<<  News and Merit Report, 2010  >>

Why make it public? So painful it is to write, I must try to sweeten the pill by adding to it some residual benefit. Hence it is also a "news report" presented annually in the open to the small number of people who might be interested in what I'm up to. The sectioning follows the standard Faculty of Arts & Science form, but with many parts suppressed.

A. Teaching

1. Courses Taught

(i) Undergraduate

• MAT 240HF Alegbra I, 3 hours per week with 280 TA hours and 80 students.

(ii) Graduate

• MAT 1350HF Alegbraic Knot Theory, 3 hours per week with no TA and 8 students.

3. Course and Curriculum Development

(iii) New pedagogical methods introduced

5. Other

• For a part of the year, I've run a weekly lunchtime research-group meeting titled "Knot at Lunch''. See http://katlas.math.toronto.edu/drorbn/index.php?title=Knot_at_Lunch.

B. Research Supervisions

(iii) New and Continuing PhD

(a) Primary supervisions.

• Karene Chu, working on "Virtual Braids" and on "Flat Knots" from May 2007 at 8 supervision hours per month.
• Zsuzsanna Dancso, working on "Kontsevich formalism for knotted trivalent graphs" from September 2006 at 4 supervision hours per month.
• Louis Leung, working on "Lie bialgebra weight systems" from September 2005 at 8 supervision hours per month.
• Jana Archibald, working on "Fermion formulas for Alexander" from September 2005 at 4 supervision hours per month.
• Peter Lee, working "Frozen feet associators, quadratic algebras" from May 2006 at 4 supervision hours per month.

(b) Supervisory committee memberships

C. Scholarly Work in Progress

• Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne, no co-authors, first listed 2009, 37 pages written this year, anticipated completion December 2010 at 120 pages as an article/monograph.
• Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots, with Iva Halacheva, Louis Leung, and Fionntan Roukema, first listed 2010, 7 pp. paper, completed and submitted for publication.

F. Invited Lectures

• (u, v, and w knots) x (topology, combinatorics, low algebra, and high algebra), 4 summer school lectures in Trieste, May 2009.
• Convolutions on Lie Groups and Lie Algebras and Ribbon 2-Knots, Conference on Knot Theory, Trieste, May 2009.
• Convolutions on Lie Groups and Lie Algebras and Ribbon 2-Knots, Journés Solstice d'été, Paris, June 2009.
• Solving the Rubik Cube Using Group Theory, short course at Mathcamp Canada/USA, July 2009.
• The Hardest Math I've Ever Really Used, lecture at Mathcamp Canada/USA, July 2009.
• Convolutions on Lie Groups and Lie Algebras and Ribbon 2-Knots, Jerusalem, July 2009.
• Convolutions on Lie Groups and Lie Algebras and Ribbon 2-Knots, Chern-Simons Gauge Theory: 20 years after conference, Bonn, August 2009.
• Kolmogorov's Solution of Hilbert's 13th Problem, Gradute Student Seminar, Toronto September 2009.
• Dessert: Hilbert's 13th Problem, in Full Colour, Workshop on Computational Differential Geometry, Topology, and Dynamics, The Fields Institute, November 2009.
• Homomorphic Expansions and w-Knots, Colloquium, University of Western Ontario, February 2010.
• 18 Conjectures, Algebraic and Quantum Topology Conference, Luminy, April 2010.
• u, v, and w-Knots: Topology, Combinatorics and Low and High Algebra, Courant Lecture Series (3 lectures), Goettingen, April 2010.

I. Current Grants and Contracts

• Knot Theory and Algebra, Discovery NSERC grant, starting April 2008 and ending March 2013 at total of $140,000 with no co-investigators.
• Knot Theory and Algebra, Discovery Accelerator Supplement (NSERC) starting April 2009 and ending March 2012 at total of $120,000 with no co-investigators.

K. University Service

(i) Department

(iii) Faculty

L. External Professional Service

• Member of the Editorial Board, Compositio Mathematica.
• Founding editor of The Knot Atlas.
• Founding Contributor to KnotTheory`, a computer knot theory package.
• Refereed about 4 papers last year and about 2 grant proposals.

M. Outreach Service

Z.