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Feynman integrals and motives

Marcolli, Matilde (2010) Feynman integrals and motives. In: Proceedings of the 5th European Congress of Mathematics. European Congress of Mathematics. European Mathematical Society , Zürich, pp. 293-332. https://resolver.caltech.edu/CaltechAUTHORS:20100921-095023951

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Abstract

This article gives an overview of recent results on the relation between quantum field theory and motives, with an emphasis on two different approaches: a “bottom-up” approach based on the algebraic geometry of varieties associated to Feynman graphs, and a “top-down” approach based on the comparison of the properties of associated categorical structures. This survey is mostly based on joint work of the author with Paolo Aluffi, along the lines of the first approach, and on previous work of the author with Alain Connes on the second approach.


Item Type:Book Section
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http://arxiv.org/abs/0907.0321arXivUNSPECIFIED
Additional Information:© 2009 European Mathematical Society. Submitted on 2 Jul 2009. A large part of what I described in this paper is based on recent joint work with Paolo Aluffi and on previous joint work with Alain Connes, whom I thank for their essential contributions to the development of these ideas and results. Although parts of this article reflect the content of the lecture I delivered at the ECM in the summer of 2008, new material developed in the intervening time was included for completeness and the actual writing was carried out in the winter 2009, during a stay at MSRI: I thank the institute for the hospitality and for support. An informal discussion with Nikolai Reshetikhin and a talk I gave in Yongbin Ruan’s seminar helped finalizing the form of this exposition. The topics covered in this survey will appear in extended form in the book [50] based on a course given at Caltech in the fall 2008.
Series Name:European Congress of Mathematics
Record Number:CaltechAUTHORS:20100921-095023951
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100921-095023951
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20066
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:22 Sep 2010 18:40
Last Modified:03 Oct 2019 02:05

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