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Abstracts for Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

Alternatively have a look at the program.

Ground states of quantum lattice systems, I

Posted in
Speaker: 
Bruno Nachtergaele
Affiliation: 
UC Davis
Date: 
Mon, 30/06/2025 - 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

Quantum Lattice Systems: observables, dynamics, ground states, GNS representation, ground state gap, examples.
 

Lattice models and topological quantum field theories I

Posted in
Speaker: 
Michael Hopkins
Affiliation: 
Harvard
Date: 
Mon, 30/06/2025 - 15:30 - 16:30
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

This series will cover the relationship between gapped Hamiltonian lattice models and topological quantum field theories, with an emphasis on a conjecture of Kitaev.    

 

Introduction to superselection sector theory I

Posted in
Speaker: 
Pieter Naaijkens
Affiliation: 
Cardiff University
Date: 
Mon, 30/06/2025 - 16:45 - 17:45
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

In this series of lectures, I will give an introduction to the
operator-algebraic (Doplicher-Haag-Roberts) approach to study the
superselection sectors of a (2D) gapped quantum spin system. The sectors have a
rich mathematical structure of a braided monoidal category. This category
describes all the algebraic properties of the `anyons' or `charges’ such
quantum spin systems can have. The aim of these lectures is to build up this
theory from first principles, using simple examples of topologically ordered

Ground states of quantum lattice systems, II

Posted in
Speaker: 
Bruno Nachtergaele
Affiliation: 
UC Davis
Date: 
Tue, 01/07/2025 - 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras" 
Quasilocality: almost local observables and interactions, Lieb-Robinson bounds, quasi-adiabatic evolution, stability I.

Lattice models and topological quantum field theories II

Posted in
Speaker: 
Michael Hopkins
Affiliation: 
Harvard
Date: 
Tue, 01/07/2025 - 15:30 - 16:30
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

This series will cover the relationship between gapped Hamiltonian lattice models and topological quantum field theories, with an emphasis on a conjecture of Kitaev.    

 

Introduction to superselection sector theory II

Posted in
Speaker: 
Pieter Naaijkens
Affiliation: 
Cardiff University
Date: 
Tue, 01/07/2025 - 16:45 - 17:45
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

In this series of lectures, I will give an introduction to the
operator-algebraic (Doplicher-Haag-Roberts) approach to study the
superselection sectors of a (2D) gapped quantum spin system. The sectors have a
rich mathematical structure of a braided monoidal category. This category
describes all the algebraic properties of the `anyons' or `charges’ such
quantum spin systems can have. The aim of these lectures is to build up this
theory from first principles, using simple examples of topologically ordered

Ground states of quantum lattice systems, III

Posted in
Speaker: 
Bruno Nachtergaele
Affiliation: 
UC Davis
Date: 
Wed, 02/07/2025 - 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras" 
Quasilocality: almost local observables and interactions, Lieb-Robinson bounds, quasi-adiabatic evolution, stability II.

Lattice models and topological quantum field theories III

Posted in
Speaker: 
Michael Hopkins
Affiliation: 
Harvard
Date: 
Wed, 02/07/2025 - 15:30 - 16:30
Location: 
MPIM Lecture Hall
Parent event: 
Twinned workshop on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"

This series will cover the relationship between gapped Hamiltonian lattice models and topological quantum field theories, with an emphasis on a conjecture of Kitaev.    

 

 

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