Picture by Linda Romppala

I am an associate professor in the Department of Mathematics, KTH Royal Institute of Technology and a Wallenberg Academy Fellow. I am partially supported by the Swedish Research Council (VR) 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. While at Columbia I was partially supported by the National Science Foundation (NSF). I received my Ph.D. in 2010 from KTH. My advisor was Michael Benedicks.

Local activities


KTH Probability Seminar.

Study group on Mathematics for Complex Data, Brummer & Partners MathDataLab.


Upcoming events


Mini workshop on log-correlated fields, December 12-14, 2017, Columbia University, NYC, USA.


Past events


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

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.




Interests


My main areas of interest are in complex analysis and probability. In particular, fine and geometric properties of Schramm-Loewner evolution (SLE) curves; discrete models related to SLE; random walks, Laplacian growth and other models related to DLA; lattice models and conformal field theory;  the Loewner equation, multifractal analysis, and boundary behavior of conformal maps. 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.


Preprints

  • 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]


  • Coulomb gas integrals for commuting SLEs: Schramm's formula and Green's function
    With J. Lenells
    [arXiv]


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


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


  • Lattice representations of the Virasoro algebra I: Discrete Gaussian free field
    With C. Hongler, K. Kytola.
    (Superseded by ``Conformal Field Theory at the Lattice Level...''.)


Publications

  • A dimension spectrum for SLE boundary collisions
    With T. Alberts, I. Binder.
    To appear in Comm. Math. Phys
    [arXiv]


  • Scaling limit of the loop-erased random walk Green's function
    With C. Benes, G. F. Lawler.
    To appear in Probab. Theory. Related Fields
    [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 PoincarĂ©  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]



Travel

  • 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