Lectures will be held Mondays 10.15-12.00, room 3721 at KTH.
NEWS: Order of presentations given. Please contact me if you wish to present but are not on the list.
Lecture notes [UPDATED 20/2, 2024.] (Patch notes: contains lecture notes of everything except the SLE and GFF level line coupling, a proof in Section 4.4, as well as a minor argument in Section 4.1, marked by [ADD THIS]).
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Update on presentations:
Monday 26/2 and Tuesday 27/2, 10-12 and 13-15.
Session 1 (Monday 10-12): Dimers and random matrices
1. Teodor Bucht -- Ginibre ensemble and the GFF
2. Nedialko Bradinoff -- Random unitary matrices and Gaussian multiplicative chaos
3. Daniel Eriksson -- Dimer models and their connections to the GFF
Session 2 (Monday 13-15): Gaussian multiplicative chaos and related objects
1. Vlad Guskov -- Log-infinitely divisible multifractal processes
2. Ellen Krusell -- Brownian loops and random surfaces
3. Alireza Tavakoli -- Imaginary multiplicative chaos
Session 3 (Tuesday 10-12): GFF and its variants and properties
1. Hampus Nyberg -- Discrete GFF
2. Frida Fejne -- Level sets of the GFF: two-valued sets and first passage sets
3. Alice Brolin -- Metric graph GFF
Session 4 (Tuesday 13-15): Extra time if needed.
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3.
Presentations should be 30 minutes long. Below are links to Doodle, where you can fill in which times work for you. Note: check all, as there is a limit to the number of times I can put in one Doodle poll. (Doodle 1 has 6 times, Doodles 2 and 3 have 20 times each.)
Students that have not yet selected a topic can either select something from the list below or send me an email with their research interests, so that I can give suggestions.
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Possible subjects for presentation:
Complex multiplicative chaos
Imaginary multiplicative chaos
Imaginary multiplicative chaos determines the GFF (that is, while it is obvious that the imaginary GMC is a deterministic function of the GFF, the converse is also true)
Level sets of the GFF: two-valued sets and first passage sets
Discrete GFF and its various properties (extrema, etc)
Metric graph GFF and its convergence to the continuum GFF
Dimer models and their connections to the GFF
Critical (gamma = 2) LQG in general and how to construct it as a limit of subcritical (gamma < 2) LQG
LQG measure via level sets
LQG metric (axiomatic definition etc.)
Liouville conformal field theory
Some of the above may already be selected by students (see below). If you find them interesting anyway, email me and we can discuss if it is reasonable to have two presentations on the same subject.
Presentations reserved:
Ginibre ensemble and the GFF [Teodor Bucht]
Imaginary multiplicative chaos [Alireza Tavakoli]
Random unitary matrices and Gaussian multiplicative chaos [Nedialko Bradinoff]
Discrete GFF [Hampus Nyberg?]
Log-infinitely divisible multifractal processes [Vlad Guskov]
Dimer models and their connections to the GFF [Daniel Eriksson]
Level sets of the GFF: two-valued sets and first passage sets [Frida Fejne]
Content:
Lecture 1 (Sept. 4). Basics of Brownian motion and conformal mappings
Lecture 2 (Sept. 11). Gaussian free field: definition and convergence
Lecture 3 (Sept. 25). Gaussian free field: convergence and regularity
Lecture 4 (Oct. 2). Regularity and conformal invariance.
Lecture 5 (Oct. 9). Markov property of the GFF.
Lecture 6 (Oct. 16). Cameron-Martin space for the GFF. Circle-averages.
Lecture 7 (Oct. 23). Construction of LQG area measure. Convergence in the L^2 phase.
Lecture 8 (Oct. 30). Convergence in the L^2 phase and weak convergence for both phases.
Lecture 9 (Nov. 6). LQG-typical points and the L^1 phase.
Lecture 10 (Nov. 13). L^1 phase and conformal coordinate change.
Lecture 11 (Nov. 27). Conformal coordinate change. Free boundary GFF and boundary length.
Lecture 12 (Dec. 11). Free boundary GFF and boundary length.
Lecture 13 (Dec. 18). Local sets of the GFF. Level line coupling of SLE and GFF.