Picture by Linda Romppala
Professor of Mathematics, KTH Royal Institute of Technology.

I am a Wallenberg Academy Fellow, supported by the Swedish Research Council, and the Ruth and Nils-Erik Stenbäck 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.

I am currently director of the Master's Programme in Mathematics at KTH.

I am on the editorial boards of Arkiv för Matematik and Analysis and Mathematical Physics.

Students and post docs: Vlad Guskov, Felix Rydell (with K. Kohn), Lukas Schoug (PhD 2019, now at University of Cambridge), Malin Palö Forsström, Atul Shekhar (now at U. Lyon 1). PhD Position available


News and upcoming


MSRI Semester, Spring 2022: The Analysis and Geometry of Random Spaces.

PhD and post doc positions: Please contact me by email if you are interested. PhD Position available (deadline Oct 8 2021.)

Random growth: from lichen to lightning
Joint work with A. Sola and A. Turner made the cover of the London Mathematical Society Newsletter.

Jeju Island Workshop 2020 (postponed)

Machine learning, probability, and physics, Invited session, Mathematics for Complex Data, KTH, June 8-11, 2020 (Postponed)




Research interests


My main areas of interest are in complex analysis, probability, and mathematical physics. In this interview from 2016 some of my activities are described. Particular topics that I work on include the geometry of Schramm-Loewner evolution (SLE) curves; critical lattice models; lattice gauge theory; random walks; Laplacian growth and aggregation models; analytic and probabilistic aspects of conformal field theory;  the Loewner equation; the Loewner energy/Weil-Petersson quasicircles and related parts of analysis. I am also interested in computer science and some aspects of applied mathematics. Pictures: A level line in a discrete Gaussian Free Field (courtesy of N.-G. Kang); a regularized Hastings-Levitov cluster with alpha=2; a loop-erased random walk derived from a 50k step simple random walk; a foliation of the unit disc generated by a measure with finite Loewner-Kufarev energy.


Papers


  • Wilson loops in the abelian lattice Higgs model
    With M. P. Forsström, J. Lenells
    [arXiv]


  • The Loewner-Kufarev Energy and Foliations by Weil-Petersson Quasicircles
    With Y. Wang
    [arXiv]


  • Percolation of the vacant set of the Brownian excursions process
    With O. Elias, J. Tykesson
    [.pdf]


  • Wilson loops in finite Abelian lattice gauge theories
    With M. P. Forsström, J. Lenells
    [arXiv]


  • Convergence of loop-erased random walk in the natural parametrization
    With G. F. Lawler.
    Forthcoming in Duke Math. J.
    [arXiv]


  • Dimensions of two-valued sets via imaginary chaos
    With L. Schoug, A. Sepulveda
    Forthcoming in Int. Math. Res. Not. (IMRN)
    [arXiv]


  • Remarks on the regularity of quasislits
    With L. Schoug, A. Shekhar
    Forthcoming in Ann. Acad. Sci. Fenn. Math
    [arXiv]


  • Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines
    With Y. Wang
    Geom. Funct. Anal. (GAFA) 30 289–321 (2020)
    [arXiv] [Journal]


  • Asymptotic analysis of Dotsenko-Fateev integrals
    With J. Lenells
    Ann. Henri Poincaré 20 (11) 3799-3848 (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 two-sided loop-erased random walks
    With C. Benes, G. F. Lawler.
    Electron. J. Probab. 24 Paper no 139, 22p (2019).
    [arXiv]


  • One-dimensional scaling limits in a planar Laplacian random growth model
    With A. Sola, A. Turner.
    Comm. Math. Phys. 371 (1) (2019)
    [arXiv] [Journal]


  • Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure
    With C. Hongler, K. Kytola.
    [arXiv]


  • Convergence of radial loop-erased random walk in the natural parametrization
    With G. F. Lawler
    [arXiv]


  • The Loewner difference equation and convergence of loop-erased random walk
    With G. F. Lawler.
    [arXiv]


  • Lattice representations of the Virasoro algebra I: Discrete Gaussian free field
    With C. Hongler, K. Kytola.
    (Superseded by arXiv:1307.4104)

  • 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 loop-erased random walk Green's function
    With C. Benes, G. F. Lawler.
    Probab. Theory. Related Fields, 166 (1-2), 271–319 (2016)
    [arXiv]


