My research interests are in complex analysis, probability and mathematical physics.
I am a Wallenberg Scholar, supported by the Swedish Research Council and the Goran Gustafsson Foundation.
Prior to returning to KTH, I was a Simons Fellow and Ritt Assistant Professor at Columbia University and then an associate professor at Uppsala University.
Editorial work: Arkiv för Matematik and Analysis and Mathematical Physics.
PhD students: Ellen Krusell, Vlad Guskov, Yan Luo (with Y. Wang), Lefteris Theodosiadis (with A. Sola, PhD 2024), Felix Rydell (with K. Kohn, PhD 2024), Lukas Schoug (PhD 2019).
Current postdocs: Erik Duse, Mingchang Liu. Former postdocs: Malin Palö Forsström, Atul Shekhar.
I am part of the Random Matrix Theory and Random Geometry research group at KTH.
We run a weekly seminar: KTH Probability and Mathematical Physics Seminar
News and recent events
Quantum fields, Probability and Geometry, Institut MittagLeffler Program, Spring 2027.
Quantum Fields and Probability II, Institut MittagLeffler, July 1519, 2024.
New PhD course, Spring 2025: Teichmuller theory.
New PhD course (with A. Sola), Fall 2023 (course start Sept 13): Quasiconformal mappings in the plane
New PhD course given by L. Schoug, Fall 2023: Gaussian fields and random surfaces
Jeju Island Workshop 2023: Random conformal geometry and related fields in Jeju
MSRI Semester, Spring 2022: The Analysis and Geometry of Random Spaces.
Quantum Fields and Probability, Institut MittagLeffler, August 812, 2022.
Random growth: from lichen to lightning. Joint work with A. Sola and A. Turner made the cover of the London Mathematical Society Newsletter.
Research interests
My main areas of interest are in complex analysis, probability, and mathematical physics, and especially problems where these areas meet. I am currently working on questions concerning Coulomb gases in the plane, the Loewner energy, HeleShaw flows, and lattice YangMills theories.
Other topics of (past and present) interest are fine geometric properties of SchrammLoewner evolution (SLE) curves; scaling limits of critical lattice models; Laplacian growth and aggregation models; analytic and probabilistic aspects of conformal field theory. Pictures: A level line in a discrete Gaussian Free Field (courtesy of N.G. Kang); a regularized HastingsLevitov cluster with alpha=2; a looperased random walk derived from a 50k step simple random walk; a foliation of the unit disc generated by a measure with finite LoewnerKufarev energy.
Papers
 Coulomb gas and the Grunsky operator on a Jordan domain with corners
With K. Johansson
[arXiv]  Free energy and quark potential in Ising lattice gauge theory via cluster expansion
With M. P. Forsström
[arXiv]  Wilson lines in the lattice Higgs model at strong coupling
With M. P. Forsström, J. Lenells
[arXiv]  Percolation for twodimensional excursion clouds and the discrete Gaussian free field
With A. Drewitz, O. Elias, A. Prevost, J. Tykesson
[arXiv]  The LoewnerKufarev Energy and Foliations by WeilPetersson Quasicircles
With Y. Wang
Forthcoming in Proc. London Math. Soc.
[arXiv]  Wilson loops in the abelian lattice Higgs model
With M. P. Forsström, J. Lenells
Probability and Mathematical Physics (PMP) 4 (2) (2023)
[arXiv]  Wilson loops in finite Abelian lattice gauge theories
With M. P. Forsström, J. Lenells
Ann. Inst. Henri Poincaré 58 (4) 21292164 (2022)
[arXiv]  Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure
With C. Hongler, K. Kytola.
Comm. Math. Phys. 395 158 (2022)
[arXiv] [Journal]

Convergence of looperased random walk in the natural parametrization
With G. F. Lawler.
Duke Math. J. 170 (10) (2021)
[arXiv] [Journal] The Loewner difference equation and convergence of looperased random walk
With G. F. Lawler.
ALEA 19 (2022)
[Journal]
 Dimensions of twovalued sets via imaginary chaos
With L. Schoug, A. Sepulveda
Int. Math. Res. Not. (IMRN) 2022 (5) (2022)
[arXiv] [Journal]  Remarks on the regularity of quasislits
With L. Schoug, A. Shekhar
Ann. Acad. Sci. Fenn. Math 46 (1) (2021)
[arXiv] [Journal]  Interplay between Loewner and Dirichlet energies via conformal welding and flowlines
With Y. Wang
Geom. Funct. Anal. (GAFA) 30 289–321 (2020)
[arXiv] [Journal]  Asymptotic analysis of DotsenkoFateev integrals
With J. Lenells
Ann. Henri Poincaré 20 (11) 37993848 (2019)
[arXiv] [Journal]  Schramm's formula and the Green's function for multiple SLE
With J. Lenells
J. Stat. Phys. 176 (4) 873–931 (2019)
[arXiv]  Transition probabilities for infinite twosided looperased random walks
With C. Benes, G. F. Lawler.
Electron. J. Probab. 24 Paper no 139, 22p (2019).
[arXiv]  Onedimensional scaling limits in a planar Laplacian random growth model
With A. Sola, A. Turner.
Comm. Math. Phys. 371 (1) (2019)
[arXiv] [Journal]  Convergence of radial looperased random walk in the natural parametrization
With G. F. Lawler
[arXiv]

