Non-commutative Geometry and its Applications

Hausdorff Center for Mathematics via YouTube

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Explore advanced mathematical concepts through this comprehensive lecture series delivered during a trimester program on non-commutative geometry and its applications at the Hausdorff Research Institute for Mathematics. Delve into cutting-edge research presented by leading mathematicians including Alain Connes, Masoud Khalkhali, and other renowned experts in the field. Learn about fundamental topics such as quantum geometry, C*-algebras, Clifford algebras, groupoid correspondences, and spectral triples through detailed presentations spanning over 80 lectures. Discover connections between non-commutative geometry and particle physics, including approaches to the Standard Model, topological insulators, and quantum field theory. Examine specialized areas including cyclic cohomology, index theory for Lie groupoids, differential algebraic K-theory, and the arithmetic applications of non-commutative methods. Study advanced mathematical structures such as Hopf algebras, spectral actions, foliations, and their geometric interpretations. Gain insights into current research directions including almost-commutative manifolds, noncommutative minimal surfaces, and applications to theoretical physics through lectures that bridge pure mathematics with physical applications.

Syllabus

Alain Connes: Geometry and the quantum
Masoud Khalkhali: Introduction to non commutative geometry 2
Xin Li: Cartan subalgebras in C*-algebras
Christian Voigt: Clifford algebras, Fermions and categorification
Martin Zirnbauer: Bott periodicity and the "Periodic Table" of topological insulators and ...
Alain Connes: Towards a Weil cohomology
Jean Renault: Groupoid correspondences and C*-correspondences
Elmar Schrohe: Fourier integral operators on manifolds with boundary and ...
Erik van Erp: Pseudodifferential Calculi and Groupoids
L. Boyle: Non-commutative geometry, non-associative geometry, and the std. model of particle physics
Ralf Meyer: A new method to classify C*-algebras up to KK-equivalence
Ralf Meyer: Symmetries in non commutative geometry 1
Jeffrey Lagarias: Splitting measures on polynomials and the field with one element
Sylvie Paycha: Traces on the noncommutative torus
Snigdhayan Mahanta: Bivariant homology theories for noncommutative spaces
Paolo Piazza: The Novikov conjecture on stratified spaces
Max Karoubi: Hermitian K theory invariants in Topology and Algebraic Geometry
Georg Tamme: Differential algebraic K theory
Harald Grosse: Non commutative quantum field theory 1
Masoud Khalkhali: Introduction to non commutative geometry 3
Erik van Erp: Lie groupoids in index theory 1
Michal Eckstein: Asymptotic and exact expansion of spectral action
Denis Perrot: Cyclic cohomology and local index theory for Lie groupoids
Pierre Cartier: Logarithmic divergences, ...
Lars Hesselholt: The big de Rham Witt complex
Pierre Bieliavsky: Universal deformation twists from evolution equations
Shane Farnsworth: Rethinking Connes' Approach to the Standard Model of Particle Physics via NCG
Jens Kaad: Differentiable absorption of Hilbert C*-modules
Thierry Fack: Non-commutative Geometry and Morse Theory for Foliation
Rudy Rodsphon: An equivariant index theorem for hypoelliptic operators
Caterina Consani: The Arithmetic Site I
Branimir Cacic:A reconstruction theorem for ConnesLandi deformations of commutative spectral tripels
Alain Connes: The Arithmetic Site II
Raimar Wulkenhaar: Exact solution of a four-dimensional field theory
Pedram Hekmati: Moduli spaces of contact instantons
Gunther Cornelissen: The Ihara zeta function and noncommutative boundaries
Masoud Khalkhali: Curvature of the determinant line bundle for noncommutative tori
Takuya Takeishi: Irreducible Representations of Bost Connes systems
Zhizhang Xie: Higher rho invariants and the moduli space of positive scalar curvature metrics
Alexander Strohmaier: Vanishing of the Wodzicki residue on ...
Masoud Khalkhali Introduction to non commutative geometry 4
Joachim Zacharias: Noncommutative covering dimension for C*-algebras and dynamical systems
Hermann Schulz-Baldes: Fredholm operators with symmetries for topological insulators
Piotr M. Hajac: Braided noncommutative join construction
Anton Savin: Index problem for elliptic operators associated with group actions and ncg
Walter van Suijlekom: Semigroup of inner perturbations in Non Commutative Geometry
Axel de Goursac: Noncommutative Supergeometry and Quantum Field Theory
Bram Mesland: Noncommutative geometry of Bianchi groups
Bruno Iochum: Spectral triples and Toeplitz operators
Ryszard Nest: Formality for algebroid stacks
Roberta Iseppi: The BV construction in the setting of NCG: application to a matrix model
Koen van den Dungen: Indefinite spectral triples and foliations of spacetime
Oliver Lorscheid: Tropicalization as base change along a non archimedean valuation
Giovanni Landi: The Weil algebra of a Hopf algebra
Erik van Erp: Lie groupoids in index theory 2
Masoud Khalkhali: Rationality of spectral action for Robertson-Walker metrics
Victor Gayral: From equivariant quantization to locally compact quantum group ...
Rainer Verch: Linear hyperbolic PDEs with non-commutative time
Fedele Lizzi: Connes Approach to the Standard Model, Grand Symmetry and the Higgs Mass
Andrzej Sitarz: Spectral action for 3+1 geometries
Yuri Kordyukov: Adiabatic limits and noncommutative geometry of foliations
Dmitri Vassilevich: Renormalization on NC torus
Ludwik Dabrowski: Asymmetric noncommutative torus
Joakim Arnlind: Noncommutative Minimal Surfaces
Markus Pflaum: The transverse index theorem for proper cocompact actions of Lie groupoids
Nicolas Franco: Causal information from Lorentzian spectral triples
Simon Brain: The Gysin Sequence for Quantum Lens Spaces
Erik van Erp: Lie groupoids in index theory 4
Harald Grosse: Non commutative quantum field theory 3
Christoph Stephan: Almost-Commutative Model Building in the LHC-Era
Harald Grosse: Non commutative quantum field theory 4
Abhishek Banerjee: Quasimodular Hecke algebras and Hopf actions
Ralf Meyer: Symmetries in non commutative geometry 2
Jord Boeijink: On globally non-trivial almost-commutative manifolds
Mairi Sakellariadou: Aspects of the bosonic spectral action
Ralf Meyer Symmetries in non commutative geometry 4
Oliver Gabriel: Functorial Rieffel deformations and (periodic) cyclic cohomology
Ralf Meyer: Symmetries in non commutative geometry 3