- 7.3. 11:15 Ethan Sussman (MIT): TBA – M2 (M233)
- 7.3. 10:15 Stephen Moore (Institute of Mathematics Polish Academy of Sciences): TBA – M2 (M233)
- 7.2. 10:15 Petri Laarne (University of Helsinki): Almost sure solution of nonlinear wave equation: from donut to plane – M2 (M233)
I discuss the recent preprint [arXiv:2211.16111] of Nikolay Barashkov and I, where we show the almost sure well-posedness of a deterministic nonlinear wave equation (cubic Klein-Gordon equation) on the plane. Here "almost sur" is in respect to the \\\\phi^4 quantum field theory. I briefly introduce the invariant measure argument and outline the solution on 2D torus due to Oh and Thomann. I then explain our main contributions: extension of periodic solutions to infinite volume, and a weaker result for nonlinear Schrödinger equation. The viewpoint is functional-analytic with a dash of probability.
- 31.1. 10:15 Kalle Koskinen (University of Helsinki): Infinite volume states of the mean-field spherical model in a random external field – M2 (M233)
One method of introducing external randomness to a Gibbs state, as opposed to the internal randomness of the Gibbs state itself, is to perturb the Hamiltonian with a term corresponding to the coupling of a random external field to the system. For the mean-field spherical model, the corresponding perturbed model can be exactly solved, in some sense, in the infinite volume limit. In this talk, we will introduce, motivate, and present some constructions and results concerning the so-called infinite volume metastases of the mean-field spherical model in a random external field. The aim of this talk is to present the general theory of disordered systems as it pertains to this particular model, and highlight the particular aspects of this model which lead to its curious behaviour as a disordered system. This talk is based on work in a recently accepted paper to appear in the Journal of Statistical Physics.
- 16.12. 11:00 Tuomas Tuukkanen (Princeton & Aalto): Fermionic Fock Spaces in Conformal Field Theory (MSc thesis presentation) – M3 (M234)
- 21.11. 11:00 Alex Karrila (Åbo Akademi): The phases of random Lipschitz functions on the honeycomb lattice – Y229a
- 3.11. 10:15 talk canceled / rescheduled to a later time: talk canceled / rescheduled to a later time –
- 27.10. 10:15 Ellen Powell (Durham University): Characterising the Gaussian free field – Y405
I will discuss recent approaches to characterising the Gaussian free field in the plane, and in higher dimensions. The talk will be based on joint work with Juhan Aru, Nathanael Berestycki, and Gourab Ray.
- 20.10. 10:15 Caroline Wormell (Sorbonne, Paris): Decay of correlations for conditional measures and some applications – Y228b
The forward evolution of chaotic systems notoriously washes out inexact information about their state. When advected by a chaotic system, physically relevant measures therefore often converge to some reference measure, usually the SRB measures. This property implies various important statistical behaviours of chaotic systems.
In this talk we discuss the behaviour of slices of these physical measures along smooth submanifolds that are reasonably generic (e.g. not stable or unstable manifolds). We give evidence that such conditional measures also have exponential convergence back to the full SRB measures, even though they lack the regularity usually required for this to occur (for example, they may be Cantor measures). Using Fourier dimension results, we will prove that CDoC holds in a class of generalised baker's maps, and we will give rigorous numerical evidence in its favour for some non-Markovian piecewise hyperbolic maps. CDoC naturally encodes the idea of long-term forecasting of systems using perfect partial observations, and appears key to a rigorous understanding of the emergence of linear response in high-dimensional systems.
- 13.10. 11:00 Augustin Lafay (Aalto): Geometrical lattice models, algebraic spiders and applications to random geometry – Y228b
- 6.10. 11:00 Mikhail Basok (University of Helsinki): Dimer model on Riemann surfaces and compactified free field – Y228b
We consider a random height function associated with the dimer model on a graph embedded into a Riemann surface. Given a sequence of such graphs approximating the surface in a certain sense we prove that the corresponding sequence of height functions converges to the compactified free field on the surface. To establish this result we follow approach developed by Dubédat: we introduce a family of observables of the model which can be expressed as determinants of discrete perturbed Cauchy-Riemann operators, we analyze the latter using Quillen curvature formula.