Fredrik Viklund   

Department of Mathematics 

KTH Royal Institute of Technology

Research interests

My main areas of interest lie 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, Hele-Shaw flows, and lattice Yang-Mills theories.

Other topics of (past and present) interest are fine geometric properties of Schramm-Loewner evolution (SLE) curves; scaling limits of critical lattice models; Laplacian growth and aggregation models; analytic and probabilistic aspects of conformal field theory. 

Papers

• Loewner--Kufarev entropy and large deviations of the Hastings--Levitov model

With N. Berestycki, V. Guskov

[arXiv]

• Planar Coulomb gas on a Jordan arc at any temperature

With K. Courteaut, K. Johansson

[arXiv]

• A current expansion and couplings for Ising lattice gauge theory

With M. P. Forsström

[arXiv] (Updated and expanded version)

• Competitive Hele-Shaw flow and quadratic differentials
  With D. Witt Nyström
  [arXiv]

• 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

Int. Math. Res. Not. (IMRN) 2025:12 (2025).
[arXiv]

• Wilson lines in the lattice Higgs model at strong coupling
  With M. P. Forsström, J. Lenells
  Ann. Appl. Probab. 35: 1 (2025).
  [arXiv]

• Percolation for two-dimensional excursion clouds and the discrete Gaussian free field
  With A. Drewitz, O. Elias, A. Prevost, J. Tykesson
  Electron. J. Probab. 29 (2024)
  [arXiv]

• The Loewner-Kufarev Energy and Foliations by Weil-Petersson Quasicircles
  With Y. Wang
  Proc. London Math. Soc. 128:2 (2024)
  [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) 2129-2164 (2022)
  [arXiv]

• Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure
  With C. Hongler, K. Kytola.
  Comm. Math. Phys. 395 1--58 (2022)
  [arXiv] [Journal]

• Convergence of loop-erased 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 loop-erased random walk
  With G. F. Lawler.
  ALEA 19 (2022)
  [Journal]

• Dimensions of two-valued 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 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]

• Convergence of radial loop-erased 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 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]

• Optimal Holder exponent for the SLE path
  With G. F. Lawler.
  Duke Math. J. 159 (3), 351-383 (2011)
  [Journal] [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]

Contact

Email: frejo --at-- kth.se

Mailing Address: 

Fredrik Viklund

Department of Mathematics, KTH Royal Institute of Technology

100 44 Stockholm, Sweden

Office:

Room 3527, Department of Mathematics, KTH
Drottning Kristinas Vag 25

Picture by Magnus Bergstrom/KAW