报告主题：Algebraic Birkhoff factorization and the locality principle in renormalization
报告人：郭锂 教授 （Rutgers University – Newark）
报告时间：2018年6月12日（周二）14:30
报告地点：校本部G507
邀请人：景乃桓教授
报告摘要：The Algebraic Birkhoff Factorization (ABF) of Connes and Kreimer gives an algebraic formulation of the renormalization process in quantum field theory. Their ABF is an factorization of an algebra homomorphism from a Hopf algebra to a Rota-Baxter algebra. This algebraic formulation facilitates the mathematical study in renormalization and allows the renormalization method to be applied to problems in mathematics. In this talk we first give an introduction to ABF with a baby model for renormalization of Riemann integrals. We then give two generalizations of ABF, one for coalgebras and one for locality Hopf algebras. The latter is an interpretation of the locality principle in renormalization, stating that a locality property is preserved in the process of renormalization. More precisely we show that if a regularization map is a locality map, then so is the corresponding renormalization map from the algebraic Birkhoff factorization. For this purpose, we introduce locality for various algebraic structures including those of a Hopf algebra, a Rota-Baxter algebra and a regularization map between the two algebras. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalize the exponential generating function which sums over the lattice points in a lattice cone.This is a joint work with P. Clavier, S. Paycha and B. Zhang.
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