## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, May 29, 2018 — 4:30 PM EDT

**Hongdi Huang, Department of Pure Mathematics, & William Dugan, Department of Combinatorics & Optimization, University of Waterloo**

"An introduction to Kreimer's Hopf algebra and Grossman-Larson Hopf algebra"

The Hopf algebra of rooted trees is introduced in Connes and Kreimer [1988], in the context of Quantum Field Theory. Considering the vector space with a basis consisting of rooted trees, then define different multiplications and coproducts to make it into different Hopf algebras. In this talk, we will introduce Kreimer's Hopf algebra and Grossman-Larson Hopf algebra. We will also conclude a description of the isomorphism between the graded dual of Kreimer's Hopf algebra and Grossman-Larson Hopf algebra. The main references will be the paper "Combinatorics of Rooted Trees and Hopf Algebras", by M. Hoffman and "An introduction to Hopf algebras of trees", by Foissy.

MC 5501

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1