Irish Geometry Conference 2011

Galway, 13-14 May 2011

(Organisers: Javier Aramayona, John Burns, James Cruickshank)

The Irish Geometry Conference is a yearly conference targeting recent developments in geometry, interpreted in a broad sense. The first edition of the conference was hosted by Galway in 2003; the last three editions took place in Maynooth (2010), Cork (2009) and Tralee (2008).

There is no registration fee. All are welcome to attend.


The following people have agreed to give a talk:


All talks will take place in AM150, Arts Millennium Building. Click here for a map of campus.

Friday 13 May

11.00-11.50 Anca Mustata TBA TBA

11.50-12.40 Brendan Owens A concordance group of links. The concordance group C of knots was introduced in 1957 by Fox and Milnor and has been the subject of a great deal of study ever since. In 1967, following a suggestion of Fox, Hosokawa described a group of equivalence classes of links containing C as a subgroup; he showed this group was in fact a direct sum of C and the integers. I will describe a different concordance group of links and discuss its properties. This is joint work with Andrew Donald.

12.40-14.10 Lunch

14.10-15.00 Martin Bridgeman Volume Identities for hyperbolic manifolds with boundary Given a finite volume hyperbolic n-manifold M with totally geodesic boundary, we show there is a real valued function $F_n$ such that the volume of any finite volume hyperbolic n-manifold M with totally geodesic boundary$M$ is the sum of values of $F_n$ on the orthogeodesic length spectrum. For $n=2$ the function $F_2$ is the Rogers L-function and the summation identities give dilogarithm identities on the Moduli space of surfaces. We will also discuss volume identities for geometrically finite Kleinian groups.

15.00-15.30 Coffee/tea

15.30-16.20 Tara Brendle Hyperelliptic Birman exact sequences Birman exact sequences are a key tool for induction-style arguments for certain classes of groups arising in geometric group theory. Motivated by a conjecture of Hain and Morifuji, we will give Birman exact sequences for symmetric mapping class groups of surfaces. We will also describe some related results on various properties of the symmetric Torelli group, a group which arises naturally in algebraic geometry and which can also be interpreted as an alternative notion of a pure braid group on a sphere. (Joint work with Dan Margalit.)

16.20-17.10 David Wraith Topology and geometry in cohomogeneity greater than one. We study manifolds admitting a compact Lie group action with cohomogeneity greater than one. In order to obtain a tractable family of manifolds, we impose conditions on the singular orbits. We investigate the topology of the resulting objects and the existence of invariant metrics with good curvature properties. This is joint work with Stefan Bechtluft-Sachs

19.30 Conference Dinner: Vina Mara, Middle Street.

Saturday 14 May

10.30-11.20 Alexey Zaytsev Reduction of abelian varieties with complex multiplication and its first truncated Barsotti-Tate group schemes Let A be an abelian variety over a number field L with complex multiplication by the full ring of integers O_K for some CM field K. We consider a good reduction at prime ideal S in L of the abelian variety A. After the reduction we get an abelian variety over a finite field of characteristic p. In this talk I explain a correspond between the decomposition of ideal pO_K into prime ideals and decomposition of the first truncated Barsotti-Tate group scheme (A mod S)[p]. In addition I will discuss a Moduli problem of abelian varieties up to isogeny.

11.20-12.10 Fran Burstall Geometry and dynamics of isothermic submanifolds This talk will have three parts: in the first, I will describe the beautiful classical theory of isothermic surfaces in the 3-sphere due to Christoffel, Darboux, Bianchi and others. Then I will indicate how the 3-sphere may be replaced by any symmetric R-space (a conjugacy class of real parabolic subalgebras with abelian nilradicals) with essentially no loss of integrable structure. Finally, I shall show how dynamics of the simplest examples (curves in the real projective space) provide a geometric interpretation of the KdV equation, its relation to the mKdV equation via the Miura transform and the BŠcklund transformations of KdV discovered by Walhquist-Estabrook.

12.10-13.00 Mikael Passare On (co)amoebas and the trigonometry of Harnack curves We will give a brief introduction to the notions of amoebas and coamoebas of algebraic varieties. Special attention will be paid to the case of plane complex curves. Some connections to other mathematical concepts, such as linkages and Mahler measures, will also be touched upon.

Travel and Accommodation

Please contact Ireland West for further information about accommodation near NUI Galway.

For further information, please keep an eye on this website which will be updated regularly, or contact Javier Aramayona (, John Burns ( or James Cruickshank (

The 2011 Irish Geometry Conference is generously supported by

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