Type: Seminar

Modified: Mon 10 Dec 2012 0935; Mon 10 Dec 2012 0939

Distribution: World

Expiry: 11 Dec 2012

Calendar2: 11 Dec 2012 1000-1600

CalLoc2: Easter Avenue Seminar Room 405

Auth: laurent@como.maths.usyd.edu.au

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