GTA mini-workshop -- Geometry and Topology

GTA mini-workshop - Monday 10 December (10-12 and 14-17) and Tuesday 11 December (10-12
and 14-16) Eastern Avenue Seminar Room 405 

Monday 10 December: 

10 -11 Nguyen Tat Thang - Topology of polynomial mapping from C^n to C^{n-1} (joint
w.w.  Ha Huy Vui) 

Abstract: Let F: C^n --> C^m be a polynomial mapping.  It is well-known that F is a
locally trivial fibration outside some subset of C^m, the smallest such set is called
the bifurcation set of the map, denoted by B(F).  It is a natural question that how to
determine the set B(F).  We know the answer for only few cases, namely polynomial
functions in two variables or functions having only isolated singularities at infinity.
In this talk, we give a description for bifurcation set of polynomial mappings from C^n
to C^{n-1} which satisfy an additional assumption.  

11am-12am Krzysztof Kurdyka - 

Reaching generalized critical values of a polynomial (joint work with Zbigniew Jelonek) 

Let $f: \K^n \to \K$ be a polynomial, $\K=\R, \,\C$.  We give an algorithm to compute
the set of generalizedcritical values.  The algorithm uses a finite dimensional space of
rational arcs along which we can reach all generalized critical values of $f$.  

14-15 Stephan Tillmann- An algorithm to decide whether a 3-manifold admits a hyperbolic
structure of finite volume 

ABSTRACT: The algorithm of the title takes as input a triangulation or an ideal
triangulation of a 3-manifold M, and decides which of the following, mutually exclusive
cases holds: 

(0) M contains an essential sphere or an essential torus; (1) M is a small Seifert
fibered space; (2) M admits a complete hyperbolic structure of finite volume.  

The main ingredients are normal surface theory, Groebner bases and computation of the
Lobachevsky function.  I will also discuss how this algorithm can be used in an
algorithmic solution to the homeomorphism problem for 3-manifolds.  

Part of this talk is based on joint work with Feng Luo (Rutgers) and Tian Yang
(Rutgers).  

15-16 Alex Suciu- Complex geometry and 3-dimensional topology 

Abstract: I will present several results relating fundamental groups of compact K\"ahler
manifolds and smooth, quasi-projective varieties to fundamental groups of 3-dimensional
manifolds with empty or toroidal boundary.  

This is joint work with Stefan Friedl.  

16-17- Papadima Stefan- Classifying spaces and homology jump loci 

Tuesday 11 December 

10-11 Gus Lehrer - Invariant vector fields for reflection groups 

11-12 Graham Denham - Duality properties for abelian covers 

14-15 Dan Knopf 

Degenerate neckpinches in Ricci flow.  

I report on work with Angenent and Isenberg in which we show that for each k\geq 3,
there is a codimension-k set of initial data that gives rise to solutions of Ricci flow
that encounter Type-II singularities at finite time T.  I describe the asymptotics of
these singularities and show that they develop at the rate (T-t)^{-2+2/k}.  I also
describe some related results on what rates of singularity formation ("blow-up spectra")
are possible for both compact and noncompact solutions.  

15-16 James Isenberg - The conformal method and solutions of the Einstein constraint
equations: a status report