Postdoctoral Scholar,

RTG
1670,

Department
of Mathematics,

University of Hamburg

I study renormalization theory from the point of view of combinatorial Hopf algebras. These Hopf algebras lead me to problems in many different fields, such as

Renormalization

Non-commutative geometry

Multiple polylogarithms

The Fundamental Lemma

I am happiest, however, when my problems are motivated by physics. I think about renormalization geometrically, and of field theories over curved space-time. I would love to learn about SYM N=4.

Here is a curriculum vitae and a full research statement.

Generalizing the Connes Moscovici Hopf algebra to contain all rooted trees (With C. Delaney) arXiv:1302.4004

Dynkin operators, renormalization and the geometric β function arXiv:1211.4466

Geometrically relating momentum cut-off and dimensional regularization International Journal of Geometric Methods in Mathematical Physics 10 (2013)

Dihedral
symmetries of multiple polylogarithms arXiv:1112.1474 (2011)

The
ß-function over curved space-time under operator regularization
arXiv:0909.4122 (2009)

A
perspective on renormalization Letters in Mathematical Physics 93
(2) pp. 187-201

The
Geometry of Renormalization Ph.D. Thesis, Johns Hopkins, 2008.

Alternative Values for sin (2b) Measured from Electron/positron
Collisions at Babar}. BS Thesis, Massachusetts Institute of
Technology, 2001

Spins,
Parity, Excitation Energies, and Octupole Structure of an Excited
Superdeformed Band in $^194$Hg and Implications for Identical Bands.
*(with
G. Hackman, T. L. Khoo, M. P. Carpenter, T. Lauritsen, A.
Lopez-Martens, I. J. Calderin, R. V. F. Janssens, D. Ackermann, I.
Ahmad, D. J. Blumenthal, S. M. Fischer, D. Nisius, P. Reiter, J.
Young, H. Amro, E. F. Moore, F. Hannachi, A. Korichi, I. Y. Lee, A.
O. Macchiavelli, T. Dossing, and T. Nakatsukasa)*
Phys.
Rev. Lett. 79, 4100 - 4103 (1997).

``Reply''
(to the Comment by R. R. Chasman) *(with
G. Hackman, T. L. Khoo, M. P. Carpenter, T. Lauritsen, A.
Lopez-Martens, I. J. Calderin, R. V. F. Janssens, D. Ackermann, I.
Ahmad, D. J. Blumenthal, S. M. Fischer, D. Nisius, P. Reiter, J.
Young, H. Amro, E. F. Moore, F. Hannachi, A. Korichi, I. Y. Lee, A.
O. Macchiavelli, T. Dossing, and T. Nakatsukasa)*
Phys.
Rev. Lett. 80, 4611 - 4611 (1998).

*At
Caltech:*

Fall 09: Functional Analysis (Ma140a)

Spring 10: Algebra (Ma5c)

Winter 11: Algebra (Ma5b)

Spring 11: Hopf Algebras and Renormalization

Fall 11: Topology (Ma109a)

Spring 12: Algebra (Ma5c)

*At
Hamburg:*

Spring 13: Topics in Categories and Geometry