The KTH Probability and Mathematical Physics seminar will be held Wednesdays 13.15-14.15 in the seminar room 3721.
Organisers: Lukas Schoug and Levi Haunschmid-Sibitz.
Below follows the list of speakers.
Fall 2025. (Previous semesters can be found here)
10 September 2025: Janne Junnila, KTH
Title: Real opers and curves with a geodesic property
Abstract: I will discuss complex projective structures with real holonomy on Riemann surfaces, in particular the punctured sphere. Such structures can be identified with certain differential operators known as real opers that appear in the semiclassical limit of Liouville quantum gravity and also play a prominent role in the analytic Langlands correspondence. A canonical example is given by the Fuchsian projective structure on a hyperbolic Riemann surface, and a result of Goldman says that on closed surfaces all other real opers can be obtained via a grafting procedure applied to the Fuchsian structure. With Bonk, Rohde and Wang we showed a similar grafting result in a certain non-compact setting, where the projective structure is induced by a piecewise geodesic Jordan curve on the punctured sphere. We also proved that the associated Schwarzian derivative is related to the derivative of the Loewner energy of the curve, a result analogous to a famous formula conjectued by Polyakov and proven by Takhtajan and Zograf in the Fuchsian case. In addition to explaining these results and giving some general background on complex projective structures, I will also showcase some explicit examples of real opers with reflection symmetry about the unit circle.
17 September 2025: No talk.
24 September 2025: Kurt Johansson, KTH
Title: Planar Coulomb gases and Loewner energy
Abstract: The asymptotics of the partition function of a planar Coulomb gas confined to a Jordan curve in the complex plane is related to the Loewner energy of that curve. I will discuss this connection and extensions to the case of a Jordan arc. Based on joint work with Klara Courteaut and Fredrik Viklund.
1 October 2025: Ellen Powell, Durham University
Title: Scaling limits of critical FK-decorated maps at q=4
Abstract: The critical Fortuin–Kasteleyn random planar map with parameter q>0 is a model of random (discretised) surfaces decorated by loops, related to the q-state Potts model. For q<4, Sheffield established a scaling limit result for these discretised surfaces, where the limit is described by a so-called Liouville quantum gravity surface decorated by a conformal loop ensemble. At q=4 a phase transition occurs, and the correct rescaling needed to obtain a limit has so far remained unclear. I will talk about joint work with William Da Silva, XinJiang Hu, and Mo Dick Wong, where we identify the right rescaling at this critical value and prove a number of convergence results.
8 October 2025: No talk.
15 October 2025: Léonie Papon, TU Wien. (OBS: time is 13.00-14.00!)
Title: On the scaling limit of interfaces in the critical planar Ising model perturbed by a magnetic field
Abstract: In this talk, I will present some recent results on the scaling limit of interfaces in the critical planar Ising model perturbed by a magnetic field. I will first consider the case when the field is a deterministic function. In this case, I will show that in the so-called near-critical regime and when the Ising model has Dobrushin boundary conditions, the interface separating $+1$ and $-1$ spins has a scaling limit whose law is conformally covariant and absolutely continuous with respect to SLE$_3$. Its limiting law is a massive version of SLE$_3$ in the sense of Makarov and Smirnov. I will also discuss the scaling limit of this interface when the magnetic perturbation is not near-critical.
In the second part of the talk, I will discuss some ongoing work with Fenglin Huang and Aoteng Xia in which we look at the case when the magnetic field is given by a collection of iid centered Gaussian random variables, one for each vertex. In this setting, in the near-critical regime, we show that almost surely in the disorder, the scaling limit of the quenched law of the $\pm 1$ interface is absolutely continuous with respect to SLE$_3$. We then show that this contrasts with the scaling limit of the quenched law of the collection of nested spin loops, which turns out to be almost surely singular with respect to nested CLE$_3$. This also contrasts with the deterministic case where it is known that in the near-critical regime, any subsequential limit of the collection of nested spin loops is absolutely continuous with respect to nested CLE$_3$.
22 October 2025: Alex Karrila, Åbo Akademi
Title: Smoothness of martingale observables and generalized Feynman-Kac formulas
Abstract: In this talk I will explicate connections between three closely related concepts:
1) parabolic linear PDEs of the form G(x)f(x, t) + df(x,t)/dt +h(x,t)=0, where G(x) is a positive semi-definite second-order operator in the spatial variables;
2) Feynman-Kac formulas, representing, in some cases, solutions to boundary-value problems for (1) as conditional expectations in terms of an Ito process X_t, in the simplest case with the generator G(x) + d/dt;
3) martingale observables, i.e., in the simplest case functions f(x,t) such that f(X_t,t) is a local martingale.
Our main result is that, assuming only the classic Hörmander criterion on the Ito process X (no ellipticity, no boundedness of the diffusion coefficients, no infinite life-time), all its martingale observables are smooth. As a consequence, we also obtain a comparatively general Feynman-Kac type formula, that provides smooth solutions to boundary-value problems for (1), while allowing for degenerate diffusions, unbounded coefficients, as well as a spatial boundary, under very mild assumptions on boundary regularity. Another application (and the speaker's original motivation) comes from Schramm-Loewner evolutions, for which the result makes a certain Girsanov transform martingale accessible via Ito calculus.
Joint work with Lauri Viitasaari (Aalto U., Finland).
29 October 2025: Sampad Lahiry, KU Leuven
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5 November 2025:
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12 November 2025: Asbjørn Bækgaard Lauritsen, Université Paris-Dauphine
19 November 2025: Titus Lupu, Sorbonne Université
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26 November 2025: TBD
3 December 2025: Sylvain Chabredier, ENS Paris
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10 December 2025: Semyon Klevtsov, Strasbourg. NOTE: Unusual time: 10:15-11:15, Room 3721.
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