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
 HansChristian 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)
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 
HansChristian 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 derivedcategory approach to the
rationality question of cubic 4folds.

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 3space 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 3fold 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 ColliotThélène 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 DonaldsonThomas 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 HauselRodriguezVillegas. 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
HirzebruchRiemannRoch theorem from the arithmetic RiemannRoch 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.

Abstracts can be seen by moving the mouse over the title of a
talk or on the printable version.
Travel and Accomodation
There is a number of hotels within walking distance to the conference
venue. The speakers will be accomodated in these two hotels.
The following are within a 20 or 25 minutes walking distance.
Organisers
Support
IGC 2015 is generously supported by