Speaker | Time | Room | Title |

Michael Handel, CUNY | 10:30-11:30 am | 151 Sloan | Distortion elements in group actions on surfaces |

Peter Teichner, UCSD | 1:30-2:30 pm | 151 Sloan | New obstructions for embedding 2-spheres into 4-manifolds |

Elizabeth Klodginski, UC Davis | 2:45-3:45 pm | 151 Sloan | Geometry of essential surfaces in 3-manifolds fibering over the circle |

Michael Hutchings, UC Berkeley | 4-5 pm | 151 Sloan | Examples of embedded contact homology |

**Michael Handel. Title:** Distortion elements in group actions
on surfaces

**Abstract:**
If G is a finitely generated group with generators
{g_{1}, . . . ,g_{j}} then an infinite order element
f in G is a *distortion element* of G provided

**Peter Teichner. Title:** New obstructions for embedding 2-spheres
into 4-manifolds

**Abstract:**
In joint work with Rob Schneiderman, we have developed a new
obstruction theory for the embedding problem for 2-spheres in
4-manifolds. It is given in terms of the intersection theory of Whitney
towers, immersed in the 4-manifold, and it is related to Milnor
invariants and the Kontsevich integral in the easiest cases (where the
4-manifold is given by attaching 2-handles to a link in the 3-sphere).
As a consequence, we give an intersection theoretic explanation of the
Milnor invariants, and we relate them to the existence of embedded
gropes in the 4-ball.

**Elizabeth Klodginski. Title:** Geometry of essential surfaces in
3-manifolds fibering over the circle

**Abstract:** Given a surface bundle over the circle M,
we find a condition of the
monodromy characterizing when certain immersed essential
surfaces have the
1-line property. As a consequence, when M is hyperbolic,
the surfaces are
not homotopic to a totally geodesic surface. Furthermore, they cannot be
the canonical surface of a non-positively curved cubed structure on M.

**Michael Hutchings. Title:** Examples of embedded contact homology

**Abstract:**
Embedded contact homology is an invariant of contact
3-manifolds which
counts certain embedded pseudoholomorphic curves in the
symplectization.
Although much remains to be done to develop this theory in general, we can
explicitly compute it for the example of the three-torus, in terms of some
nontrivial combinatorics involving convex polygons in the plane with vertices
at lattice points. We obtain evidence for the possibly surprising conjecture
that embedded contact homology is isomorphic to a version of
Seiberg-Witten
Floer homology, and in particular is independent of the contact structure.
(joint work with Michael Sullivan)