Operator Algebras and Applications: June 17 – 21, 2019

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Organized by: Stefan Hollands, Vaughan Jones, Gandalf Lechner, Roberto Longo

Since Heisenberg’s and Jordan’s “matrix formulation” of quantum mechanics about one hundred years ago, theoretical quantum physics has been a major incentive for mathematical research into operator algebras. The stimulus from physics has helped the development of this field, founded by von Neumann with the motivation to clarify the mathematical structure of quantum mechanics. At the same time, theoretical quantum physics has benefited tremendously from new results in operator algebras, making the link between the two fields one of the most fruitful interdisciplinary research programs of the 20th and 21st century.

Nowadays, both the quantum physics and operator algebras groups have grown into large and diverse communities with many subareas and new links to other fields. For example, in the last decades, we have witnessed connections between operator algebras and knot theory, free probability, K-theory, and further topics. In quantum physics, the most active fields that have a close link to operator algebras are quantum field theory and quantum statistical mechanics. More recently, also connections between quantum information theory and operator algebras began to emerge.

Despite its enormous phenomenological success, quantum field theory still contains many challenging open questions, for example regarding its proper place within mathematics in general, as well as the mathematical status of various field theoretic models, including in particular the types of models quantitatively describing the interactions of elementary particles. It is widely expected that new mathematical insights are needed in order to make further progress on these fronts.

The aim of this workshop is to bring together established experts and young researchers in these fields, focusing on operator-algebraic approaches to quantum field theory, subfactor theory, and quantum information theory.

This workshop is associated with the program Operator Algebras and Quantum Physics: June 3-30, 2019

Talk Schedule


Time Title Speaker Location
10:00am Rigorous results about relative entropy in QFT Feng Xu SCGP 102
11:00am Coffee Break N/A Simons Center Cafe
11:30am A topological approach to the classification of discrete amenable group actions on nuclear C* algebras Masaki Izumi SCGP 102
12:30pm Lunch N/A Simons Center Cafe
2:00pm Local Unitaries in Quantum Field Theory Nima Lashkari SCGP 102
2:30pm Coffee Break N/A Simons Center Cafe
3:00pm Roles of exposed indecomposable positive multi-linear maps in quantum information theory Seung-Hyeok Kye SCGP 102
3:35pm Non-commutative disintegrations Arthur Parzygnat SCGP 102
4:30pm Wine and Cheese N/A SCGP Cafe

Time Title Speaker Location
10:00am Unitary representations of Thompson groups Vaughan Jones SCGP 102
11:00am Coffee Break N/A Simons Center Cafe
11:30am Degrees of Noncommutativity for Subfactors Dietmar Bisch SCGP 102
12:30pm Lunch N/A Simons Center Cafe
2:00pm Weak quasi-Hopf algebras, quantum groups, and conformal field theory Claudia Pinzari SCGP 102
2:30pm Coffee Break N/A Simons Center Cafe
3:00pm UV finiteness and adiabatic limit on Quantum Spacetime through perturbative Algebraic QFT Gerardo Morsella SCGP 102
3:35pm Jones action of the Thompson groups Arnaud Brothier SCGP 102

Time Title Speaker Location
10:00am Classical dynamics, arrow of time, and the Heisenberg commutation relations Detlev Buchholz SCGP 102
11:00am Coffee Break N/A Simons Center Cafe
11:30am A unified perspective on 2d chiral CFT James Tener SCGP 102
12:30pm Lunch N/A Simons Center Cafe
2:00pm Constructing the net of von Neumann algebras for the sine-Gordon model Kasia Rejzner SCGP 102
2:30pm Coffee Break N/A Simons Center Cafe
3:00pm Scale and Mobius covariance in 2d Haag-Kastler nets Vincenzo Morinelli SCGP 102

Time Title Speaker Location
10:00am Finite dimensional endomorphism semigroups of standard subspaces Karl-Hermann Neeb SCGP 102
11:00am Coffee Break N/A Simons Center Cafe
11:30am Modular invariant partition functions return from the dead Terry Gannon SCGP 102
12:30pm Lunch N/A Simons Center Cafe
2:00pm Automorphisms and endomorphisms of simple C*-algebras generated by isometries Roberto Conti SCGP 102
2:30pm Coffee Break N/A Simons Center Cafe
3:00pm Coideal Algebras and Subfactors Hans Wenzl SCGP 102
3:35pm A survey of G-crossed braided fusion categories Corey Jones SCGP 102

Time Title Speaker Location
10:00am A hydrodynamic exercise in free probability: free euler equations Dan Voiculescu SCGP 102
11:00am Coffee Break N/A Simons Center Cafe
11:30am Anyons, matrix product operator algebras and subfactors Yasuyuki Kawahigashi SCGP 102
12:30pm Lunch N/A Simons Center Cafe
2:00pm CFT on two-dimensional de Sitter space Christian Jäkel SCGP 102
2:30pm Coffee Break N/A Simons Center Cafe