  • Small particle limits in a regularized Laplacian random growth model
    With A. Sola, A. Turner.
    Comm. Math. Phys. 334 (1), 331-366, (2015)
    [arXiv] [Simulations]


  • Convergence rates for loop-erased random walk and other Loewner curves
    Ann. Probab. 43 (1), 119-165 (2015)
    [arXiv]


  • On the continuity of SLE(k) in k
    With S. Rohde, C. Wong.
    Probab. Theory Related Fields 159 (3), 413-433 (2014)
    [arXiv]

  • Some remarks on SLE bubbles and Schramm's two-point observable
    With D. Beliaev.
    Comm. Math. Phys. 320 (2), 379-394 (2013)
    [arXiv]

  • Almost sure multifractal spectrum for the tip of an SLE curve
    With G. F. Lawler.
    Acta Math. 209, 265-322 (2012)
    [arXiv]
  • On the rate of convergence of loop-erased random walk to SLE(2)
    With C. Benes and M. Kozdron.
    Comm. Math. Phys. 308 (2), 307-354 (2013)
    [arXiv]

  • Scaling limits of anisotropic Hastings-Levitov clusters
    With A. Sola and A. Turner.
    Ann. Inst. Henri Poincaré  48, 235-257 (2012)
    [Journal] [arXiv]

  • On the scaling limit of loop-erased random walk excursion

    Ark. Mat. 50 (2) (2012)

    [Journal]

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

  • Rescaled Levy-Loewner hulls and random growth
    With A. Sola.
    Bull. Sci. Math. 133, 238-256 (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 (currently in hibernation).

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


Upcoming: MSRI Graduate Summer School, July 2021: Random Conformal Geometry.

Invited Session, SPA 2019, July 8-12, Evanston, IL, USA.

The analysis of Random Shapes, Jan 7-11, 2019, IPAM/UCLA, Los Angeles, CA, USA.

Invited Session, SPA 2018, June 11-15, 2018, Gothenburg, Sweden.

Random Conformal Geometry and Related Field, June 18-22, 2018, KIAS, Seoul, Korea. Funded by NSF, Samsung Science and Technology Foundation.

Mini workshop on Constructive Field Theory, March 13-15, 2018, Columbia University, NYC, USA. NSF funded.

Mini workshop on Log-Correlated Random Fields, Dec. 12-14, 2017, Columbia University, NYC, USA. NSF funded.

SLE, GFF and LQG in NYC, March 13-17, 2017, Columbia University, New York City, USA. NSF funded.

Institut Mittag-Leffler Workshop: Recent Developments in SLE, June 13-17, 2016, Djursholm, Sweden. Group photo.

One-day conference: Stockholm-Uppsala Analysis and Probability Day 2015, November 26, 2015, Uppsala, Sweden.

ICM Satellite meeting: Recent Progress in Random Conformal Geometry, August 11-12, Seoul, Korea.

One-day conference: Stockholm-Uppsala Analysis and Probability Day 2014, September 19, Stockholm, Sweden.


Travel


  • June 10-21, 2019, Probability and quantum field theory, Porquerolles, France
  • May 21-24, 2019, ETH Zurich
  • Feb 2019, Workshop on statistical mechanics, Les Diablerets, Switzerland.
  • Jan 7-12, 2019, Analysis and geometry of Random Shapes, IPAM workshop, UCLA, USA.
  • March 12-17, 2018, Mini-workshop on Constructive Field Theory, Columbia University, New York, USA
  • February 11-16, 2018, Topics in Geometric Function Theory, Les Diablerets, Switzerland
  • January 18, 2018, Chalmers, Gothenburg
  • December 10-16, 2017, Columbia University, NYC
  • Nov 10-13, 2017, University of Bristol, University of Bath
  • April 24, 2017, University of Geneva.
  • March 19-21, 2017, MIT, Cambridge
  • March 12-18, 2017, Columbia University, NYC
  • January 24-25, 2017, IRS, Paris.
  • December 14, 2016, Lund University.
  • Oct 17-Nov 16, 2016, Columbia University.
  • March 6-13, 2016, Everything is Complex, Saas Fee, Switzerland.

Picture by Linda Romppala