Picture by Linda Romppala

Associate professor, Department of Mathematics, KTH Royal Institute of Technology. I am a Wallenberg Academy Fellow and supported by the Swedish Research Council (VR) and the Gustafsson foundation.

Prior to returning to KTH, I was a Simons Fellow and Ritt Assistant Professor at Columbia University and then associate professor at Uppsala University. I received my Ph.D. in 2010 from KTH.

Local activities


KTH Probability Seminar.

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

Graduate course on Geometric Function Theory, Spring 2018.


Upcoming events


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.

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

The Analysis and Geometry of Random Shapes, MSRI Semester, Berkeley, CA, USA. To be held 2021 or 2022.

Past events


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.




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

  • One-dimensional scaling limits in a planar Laplacian random growth model
    With A. Sola, A. Turner.
    [arXiv]


  • 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]


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


  • 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

  • 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