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 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
Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics,
lecture notes for a master-level course given at KTH in 2017, revised May 2018.
Fermionic behavior of ideal anyons,
(with R. Seiringer), December 2017, to appear in Lett. Math. Phys. [DOI].
Local density approximation for almost-bosonic anyons,
(with M. Correggi and N. Rougerie), Contribution to the proceedings of QMath13: Mathematical Results in Quantum Physics, 8-11 October 2016, Atlanta, US.
Local density approximation for the almost-bosonic anyon gas,
(with M. Correggi and N. Rougerie), Analysis & PDE 10 (2017), 1169-1200 [DOI].
Many-anyon trial states,
Phys. Rev. A 96 (2017), 012116 [DOI] [kaleidoscope].
Exclusion bounds for extended anyons,
(with S. Larson), Arch. Rational Mech. Anal. 227 (2018) 309-365. [DOI].
Emergence of fractional statistics for tracer particles in a Laughlin liquid,
(with N. Rougerie), Phys. Rev. Lett. 116 (2016), 170401 [DOI].
The average field approximation for almost bosonic extended anyons,
(with N. Rougerie), J. Stat. Phys. 161 (2015), 1236-1267 [DOI].
Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems,
(with P. T. Nam and F. Portmann), Arch. Rational Mech. Anal. 219 (2016), 1343-1382 [DOI].
Lieb-Thirring Bounds for Interacting Bose Gases,
(with F. Portmann and J. P. Solovej), Commun. Math. Phys. 335 (2015), 1019-1056 [DOI].
Anyon wave functions and probability distributions,
IHES/P/13/25, August 2013.
Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics,
(with J. P. Solovej), Ann. Henri Poincaré 15 (2014), 1061-1107 [DOI].
Local exclusion principle for identical particles obeying intermediate and fractional statistics,
(with J. P. Solovej), Phys. Rev. A 88 (2013), 062106 [DOI].
Hardy and Lieb-Thirring inequalities for anyons,
(with J. P. Solovej), Commun. Math. Phys. 322 (2013), 883-908 [DOI].
Geometric extensions of many-particle Hardy inequalities,
J. Phys. A: Math. Theor. 48 (2015) 175203 [DOI].
Partial Hamiltonian reduction of relativistic extended objects in light-cone gauge,
(with J. de Woul and J. Hoppe), JHEP 01 (2011) 031 [DOI].
Zero-energy states in supersymmetric matrix models,
PhD thesis, May 2010. Corrections
A dynamical symmetry for supermembranes,
(with J. de Woul, J. Hoppe and M. Sundin), JHEP 03 (2011) 134 [DOI].
Some spectral bounds for Schrödinger operators with Hardy-type potentials,
November 2009 (published as part of Ph.D. thesis).
Clifford algebra, geometric algebra, and applications,
(with L. Svensson), July 2009 (lecture notes).
Weighted Supermembrane Toy Model,
Lett. Math. Phys. 92 (2010), 125-141 [DOI].
Spin(9) Average of SU(N) Matrix Models I. Hamiltonian
(with J. Hoppe and M. Trzetrzelewski), J. Math. Phys. 50 (2009), 043510 [DOI].
Construction of the Zero-Energy State of SU(2)-Matrix Theory: Near the Origin
(with J. Hoppe and M. Trzetrzelewski), Nucl. Phys. B 817 (2009), 155-166 [DOI].
Octonionic twists for supermembrane matrix models
(with J. Hoppe and M. Trzetrzelewski), Ann. Henri Poincaré 10 (2009), 339-356 [DOI].
On the Geometry of Supersymmetric Quantum Mechanical Systems,
J. Math. Phys. 49 (2008), 062101 [DOI].
Dynamical Symmetries in Supersymmetric Matrix Models
(with V. Bach and J. Hoppe), Documenta Math. 13 (2008), 103-116 [DOI].
On the Construction of Zero Energy States in Supersymmetric Matrix Models IV
(with J. Hoppe), June 2007.
Geometric (Clifford) algebra and its applications, MSc thesis, January 2006.

Talks and lectures
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
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
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).