# Douglas Lundholm

## Researcher

in the Differential Geometry and Mathematical Physics research group.Funded by a Swedish Research Council Junior Researcher Project Grant for the period 2014-2017/18 with my project "Spectral theory of quantum systems with exotic symmetries".

Recipient of a Göran Gustafsson Prize for Young Researchers, 2018.

During the summer term 2019 I am a professor (W3, Vertretung for Christian Hainzl) at LMU Munich.

During the spring 2013 I was a CARMIN postdoc visiting:

IHÉS, January - April, 2013.

IHP, April - July, 2013, for the trimester program Variational and Spectral

Methods in Quantum Mechanics.

During the fall 2012 I was a postdoc at Institut Mittag-Leffler in the program Hamiltonians in Magnetic Fields.

During 2011-2012 I was an EPDI laureate visiting:

IHÉS, September - October, 2011.

FIM, ETH Zurich, November - December, 2011, and April - August, 2012.

INIMS Cambridge, January - March, 2012.

During 2010-2011 I was a postdoc at the University of Copenhagen.

Address: |
Department of Mathematics, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden |

Visiting address: |
Room 3646, Floor 6, Lindstedtsv. 25, KTH |

Phone: | +46 8 790 7504 |

Fax: | +46 8 723 1788 |

Department phone: | +46 8 790 6000 |

E-mail: | dogge (ª) math.kth.se |

**Research interests**

Mathematical physics, including: spectral theory of quantum mechanical systems (typically incolving supersymmetry - such as supermembrane matrix models, or exotic particle statistics - anyons), Clifford (geometric) algebras and their applications, quantum gravity and quantum geometry.

Click here to read more about my research and find some ideas for student projects. I encourage any interested students to contact me if you are looking for a suitable project.

**Curriculum vitae:**PDF

**Preprints and publications**

**Talks and lectures**

Mathematical methods for uncertainty and exclusion in quantum mechanics,
LMU Colloquium, Munich, May 2019. |

Exchange and exclusion for non-abelian anyons,
Tübingen, January 2019. |

Recent studies of anyons,
Oberwolfach, September 2016. |

Recent studies of anyons,
at YRS on the Occasion of the 70th Birthday of Barry Simon, Fields Institute, Toronto, August 2016. |

Spectral properties of the (super)membrane matrix models,
in Aspects of Membrane Dynamics, KTH / Nordita, June 2016. |

Identiska partiklar
(in Swedish for high-school students), KTH, March 2016. |

Rigorous studies of anyons,
ICMP, Santiago, July 2015. |

Lieb-Thirring bounds for interacting Bose gases (general),
Rome, January 2015. |

Lieb-Thirring bounds for interacting Bose gases (detailed),
Zürich, October 2014. |

Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics,
Paris, June 2013. |

Zero-energy states in supermembrane matrix models,
Cambridge, March 2012. |

**Supervision**

Simon Larson, Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization, PhD thesis, 2019. |

Gustav Brage and Erik Sönnerlind, Braid group statistics and exchange matrices of non-abelian anyons, with representations in Clifford algebra, BSc thesis, 2018 [PDF]. |

Joel Wiklund, Braiding non-abelian anyons with representations in Clifford algebra, with representations in Clifford algebra, BSc thesis, 2018 . |

Elias Riedel Gårding, Geometric algebra, conformal geometry and the common curves problem, BSc thesis, 2017 [PDF]. |

Viktor Qvarfordt, Non-Abelian Anyons: Statistical Repulsion and Topological Quantum Computation, MSc thesis, 2017 [PDF]. |

Emil Jacobsen and Erika Lind, Triangles in particle interactions and applications of Clifford algebra, BSc thesis, 2016 [PDF]. |

Oskar Weinberger, The braid group, representations and non-abelian anyons, BSc thesis, 2015 [PDF]. |

**Courses**

Topics in mathematics IV: Methods of modern mathematical physics, KTH, Spring 2017 (Master course).

Clifford algebra, geometric algebra, and applications, KTH, Spring 2009 and Spring 2016 (PhD course).

**Conferences**

Mathematical physics of anyons and topological states of matter, Nordita, Stockholm, March 2019. |

The Mathematical Physics session at the 27th Nordic Congress of Mathematicians, Stockholm, March 2016 (co-organizer). |

A one-day conference in honor of the 65th birthday of Lars Svensson, KTH, January 2014 (in Swedish). |

**Seminar series**

Talks in Mathematical Physics in the Stockholm area, learning seminar (co-organizer).