Research interests

My research interest are in probability, statistical physics and complex analysis.

I have been studying several questions related to the Schramm-Loewner evolutions (SLE). Those questions include proofs of conformal invariance in two-dimensional lattice models of statistical physics and related mathematical tools.

I'm also interested in other applications of stochastics. 

Events organized

Conference: Conformal Invariance, Discrete Holomorphicity and Integrability, June 2012

Minicourses on Random Geometry, June 2013

Mathematics Meets Physics, June 24-27 2014

Photos

From these and other events, link

Teaching

Introduction to mathematical physics: Schramm-Loewner evolution, fall 2011

Todennäköisyys ja statistinen fysiikka, spring 2014

Introduction to mathematical physics: Schramm-Loewner evolution, spring 2016

Stochastic methods, fall 2017

Publications

Preprints

A.Kemppainen and S. Smirnov: Conformal invariance in random cluster models. II. Full scaling limit as a branching SLE. (2016)
Submitted. Preprint version: arxiv:1609.08527 [math-ph]

Peer-reviewed research articles

1. K.Kytölä and A.Kemppainen: SLE Local Martingales, Reversibility and Duality. (2006)
Journal of Physics A: Mathematical and General, Vol. 39 No. 46 L657-L666. Preprint version: arXiv:math-ph/0605058

2. A.Kemppainen: Stationarity of SLE. (2010)
Journal of Statistical Physics, Vol 139, No 1, 108-121. Preprint version: arXiv:0910.5832 [math-ph]

3. D.Chelkak, H.Duminil-Copin, C.Hongler, A.Kemppainen and S. Smirnov: Convergence of Ising interfaces to Schramm's SLE curves. (2014)
Comptes Rendus de l'Académie des Sciences, Vol 352, Issue 2, 157–161. Preprint version: arXiv:1312.0533 [math-ph]

4. A.Kemppainen and W. Werner: The nested simple conformal loop ensembles in the Riemann sphere. (2016)
Probability Theory and Related Fields 165: 835. Preprint version: arXiv:1402.2433 [math.PR]

5. A.Kemppainen and S. Smirnov: Random curves, scaling limits and Loewner evolutions. (2017)
Annals of Probability, Vol 45, No 2 , 698-779. Preprint version: arXiv:1212.6215 [math-ph]

6. A. Kemppainen and S. Smirnov: Configurations of FK Ising interfaces and hypergeometric SLE. (2018)
Mathematical Research Letters, 25, No 3, 875-889. Preprint version: arXiv:1704.02823 [math-ph]

7. A.Kemppainen and S. Smirnov: Conformal invariance of boundary touching loops of FK Ising model. (2019)
Communication in mathematical physics, 369, No 1, 49-98.. Preprint version: arXiv:1509.08858 [math-ph]

Books

8. A.Kemppainen: Schramm-Loewner evolution. (2017)
SpringerBriefs in Mathematical Physics. DOI: 10.1007/978-3-319-65329-7 . Preprint version and extra material available at http://www.helsinki.fi/sle-book (redirects to this linked page). (See also the course page, spring 2016.)

Articles in professional journals

9. A.Kemppainen: Konformi-invarianssia tilastollisessa fysiikassa. (2011)
Arkhimedes 2011: 1, 16-30. The article