## Seminars and Colloquia by Series

### Surface diagrams of smooth 4-manifolds

Series
Geometry Topology Seminar
Time
Monday, October 24, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jonathan WilliamsUGA
I will describe a new way to depict any smooth, closed oriented 4-manifold using a surface decorated with circles, along with a set of moves that relate any pair of such depictions.

### School Holiday - No Seminar Today

Series
Geometry Topology Seminar
Time
Monday, October 17, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
None
Speaker
NoneNone

### How to categorify quantum sl(2) and its finite dimensional representations?

Series
Geometry Topology Seminar
Time
Wednesday, October 12, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
A. BeliakovaUniversity of Zurich
I will explain in details starting with the basics, how the bimodules over some polynomial rings (cohomology of grasmanians) categorify the irreducible representations of sl(2) or U_q(sl(2).The main goal is to give an introduction to categorification theory. The talk will be accessible to graduate students.

### Congruence subgroups and homological stability

Series
Geometry Topology Seminar
Time
Monday, October 10, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andy PutmanRice U
An important structural feature of the kth homology group of SL_n(Z) is that it is independent of n once n is sufficiently large. This property is called "homological stability" for SL_n(Z). Congruence subgroups of SL_n(Z) do not satisfy homological stability; however, I will discuss a theorem that says that they do satisfy a certain equivariant version of homological stability.

### Morse 2-functions on 4-manifolds

Series
Geometry Topology Seminar
Time
Monday, October 3, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
David GayUGA
Rob Kirby and I have been thinking for a while now about stable maps to 2-manifolds, which we call "Morse 2-functions", to stress the analogy with standard Morse theory, which studies stable maps to 1-manifolds. In this talk I will focus on the extent to which we can extend that analogy to the way in which handle decompositions combinatorialize Morse functions, especially in low dimensions. By drawing the images of attaching maps and some extra data, one describes the total space of a Morse function and the Morse function, up to diffeomorphism. I will discuss how much of that works in the context of Morse 2-functions. This is important because Rob Kirby and I have spent most of our time thinking about stable homotopies between Morse 2-functions, which should be thought of as giving "moves" between Morse 2-functions, but to honestly call them "moves" we need to make sure we have a reasonable way to combinatorialize Morse 2-functions to begin with.

### On the slice-ribbon conjecture for Montesinos knots

Series
Geometry Topology Seminar
Time
Monday, September 19, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ana Garcia LecuonaPenn State University
The slice-ribbon conjecture states that a knot in $S^3=partial D^4$ is the boundary of an embedded disc in $D^4$ if and only if it bounds a disc in $S^3$ which has only ribbon singularities. In this seminar we will prove the conjecture for a family of Montesinos knots. The proof is based on Donaldson's diagonalization theorem for definite four manifolds.

### Dynamics in eigendirections of pseudo-Anosov maps on certain doubly periodic flat surfaces

Series
Geometry Topology Seminar
Time
Monday, September 12, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Martin SchmollClemson U
We consider particle dynamics in the (unfolded) Ehrenfest Windtree Model and theflow along straight lines on a certain folded complex plane. Fixing some parameters,it turns out that both doubly periodic models cover one and the same L-shaped surface.We look at the case for which that L-shaped surface has a (certain kind of) structure preservingpseudo-Anosov. The dynamics in the eigendirection(s) of the pseudo-Anosovon both periodic covers is very different:The orbit diverges on the Ehrenfest model, but is dense on the folded complex plane.We show relations between the two models and present constructions of folded complex planes.If there is time we sketch some of the arguments needed to show escaping & density of orbits.There will be some figures showing the trajectories in different settings.

### School Holiday - No Seminar Today

Series
Geometry Topology Seminar
Time
Monday, September 5, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
None
Speaker
NoneNone

### Representation stability of the Torelli group

Series
Geometry Topology Seminar
Time
Monday, August 29, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Stavros GaroufalidisGeorgia Tech
I will discuss a computation of the lower central series of the Torelli group as a symplectic module, which depends on some conjectures and was performed 15 years ago in unpublished joint work with Ezra Getzler. Renewed interest in this computation comes from recent work of Benson Farb on representation stability.

### Hypersurfaces with a canonical principal direction

Series
Geometry Topology Seminar
Time
Monday, June 13, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gabriel RuizNational Autonomous University of Mexico
Given a non-null vector field X in a Riemannian manifold, a hypersurfaceis said to have a canonical principal direction relative to $X$ if theprojection of X onto the tangent space of the hypersurface gives aprincipal direction. We give different ways for building thesehypersurfaces, as well as a number of useful characterizations. Inparticular, we relate them with transnormal functions and eikonalequations. Finally, we impose the further condition of having constantmean curvature to characterize the canonical principal direction surfacesin Euclidean space as Delaunay surfaces.