Publications

Preprints

• Slit-strip Ising boundary conformal field theory 2: Scaling limits of fusion coefficients

  Ameen, Taha; Kytölä, Kalle; Park, S.C.

  https://arxiv.org/abs/2108.05105
• Slit-strip Ising boundary conformal field theory 1: Discrete and continuous function spaces

  Ameen, Taha; Kytölä, Kalle; Park, S.C.; Radnell, David

  https://arxiv.org/abs/2009.13624

Published articles

• Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure.

  Hongler, Clément; Kytölä, Kalle; Viklund, Fredrik

  Communications in Mathematical Physics 395:1-58, 2022

  Preprint version: https://arxiv.org/abs/1307.4104
• The quantum group dual of the first-row subcategory for the generic Virasoro VOA

  Koshida, Shinji; Kytölä, Kalle

  Communications in Mathematical Physics 389:1135–1213, 2022

  Preprint version: https://arxiv.org/abs/2105.13839
• Boundary correlations in planar LERW and UST, 2020.

  Karrila, Alex; Kytölä, Kalle; Peltola, Eveliina

  Communications in Mathematical Physics 376:2065-2145, 2020

  Preprint version: https://arxiv.org/abs/1702.03261
• Conformal blocks, q-combinatorics, and quantum group symmetry

  Karrila, Alex; Kytölä, Kalle; Peltola, Eveliina

  Annales de l’Institut Henri Poincaré D 6(3):449-487, 2019.

  Preprint version: https://arxiv.org/abs/1709.00249
• Conformally covariant boundary correlation functions with a quantum group

  Kytölä, Kalle; Peltola, Eveliina

  Journal of the European Mathematical Society 22(1):55-118, 2020 (to appear in print).

  Preprint version: https://arxiv.org/abs/1408.1384
• Pure partition functions of multiple SLEs

  Kytölä, Kalle; Peltola, Eveliina

  Communications in Mathematical Physics 346:237-292, 2016.

  Preprint version: https://arxiv.org/abs/1506.02476
• SLE boundary visits

  Jokela, Niko; Järvinen, Matti; Kytölä, Kalle

  Annales Henri Poincaré 17(6):1263-1330, 2016.

  Preprint version: https://arxiv.org/abs/1311.2297
• Discrete holomorphicity and Ising model operator formalism

  Hongler, Clément; Kytölä, Kalle; Zahabi, Ali

  Contemporary Mathematics 644:79-115, 2015.

  Preprint version: https://arxiv.org/abs/1211.7299
• Ising interfaces and free boundary conditions

  Hongler, Clément; Kytölä, Kalle

  Journal of the American Mathematical Society 26:1107-1189, 2013.

  Preprint version: https://arxiv.org/abs/1108.0643
• Hadamard’s formula and couplings of SLEs with free field

  Izyurov, Konstantin; Kytölä, Kalle

  Probability Theory and Related Fields 155(1-2):35-69, 2013.

  Preprint version: https://arxiv.org/abs/1006.1853
• SLE local martingales in logarithmic representations

  Kytölä, Kalle

  Journal of Statistical Mechanics: Theory and Experiment (P08005):1-39, 2009.

  Preprint version: https://arxiv.org/abs/0804.2612
• On staggered indecomposable Virasoro modules

  Kytölä, Kalle; Ridout, David

  Journal of Mathematical Physics 50(123503), 2009.

  Preprint version: https://arxiv.org/abs/0905.0108
• LERW as an example of off-critical SLEs

  Bauer, Michel; Bernard, Denis; Kytölä, Kalle

  Journal of Statistical Physics 132(4):721-754, 2008.

  Preprint version: https://arxiv.org/abs/0712.1952
• Virasoro module structure of local martingales of SLE variants

  Kytölä, Kalle

  Reviews in Mathematical Physics 19(5):455-509, 2007.

  Preprint version: https://arxiv.org/abs/math-ph/0604047
• On conformal field theory of SLE(kappa;rho)

  Kytölä, Kalle

  Journal of Statistical Physics 123(6):1169-1181, 2006.

  Preprint version: https://arxiv.org/abs/math-ph/0504057
• SLE local martingales, reversibility and duality

  Kytölä, Kalle; Kemppainen, Antti

  Journal of Physics A: Mathematical and General 39(46):L657-666, 2006.

  Preprint version: https://arxiv.org/abs/math-ph/0605058
• Multiple Schramm-Loewner evolutions and statistical mechanics martingales

  Bauer, Michel; Bernard, Denis; Kytölä, Kalle

  Journal of Statistical Physics 120(5-6):1125-1163, 2005.

  Preprint version: https://arxiv.org/abs/math-ph/0503024
• Elastic manifolds in disordered environments: energy statistics

  Kytola, K.P, Seppala, E.T,; Alava, M.J.

  Europhysics Letters 62, 35-41, 2003.

  Preprint version: https://arxiv.org/abs/cond-mat/0301604

Theses

• Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions.

  Yliopistopaino, Helsinki 2006.

  PhD thesis, Faculty of Science, Department of Mathematics and Statistics, University of Helsinki.
• On models of two-dimensional statistical physics and the Coulomb gas.

  Masters thesis (2004),

  Department of Mathematics at University of Helsinki.

Lecture notes

• Metric Spaces

  Aalto University, Spring 2022 and Spring 2021.
• Lie groups and Lie algebras

  Aalto University, Fall 2019.
• Kompleksianalyysi (Complex Analysis)

  Aalto University, Fall 2018.
• Large random systems

  Aalto University, Spring 2014, Spring 2015, Spring 2017, Spring 2019.
• Probability theory

  Aalto University, Spring 2016, Spring 2017, Spring 2018, Spring 2019.
• Todennäköisyys ja statistinen fysiikka (Probability and statistical physics)

  University of Helsinki, Spring 2014. Lectured jointly with Antti Kemppainen.
• Introduction to Hopf algebras and representations

  University of Helsinki, Spring 2011.
• Random conformally invariant curves

  Iceland, Summer School in Random Geometry, August 2011.

Other

I enjoy formalization of mathematics in Lean. A sample:

• A (sorry-free but amateurish) formalization of the Portmanteau theorem

  2021.

An expository article in Finnish about the formalization of mathematics:

• Todistuspeli

  Solmu 3/2021.