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The Erwin Schroedinger Institute for Mathematical Physics

Eric Bergshoeff (U Groningen): Applied Newton-Cartan Geometry

Advanced Graduate Lecture Course:

Lecture Course (260053 VO): January 10 to 29, 2018

Time: 9:15 - 10:45 a.m

Start: Wednesday, January 10, 2018
Further Dates: Friday, January 12, 2018, Friday January 19, 2018, Wednesday, January 24, 2018, Friday, January 26, 2018
End: Monday, January 29, 2018


In the he first part of the course I give an extensive introduction into the frame-independent formulation of Newtonian Gravity developed by Elie Cartan, the so-called Newton-Cartan Gravity. Examples from General relativity are used to explain the construction of this Newton-Cartan formulation.

In the second part of the course I will discuss three more specialistic topics: (i) Non-relativistic limits, (ii) Non-relativistic supersymmetry and (iii) Applications to a concrete model: the Quantum Hall Effect.


Content of the course:

  • Lecture 1: an overview of those aspects of General Relativity that are relevant for the remaining part of the course 
  • Lecture 2: The kinematics of General Relativity will be derived by applying the gauging technique to the Poincare algebra 
  • Lecture 3: The gauging technique will be applied to construct the kinematics of Newton-Cartan Gravity 
  • Lecture 4: Different non-relativistic limits are discussed that relate relativistic gravity or matter theories to non-relativistic ones. 
  • Lecture 5: An introduction to non-relativistic supersymmetry will be given with an emphasis on supersymmetry in a curved background in view of applications of the so-called Supersymmetric Localization technique. 
  • Lecture 6: The Newton-Cartan formalism will be applied to the concrete example of the The Quantum Hall Effect


Aims for the course: 

  1. Understanding the Newton-Cartan Formalism 
  2. understanding relating relativistic gravity and matter theories to non-relativistic ones by taking limits 
  3. being able to work with non-relativistic supersymmetry 
  4. being able to apply the Newton-Cartan formalism to a concrete example: the Quantum Hall Effect


Link to the course directory

At a glance

Type: SRF course
When: Jan 10, 2018 to
Jan 29, 2018
Where: ESI, Schrödinger Lecture Hall
Organizers: Christoph Dellago (ESI, U Vienna)
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