Clay–Mahler lectures (3), University of Adelaide
Name: | Clay–Mahler lectures (3), University of Adelaide |
Calendar: | 1-day meetings & lectures |
When: | Fri, September 25, 2009, 1:40 pm - 5:30 pm |
Description: | The Mahler lectures are a biennial activity organised by the Australian Mathematical Society. In 2009 we have partnered with the Clay Mathematical Institute to combine the Mahler Lectures and the Clay Lectures into the 2009 Clay–Mahler Lecture Tour, with funding also from the Australian Mathematical Sciences Institute.
Lecture slides in PDF format (467 kbyte)
Enquiries: Maths Admin, Tel. +61 8 8303 5407 Abstract: (Abouzaid) Understanding hypersurfaces through tropical geometryGiven a polynomial in two or more variables, one may study the zero locus from the point of view of different mathematical subjects (number theory, algebraic geometry, ...). I will explain how tropical geometry allows to encode all topological aspects by elementary combinatorial objects called tropical varieties. Abstract: (Calegari) Stable commutator lengthThe scl (stable commutator length) answers the question: what is the simplest surface in a given space with prescribed boundary? where simplest is interpreted in topological terms. This topological definition is complemented by several equivalent definitions:
On the topological side, scl is concerned with questions such as computing the genus of a knot, or finding the simplest 4-manifold that bounds a given 3-manifold. On the linear programming side, scl is measured in terms of certain functions called quasimorphisms, which arise from hyperbolic geometry (negative curvature) and symplectic geometry (causal structures). We will discuss how scl in free and surface groups is connected to such diverse phenomena as the existence of closed surface subgroups in graphs of groups, rigidity and discreteness of symplectic representations, bounding immersed curves on a surface by immersed subsurfaces, and the theory of multi-dimensional continued fractions and Klein polyhedra. Abstract: (Tao) The proof of the Poincaré conjectureIn a series of three papers from 2002–2003, Grigori Perelman gave a spectacular proof of the Poincaré conjecture (every smooth compact simply connected three-dimensional manifold is topologically isomorphic to a sphere), one of the most famous open problems in mathematics, by developing several new ground-breaking advances in Hamilton's theory of Ricci flow on manifolds. In this talk I describe in broad detail how the proof proceeds, and briefly discuss some of the key turning points in the argument. |
Location: | University of Adelaide Map |
URL: | /tiki-read_article.php?articleId=61 |
Created: | 09 Aug 2009 12:13 am UTC |
Modified: | 08 Sep 2009 12:55 am UTC |
By: | rmoore |
Status: | Confirmed |