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Algebraic Structures in Perturbative Quantum Field Theory

Institut des Hautes Etudes Scientifiques (IHES) via YouTube

Overview

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Attend a comprehensive conference celebrating the intersection of mathematics and physics in perturbative quantum field theory, featuring 23 hours and 43 minutes of expert presentations from leading researchers worldwide. Explore the profound mathematical structures underlying Feynman diagrams, renormalization theory, and quantum field calculations that are essential for precision physics at facilities like the LHC. Discover connections between quantum field theory and diverse mathematical areas including algebraic geometry, combinatorial Hopf algebras, noncommutative geometry, tropical curves, and moduli spaces. Learn from established scientists and emerging researchers as they present cutting-edge work on topics ranging from Feynman integral calculations and geometric splitting techniques to Wick products, gauge theories, and random loops. Examine the role of combinatorial structures in renormalization, multiple zeta values, graph complexes, and their applications to understanding fundamental physics. Gain insights into advanced mathematical tools including regularity structures, Bogoliubov recursions, toric Hall algebras, and resurgent trans-series analysis. Participate in discussions of open problems and future directions in this rapidly evolving field that bridges pure mathematics and theoretical physics. Experience presentations on worldline integration techniques, elliptic curves associated with loop graphs, solvable Dyson-Schwinger equations, and applications to quantum gravity calculations, all delivered by internationally recognized experts in mathematical physics and quantum field theory.

Syllabus

Andrei DAVYDYCHEV - Geometrical Splitting and Reduction of N-point Feynman Diagrams
Kurusch EBRAHIMI-FARD - Wick Products and Combinatorial Hopf Algebras
Walter Van SUIJLEKOM - Renormalization Hopf Algebras and Gauge Theories
Martin HAIRER - Random Loops and T-algebras
Yvain BRUNED - Bogoliubov Type Recursions for Renormalisation in Regularity Structures
Sylvie PAYCHA - From Complementations on Lattices to Locality
Dominique MANCHON - On Multiple Zeta Values and their q-analogues
Loïc FOISSY - Cointeracting Bialgebras
Ali Assem MAHMOUD - On the enumerative structures in QFT
Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
Ralph KAUFMANN - Categorical Interactions in Algebra, Geometry and Physics
Karen VOGTMANN - Spaces of Graphs, Tori and Other Flat Gamma-complexes
Francis BROWN - Graph Complexes, Invariant Differential Forms and Feynman integrals
Hadleigh FROST - The Double Copy & Lie polynomials
Marko BERGHOFF - On a Theorem of Kreimer
Spencer BLOCH - Elliptic Curves Associated to Two-loop Graphs
John GRACEY - Generalized Gross-Neveu Universality Class with Non-abelian Symmetry
Raimar WULKENHAAR - Solvable Dyson-Schwinger Equations
Thomas KRAJEWSKI - Connes-Kreimer Hopf Algebras...
Gérald DUNNE - Resurgent Trans-series Analysis of Hopf Algebraic Renormalization
Christian SCHUBERT - New Techniques for Worldline Integration
Alexander HOCK - Solution of ϕ44 on the Moyal Space
Oliver SCHNETZ - 2010-2020: a Decade of Quantum Computing
Michael BORINSKY - The Euler Characteristic of Out(Fn) and the Hopf Algebra of Graphs
Marc BELLON - Dirk Kreimer through my Looking Glass
Lukas NABERGALL - Tree-like Equations from the Connes-Kreimer Hopf Algebra...
Johannes BLÜMLEIN - Classical Gravity at High Precision
David BROADHURST - Tasmanian Adventures

Taught by

Institut des Hautes Etudes Scientifiques (IHES)

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