Office:
579 Central Academic Building
Mailing Address:
Department of Mathematical Sciences
University of Alberta
Edmonton, Alberta
T6G 2G1
Canada
Phone:
+1 780 492 3988
Fax:
+1 780 492 6826
Email: tgannon@math.ualberta.ca

Research Interests:

I am interested in a fairly wide range of math, especially the interactions of algebra, number theory, and mathematical physics, but most of my work (so far at least) is related somehow to a rich structure discovered in mathematical physics called conformal field theory. A lot of my energy has been directed toward their classification,in particular that of their partition functions, which in the most interesting cases are sesquilinear modular invariant combinations of Kac-Moody characters. This is a long-term project involving Lie theory and number theory [28-26,21-19,17,16,14-11,9-6]. I have also worked on monstrous moonshine, an area of many conjectures and few proofs concerning unexpected relationships between certain finite groups and modular functions [22]. See [29] for a review article on both these topics. Another project of interest to me involves a certain action of the absolute Galois group of the rationals on various quantities associated to e.g. conformal field theories and knots [24,18,10]. Additional projects I am interested in include the general structure of CFT [31], fusion rings [34,25,23], permutations with forbidden subpatterns [30], vertex algebras, string theory [32,5,1], and lattices [4-2].
In short, I enjoy math which spills over boundaries, and I love to learn new stuff.
Complete Publication List:
34. T. Gannon, ``The automorphisms of affine fusion rings'', 24 pp,  submitted (math.QA/0002044).
33. A. Coste, T. Gannon, and P. Ruelle, ``Finite group modular data'', 38 pp, submitted (hep-th/0001158).
32. T. Gannon, ``Integers in the open string'',  Phys. Lett. B473 (2000), 80-85. 
31. A. Coste and T. Gannon, ``Congruence subgroups and rational conformal field theory'', 20 pp, submitted (math.QA/9909080)
30. T. Gannon, ``The cyclic structure of unimodal permutations'', 9 pp, submitted (math.DS/9906207)
29. T. Gannon, ``Monstrous Moonshine and the Classification of CFT'', 66 pp, submitted to the Workshop Proceedings, Istanbul 1998 (math.QA/9906167)
28. T. Gannon,  ``The Cappelli-Itzykson-Zuber A-D-E classification'', 9 pp, to appear in Rev. Math. Phys. (math.QA/9902064)
27. T. Gannon, ``The level 2 and 3 modular invariants for the orthogonal  algebras'', 17 pp, to appear in Can. J. Math. (math.QA/9809020)
26. T. Gannon and M.A. Walton, ``Heterotic modular invariants and level-rank duality'', Nucl. Phys. B536 (1999), 553-574.
25. T. Gannon and M.A. Walton, ``On Fusion Algebras and Modular Matrices'', Commun. Math. Phys. 206 (1999), 1-22.
24. T. Gannon, ``Galois Action on Braids, Knots and their Invariants'', 13 pp, submitted to Nankai conference proceedings.
23. T. Gannon and M.A. Walton, ``Fusion Rings and their Generators'',12 pp, submitted to Nankai conference proceedings.
22. C. J. Cummins and T. Gannon, ``Modular Equations and the Genus Zero Property of Moonshine Functions'', Invent. Math. 129 (1997), 413-443.
21. T. Gannon, ``U(1)$^m$ Modular Invariants, N=2 Minimal Models, and the Quantum Hall Effect'', Nucl. Phys. B491 (1997), 659-688.
20. T. Gannon, ``The Level Two and Three Modular Invariants of $SU(n)$'', Lett. Math. Phys. 39 (1997), 289-298.
19. T. Gannon, Ph. Ruelle, and M. A. Walton, ``Spectra of Conformal Field Theories with Current Algebras'', In: Field Theory, Integrable Systems and Symmetries, ed. by F. Khanna and L. Vinet (1997).
18. T. Gannon and M. A. Walton, ``Galois Relations on Knot Invariants'', Lett. Math. Phys. 38 (1996), 185-194.
17. T. Gannon, Ph. Ruelle and M. A. Walton, ``Automorphism Modular Invariants of Current Algebras'', Commun. Math. Phys. 179 (1996), 121-156.
16. T. Gannon, ``Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras'', Invent. Math. 122 (1995), 341-357.
15. T. Gannon, C. Jakovljevic and  M. A. Walton, ``Lie Group Weight Multiplicities from Conformal Field Theory'', J. Phys.: Math. Gen. A28 (1995), 2617-2625.
14. T. Gannon, ``The Classification of SU(3) Modular Invariants Revisited'', Annales de L'Institut Henri Poincare: Phys. Theor. 65 (1996), 15-55.
13. T. Gannon and M. A. Walton, ``On the Classification of Diagonal Coset Modular Invariants'', Commun. Math. Phys. 173 (1995), 175-197.
12. T. Gannon and Q. Ho-Kim, ``The Rank-Four Heterotic Modular Invariant Partition Functions'', Nucl. Phys. B425 (1994), 319-342.
11. T. Gannon, ``Toward a Classification of su(2)+...+su(2) Modular Invariant Partition Functions'',  J. Math. Phys. 36 (1995), 675-706.
10. A. Coste and T. Gannon, ``Remarks on Galois Symmetry in Rational Conformal Field Theory'', Phys. Lett. B323 (1994), 316-321.
9. T. Gannon and Q. Ho-Kim, ``The Low Level Modular Invariant Partition Functions of Rank-Two Algebras'', Int. J. Mod. Phys. A9 (1994), 2667-2686.
8. T. Gannon, ``The Classification of Affine SU(3) Modular Invariant Partition Functions'', Commun. Math. Phys. 161 (1994), 233-264.
7. T. Gannon, ``Partition Functions of Heterotic WZW Models'', Nucl. Phys.B402 (1993), 729-753.
6. T. Gannon, ``WZW Commutants, Lattices, and Level-One Partition Functions'', Nucl. Phys. B396 (1993), 708-736.
5. T. Gannon and C.S. Lam, ``Can a Lattice String Have a Vanishing Cosmological Constant?'', Phys. Rev. D46 (1992), 1710-1720.
4. T. Gannon and C.S. Lam, ``Lattices and Theta-function Identities II: Theta Series'', J. Math. Phys. 33 (1992), 871-887.
3. T. Gannon and C.S. Lam, ``Lattices and Theta-function Identities I: Theta Constants'', J. Math. Phys. 33 (1992), 854-870.
2. T. Gannon and C.S. Lam, ``Gluing and Shifting Lattice Constructions and Rational Equivalence'', Rev. Math. Phys. 3 (1991), 331-369.
1. T. Gannon and C.S. Lam, ``Construction of Four-Dimensional Strings'', Phys. Rev. D41 (1990), 492-506.
1999-2000 Courses:

             Fall: Math 322: Graph Theory
            Winter: Math 682: Topics in Algebra (Monstrous Moonshine)


Last updated November 2, 1999