Graphs, Knots, and Algebras

ACO Distinguished Lecture
Tuesday, January 28, 2014 - 4:30pm
1 hour (actually 50 minutes)
Clough Commons Room 152
University of Amsterdam and CWI Amsterdam

Alexander Schrijver is Professor of Mathematics at the
University of Amsterdam and researcher at the Center for
Mathematics and Computer Science (CWI) in Amsterdam.
His research focuses on discrete mathematics and optimization,
in particular on applying methods from fundamental mathematics.
He is the author of four books, including 'Theory of Linear and
Integer Programming' and 'Combinatorial Optimization - Polyhedra
and Efficiency'.

He received Fulkerson Prizes in 1982 and 2003, Lanchester Prizes in
1987 and 2004, a Dantzig Prize in 2003, a Spinoza Prize in 2005,
a Von Neumann Theory Prize in 2006, and an Edelman Award in 2008.
He is a member of the Royal Netherlands Academy of Arts and Sciences
since 1995 and of three foreign academies, received honorary
doctorates from the Universities of Waterloo and Budapest, and was
knighted by the Dutch Queen in 2005.

Many graph invariants can be described as 'partition functions' (in the sense of de la Harpe and Jones). In the talk we give an introduction to this and we present characterizations of such partition functions among all graph invariants. We show how similar methods describe knot invariants and give rise to varieties parametrizing all partition functions. We relate this to the Vassiliev knot invariants, and show that its Lie algebra weight systems are precisely those weight systems that are 'reflection positive'. The talk will be introductory and does not assume any specific knowledge on graphs, knots, or algebras.