector bundles over a curve. I will discuss an explicit formula for the above problem and its relation to the conjectural formula of Hausel-Rodriguez-Villegas. This is a joint project with Olivier Schiffmann.
tea/coffee
11.30 – 12.20	Fabian Reede	Vector bundles and Arakelov Geometry We study vector bundles on the projective line over the integers and apply concepts of Arakelov geometry to these bundles. For example we compute their arithmetic Chern classes and derive the arithmetic Hirzebruch-Riemann-Roch theorem from the arithmetic Riemann-Roch theorem due to Gillet and Soulé. As an application we will compute the Ray Singer analytic torsion for all line bundles on the Riemann sphere.
12.30 – 13.20	Benjamin McKay	Bending metal sheets, Riemann surfaces and integrable systems When you bend a metal sheet, without stretching, it deforms through isometric immersions of a Riemannian metric. Problem: for which surfaces is the differential equation of isometric immersion an integrable system? We find the first examples. We use ideas of Darboux relating complex geometry and integrable systems. Joint work with Jeanne Clelland, Tom Ivey and Peter Vassiliou.