Wednesday, October 12, 2011 - 14:00 , Location: Skiles 005 , A. Beliakova , University of Zurich , Organizer: Thang Le
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.
Monday, October 10, 2011 - 14:05 , Location: Skiles 005 , Andy Putman , Rice U , Organizer: Dan Margalit
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.
Monday, October 3, 2011 - 14:00 , Location: Skiles 005 , David Gay , UGA , Organizer: John Etnyre
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.
Monday, September 19, 2011 - 14:00 , Location: Skiles 005 , Ana Garcia Lecuona , Penn State University , Organizer: John Etnyre
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.
Monday, September 12, 2011 - 14:05 , Location: Skiles 005 , Martin Schmoll , Clemson U , Organizer: Dan Margalit
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.
Monday, August 29, 2011 - 14:05 , Location: Skiles 005 , Stavros Garoufalidis , Georgia Tech , email@example.com , Organizer: Stavros Garoufalidis
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.
Monday, June 13, 2011 - 14:00 , Location: Skiles 006 , Gabriel Ruiz , National Autonomous University of Mexico , Organizer: Mohammad Ghomi
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.
Tuesday, May 31, 2011 - 13:05 , Location: Skiles 006 , Ingrid Irmer , U Bonn , Organizer: Dan Margalit
In this talk a curve complex HC(S) closely related to the "Cyclic Cycle Complex" (Bestvina-Bux-Margalit) and the "Complex of Cycles" (Hatcher) is defined for an orientable surface of genus g at least 2. The main result is a simple algorithm for calculating distances and constructing quasi-geodesics in HC(S). Distances between two vertices in HC(S) are related to the "Seifert genus" of the corresponding link in S x R, and behave quite differently from distances in other curve complexes with regards to subsurface projections.