Venue
Nordita, Stockholm, Sweden
Scope
The goal of this workshop is to gather researchers from the Stockholm and Helsinki areas, working in probability and mathematical physics.
Themes and preliminary program schedule
Thursday 19/11 | Seminar room 4205, Albano Building 3, Floor 4
13.15 - 14.00: Nedialko Bradinoff
14.10 - 14.55: Joona Oikarinen
14.55 - 15.20: Coffee break and discussion
15.20 - 16.05: Cillian Doherty
16.15 - 17.00: Antti Haimi
18.00: Dinner buffet at Proviant Albano (don't forget to reply to the invite!)
Friday 20/11 | Seminar room 4205, Albano Building 3, Floor 4
09.15 - 10.00: Aapo Pajala
10.10 - 10.55: Konstantin Zarembo
10.55 - 11.20: Coffee break and discussion
11.20 - 12.05: Tuomas Virtanen
12.15 - 13.00: Olof Rubin
Invited speakers, titles and abstracts
Konstantin Zarembo (SU/Nordita)
Title: Wilson loops from Fredholm determinants
Abstract: Wilson loops in the N=4 supersymmetric Yang-Mills theory are described by exponential correlators in the Hermitian matrix model and as such admit a remarkable Fredholm-determinant representation with an integrable kernel. Tracy-Widom theory described this Fredholm determinant as a solution of non-linear differential equations whose WKB expansion is equivalent to the 1/N expansion in the original matrix model. This approach has applications to non-perturbative effects in the super-Yang-Mills theory and to string theory via the holographic duality.
Antti Haimi (Åbo)
Title:
Abstract:
Cillian Doherty (KTH)
Title: On the removability properties of the graph of Brownian motion
Abstract: A compact subset K of the complex plane is said to be conformally removable if any homeomorphism from the plane to itself which is conformal on C\K, is automatically conformal on all of C. This property is true for example for points and line segments, but false for sets with non-empty interior, and in general there is no simple condition to determine whether a given set is removable or not. Sobolev or W^{1,p} removability is a related family of removability properties defined for each p in [1, ∞]. In certain cases, there is a link between removability and how “rough” the set K is. In particular, if K is the graph of a function, it is known that its Hölder continuity is related to its removability. We will present some results on the removability of the graph of a one-dimensional Brownian motion on an interval and show that it is almost surely not W^{1,p} removable for finite p, but is removable for p = ∞. This talk is based on joint work with Jason Miller.
Joona Oikarinen (Aalto)
Title: Gaussian multiplicative chaos and the infinite-volume limit of the Sinh—Gordon model
Abstract: I review recent progress (by several different groups) on rigorous understanding of the infinite-volume limit of the Sinh—Gordon model.
I also sketch how the behavior of the infinite-volume limit leads to an approach for deriving upper and lower bounds for small deviation probabilities for general Gaussian multiplicative chaos measures in all dimensions (this part is joint work with Nikolay Barashkov and Mo Dick Wong).
Olof Rubin (KTH)
Title: Chebyshev polynomials for Jordan arcs
Abstract: Given a compact set K ⊆ C containing infinitely many points, there is a unique monic polynomial of degree n that minimizes the uniform norm on K. This polynomial is called the Chebyshev polynomial of degree n for K. A classical problem is to understand how the geometric properties of K are reflected in the asymptotic behavior of the associated Chebyshev polynomials as n grows.
This picture is more or less complete when K consists of smooth Jordan curves that are mutually disjoint. Faber considered the case of a single analytic Jordan curve in 1920, and Widom considered several curves in 1969.
Chebyshev polynomials for Jordan arcs have proven more difficult to understand. Widom conjectured in 1969 that the interval should provide the model behavior in this setting. However, this conjecture was shown to be false by a counterexample involving arcs on the unit circle. Instead, the two sides of the arc turn out to play a crucial role. In this talk, I will explain recent progress toward a revised conjecture by Christiansen, Simon, and Zinchenko.
This is based on joint work with Benedikt Buchecker, Benjamin Eichinger and Aron Wennman.
Tuomas Virtanen (Helsinki)
Title: Operator Product Expansions in the sine-Gordon model
Abstract: The sine-Gordon model is a fundamental example of an interacting quantum field theory, defined as a perturbation of the Gaussian free field by a cosine interaction. Operator product expansions (OPEs) describe the local behavior of fields as their insertion points merge. In this talk I will explain how OPEs change when the interaction is switched on.
Below the first threshold of collapse (β < 4π), the singular terms in the OPEs of the derivative fields ∂φ and ¯∂φ can be identified explicitly: in addition to the free-field terms, the interaction contributes new singular terms whose coefficient field is the interaction density itself. The proof is based on an expansion in the coupling constant and on Onsager-type inequalities. This is joint work with A. Karrila and C. Webb.
I will also present the auto-formalization project of the main theorem in Lean 4, developed with Claude Code, and discuss future directions.
Nedialko Bradinoff (KTH)
Title:
Abstract:
Aapo Pajala (Aalto)
Title:
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Accommodation
Nordita has reserved a block of rooms at the following hotels:
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Elite Hotel Arcadia | 10 rooms for single use - For details and reserving a room, click here. Last day to book your room is 22nd of October.
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Biz Apartment Gärdet | 10 Studio medium (for single or double use) - For reserving a room, contact at reservations@bizapartment.se. You can inform the hotel that you are making a reservation for the workshop by referring the code “HSPM26”. Last day to book your room is 19th of October.
Nightly rate for studio medium - 1390 SEK/night incl. breakfast
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All reservations, payments, date adjustments and/or cancellations are to be made by the interested participant directly with the hotels.
Please be aware that scammers sometimes approach participants claiming to be able to provide accommodation and asking for credit card details. Do not give this information to them! If you are in any doubt about the legitimacy of an approach, please get in contact with the organizers.
Application/Registration
The workshop is free and open for anybody to attend, but please fill in the registration form.
Sponsored by:
