Last updated: September 29, 2006

Northeastern University

Mathematics Department

Maurice Auslander

Distinguished Lectures*

October 5 - 6, 2006

Pierre Vogel

(University of Paris 7)

Schedule

Date and Time

Location Titles

Thursday, Oct. 5, 4:30 - 5:30

315 Shillman Hall The Universal Lie Algebra Friday, Oct. 6, 10:30 - 11:30

511 Lake Hall The Coefficient Ring of the Universal Lie Algebra

Social Program

Date and Time

Event

Location

Thursday, Oct. 5, 5:45 - 7:00

Reception

340 Egan

Thursday, Oct. 5, 7:30

Dinner

TBA

Titles and Abstracts

To register or for further information, contact Alex Martsinkovsky alexmart >at< neu >dot< edu

- Lecture 1 The Universal Lie Algebra

Abstract: The properties of simple Lie algebras or simple Lie superalgebras can be globalized in a categorical way in order to produce an object called the universal Lie algebra. This object is an R-linear tensor category where R is a commutative ring. It is useful for understanding many properties of Lie algebras and representations of Lie algebras. It is also useful for producing finite type invariants of knots, links, and 3-dimensional manifolds. The coefficient ring R is highly unknown but a complete description of it is conjectured.

- Lecture 2 The Coefficient Ring of the Universal Lie Algebra

Abstract: The coefficient ring of the universal Lie algebra L is a graded commutative algebra Λ[δ], where δ is in some sense the dimension of L and Λ is a graded algebra generated by trivalent diagrams. This algebra is essentially unknown but it captures all finite-typeinvariants of three-dimensional manifolds. Each simple Lie (super)-algebra over K produces a ring homomorphism from Λ to K, and Λ is known up to degree 10. I propose a conjecture, related to a conjecture of Deligne, giving a complete description of this algebra. I prove a part of this conjecture and show many consequences of it in the theory of quantum invariants in low-dimensional topology.

Concurrent Activities

Registered Participants (as of September 29, 2006)

NAME AFFILIATION Thomas Bruestle Bishop's University and Universtity of Sherbrooke Dieter Happel TU Chemnitz Ivan Horozov Brandeis University Kiyoshi Igusa Brandeis University Naihuan Jing NCSU Mark Kleiner Syracuse University Alex Martsinkovsky Northeastern University Jean-Philippe Morin University of Sherbrooke Mara Neusel Texas Tech Charles Paquette University of Sherbrooke Pierre-Guy Plamondon University of Sherbrooke Ralf Schiffler University of Massashusetts, Amherst Gordana Todorov Northeastern University Jerzy Weyman Northeastern University

Archive: 2005 2004 2003 2002

* Sponsored by Bernice Auslander