# MathemAmplitudes 2019: Intersection Theory & Feynman Integrals

MA2019
18-20 December 2019
published February 15, 2022

This initiative aimed at bringing together mathematicians and theoretical physicists with interdisciplinary expertise, ranging from Differential and Algebraic Geometry, Topology and Number Theory, to Feynman Calculus and Scattering Amplitudes, with the goal of discussing the recently discovered role of Intersection Theory for twisted de-Rham cohomologies in the evaluation of Feynman integrals. The goal of the meeting is to identify and propose new, interdisciplinary, common research directions.

### Editorial Board

• Hjalte Axel Frellesvig
 Session 1: Hypergeometric Functions and Intersection Theory Product of Hessians and Discriminant of Critical Points of Level Function for Hypergeometric Integrals PoS(MA2019)009 K. Aomoto and M. Ito Schwarz maps for the hypergeometric function PoS(MA2019)011 M. Yoshida Introduction to the Intersection Theory for Twisted Homology and Cohomology Groups PoS(MA2019)007 K. Matsumoto Intersection theory, characteristic classes, and algebro-geometric Feynman rules PoS(MA2019)012 P. Aluffi and M. Marcolli Connection formulas related with Appell's hypergeometric function $F_1$ PoS(MA2019)010 K. Mimachi Appell-Lauricella's hypergeometric functions and intersection theory PoS(MA2019)008 Y. Goto Computing cohomology intersection numbers of GKZ hypergeometric systems PoS(MA2019)013 S.J. Matsubara-Heo Session 2: Intersection Theory, Integral Relations and Applications to Physics From Diagrammar to Diagrammalgebra PoS(MA2019)015 P. Mastrolia Status of Intersection Theory and Feynman Integrals PoS(MA2019)016 S. Mizera On the Application of Intersection Theory to Feynman Integrals: the univariate case PoS(MA2019)017 H.A. Frellesvig and L. Mattiazzi On the Application of Intersection Theory to Feynman Integrals: the multivariate case PoS(MA2019)019 M.K. Mandal and F. Gasparotto Four-loop master integrals and hypergeometric functions PoS(MA2019)023 S. Laporta Applications of intersection numbers in physics PoS(MA2019)021 S. Weinzierl A double integral of dlog forms which is not polylogarithmic PoS(MA2019)005 C. Duhr and F. Brown Building blocks of closed and open string amplitudes PoS(MA2019)022 P. Vanhove and F. Zerbini Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals PoS(MA2019)004 J. Boehm, D. Bendle, W. Decker, A. Georgoudis, F.J. Pfreundt, M. Rahn and Y. Zhang Maximal Cuts and Wick Rotations PoS(MA2019)002 E. Remiddi