Research and Publications
I am interested in algebra, topology, and combinatorics.
My current research is mainly on multiple zeta
values and related topics. Recent publications:
- `The Hopf algebra structure of multiple harmonic sums,'
Nuclear Physics B (Proc. Suppl.) 135 (2004), 215-219.
- `Algebraic aspects of multiple zeta values,'
in Zeta functions, topology and quantum physics,
Springer, 2005; preprint
math.QA/0309425.
- `Quasi-symmetric functions, multiple zeta values, and rooted trees,'
Oberwolfach Reports 3 (2006), 1259-1262;
preprint
math.QA/0609413.
- `Quasi-symmetric functions and mod p multiple harmonic sums,' preprint
math.NT/0401319.
- `Updown categories,' preprint
math.CO/0402450.
- `(Non)Commutative Hopf algebras of trees and (quasi)symmetric functions,'
preprint
0710.3739.
Recent presentations:
- ``Hopf Algebras of Forests," USNA Mathematics Colloquium, February
14, 2007
(slides available).
- ``An Algebra of Arithmetic Functions," USNA Mathematics Colloquium,
September 19, 2007
(slides available).
- ``Unrenormalizing the Positive Integers," combinatorics seminar,
George Washington University, Washington, DC, November 7, 2007
(slides available).
- ``Multiple Zeta Values: From Euler to the Present," MAA Sectional
Meeting, Annapolis, Maryland, November 10, 2007
(slides available).
A list of older talks is available, as well as
a full publication list and detailed
research description. Mainly for my own
convenience I have assembled a page of professional
links.
The material above is my own research and a
disclaimer applies to it.
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