A dimension spectrum for SLE boundary collisions
With T. Alberts, I. Binder.
Comm. Math. Phys 348 (1) 273–298, (2016)
[arXiv]

Scaling limit of the looperased random walk Green's function
With C. Benes, G. F. Lawler.
Probab. Theory. Related Fields, 166 (12), 271–319 (2016)
[arXiv]

Small particle limits in a regularized Laplacian random growth model
With A. Sola, A. Turner.
Comm. Math. Phys. 334 (1), 331366, (2015)
[arXiv] [Simulations]

Convergence rates for looperased random walk and other Loewner curves
Ann. Probab. 43 (1), 119165 (2015)
[arXiv]
On the continuity of SLE(k) in k
With S. Rohde, C. Wong.
Probab. Theory Related Fields 159 (3), 413433 (2014)
[arXiv]

Some remarks on SLE bubbles and Schramm's twopoint observable
With D. Beliaev.
Comm. Math. Phys. 320 (2), 379394 (2013)
[arXiv]
 Almost sure multifractal spectrum for the tip of an
SLE curve
With G. F. Lawler.
Acta Math. 209, 265322 (2012)
[arXiv]

On the rate of convergence of looperased random walk to SLE(2)
With C. Benes and M. Kozdron.
Comm. Math. Phys. 308 (2), 307354 (2013)
[arXiv]

Optimal Holder exponent for the SLE path
With G. F. Lawler.
Duke Math. J. 159 (3), 351383 (2011)
[Journal] [arXiv]

Scaling limits of anisotropic HastingsLevitov clusters
With A. Sola and A. Turner.
Ann. Inst. Henri Poincaré 48, 235257 (2012)
[Journal] [arXiv]

On the scaling limit of looperased random walk excursion
Ark. Mat. 50 (2) (2012)
[Journal]

Random Loewner Chains
Doctoral Thesis from KTH Royal Institute of Technology, April 2010.

Rescaled LevyLoewner hulls and random growth
With A. Sola.
Bull. Sci. Math. 133, 238256 (2009)
[Journal] [arXiv]
Local activities
Informal summer school 2020: Grunsky operators, Fuchsian equations, inverse limits
Graduate course on geometric function theory, Fall 2020.
Selected topics in analysis: lattice models and random walk (new master's course), SF2716, Spring 2021.
Advanced complex analysis, SF2745 (new master's course), Spring 2020
KTH Probability Seminar (Since Spring 2023 merged with the Random Matrix Theory Seminar to form the Probability and Mathematical Physics Seminar.)
I was involved in a study group on Mathematics for Complex Data, Brummer & Partners MathDataLab.
Graduate course on Geometric Function Theory, Spring 2018.
Past events
HelsinkiStockholm Probability and Mathematical Physics Days, Oct 2627 2023, Helsinki.MSRI Graduate Summer School, July 2021: Random Conformal Geometry.
Invited Session, SPA 2019, July 812, Evanston, IL, USA.
The analysis of Random Shapes, Jan 711, 2019, IPAM/UCLA, Los Angeles, CA, USA.
Invited Session, SPA 2018, June 1115, 2018, Gothenburg, Sweden.
Random Conformal Geometry and Related Field, June 1822, 2018, KIAS, Seoul, Korea. Funded by NSF, Samsung Science and Technology Foundation.
Mini workshop on Constructive Field Theory, March 1315, 2018, Columbia University, NYC, USA. NSF funded.
Mini workshop on LogCorrelated Random Fields, Dec. 1214, 2017, Columbia University, NYC, USA. NSF funded.
SLE, GFF and LQG in NYC, March 1317, 2017, Columbia University, New York City, USA. NSF funded.
Institut MittagLeffler Workshop: Recent Developments in SLE, June 1317, 2016, Djursholm, Sweden. Group photo.
Oneday conference: StockholmUppsala Analysis and Probability Day 2015, November 26, 2015, Uppsala, Sweden.
ICM Satellite meeting: Recent Progress in Random Conformal Geometry, August 1112, Seoul, Korea.
Oneday conference: StockholmUppsala Analysis and Probability Day 2014, September 19, Stockholm, Sweden.
Travel
 June 1021, 2019, Probability and quantum field theory, Porquerolles, France
 May 2124, 2019, ETH Zurich
 Feb 2019, Workshop on statistical mechanics, Les Diablerets, Switzerland.
 Jan 712, 2019, Analysis and geometry of Random Shapes, IPAM workshop, UCLA, USA.
 March 1217, 2018, Miniworkshop on Constructive Field Theory, Columbia University, New York, USA
 February 1116, 2018, Topics in Geometric Function Theory, Les Diablerets, Switzerland
 January 18, 2018, Chalmers, Gothenburg
 December 1016, 2017, Columbia University, NYC
 Nov 1013, 2017, University of Bristol, University of Bath
 April 24, 2017, University of Geneva.
 March 1921, 2017, MIT, Cambridge
 March 1218, 2017, Columbia University, NYC
 January 2425, 2017, IRS, Paris.
 December 14, 2016, Lund University.
 Oct 17Nov 16, 2016, Columbia University.
 March 613, 2016, Everything is Complex, Saas Fee, Switzerland.
 April 48, 2016: UK Easter Probability Meeting. (Universtity of Lancaster.)