* Seuraavan viikon tapahtumat merkitty tähdellä
Léonie Papon (Durham)
Interface scaling limit for the critical planar Ising model perturbed by a magnetic field
* Tuesday 18 March 2025, 10:15, M3 (M234)
In this talk, I will consider the interface separating $+1$ and $-1$ spins in the critical planar Ising model with Dobrushin boundary conditions perturbed by an external magnetic field. I will prove that this interface has a scaling limit. This result holds when the Ising model is defined on a bounded and simply connected subgraph of $\delta \mathbb{Z}^2$, with $\delta >0$. I will show that if the scaling of the external field is of order $\delta^{15/8}$, then, as $\delta \to 0$, the interface converges in law to a random curve whose law is conformally covariant and absolutely continuous with respect to SLE$_3$. This limiting law is a massive version of SLE$_3$ in the sense of Makarov and Smirnov and I will give an explicit expression for its Radon-Nikodym derivative with respect to SLE$_3$. I will also prove that if the scaling of the external field is of order $\delta^{15/8}g_1(\delta)$ with $g_1(\delta)\to 0$, then the interface converges in law to SLE$_3$. In contrast, I will show that if the scaling of the external field is of order $\delta^{15/8}g_2(\delta)$ with $g_2(\delta) \to \infty$, then the interface degenerates to a boundary arc.
Tuomas Kelomäki (Aalto)
Khovanov homology: computations and obstructions
* Friday 21 March 2025, 10:15, M3 (M234)
Khovanov homology is a combinatorial homology theory which associates homology groups to knots and links. The theory is also functorial, which in this context means that smooth cobordisms between knots (surfaces in a 4-ball) get associated with homomorphisms between the Khovanov homologies.
The goal of this talk is to give an overview on smooth obstructions from Khovanov homology which allows one to tap into smooth/topological dichotomy of 4D with combinatorics. Additionally, some more recent combinatorial obstructions for tangle replacements are presented as well as some original methods for computing Khovanov homology.
Mikhail Basok (University of Helsinki)
TBA
Tuesday 25 March 2025, 10:15, M3 (M234)
Nageswari Shanmugalingam (University of Cincinnati)
TBA
Wednesday 26 March 2025, 10:15, M2 (M233)
Seminar on analysis and geometry
Vlad Margarint (University of North Carolina at Charlotte)
TBA
Thursday 27 March 2025, 11:15, M2 (M233)
Estibalitz Durand Cartagena (UNED, Madrid)
TBA
Wednesday 02 April 2025, 10:15, M2 (M233)
Seminar on analysis and geometry
Yoh Tanimoto (University of Rome Tor Vergata)
Wightman and Osterwalder-Schrader axioms for two-dimensional CFT
Tuesday 08 April 2025, 10:15, M3 (M234)
We give an overview of various approaches to quantum field theory in general and an algebraic framework specific to two-dimensional CFT, (full) vertex operator algebras. One can define correlation functions in a full vertex algebra under some regularity conditions. We show that, under unitarity, they satisfy the Osterwalder-Schrader axioms. We sketch how the Wightman fields are recovered. (joint with Maria Stella Adamo, Luca Giorgetti and Yuto Moriwaki)
Aleksis Koski
The internal Douglas condition
Wednesday 09 April 2025, 10:15, M3 (M234)
The Sobolev Jordan-Schoenflies problem asks a simple question: When does an embedding of the unit circle into the plane admit a homeomorphic extension in the Sobolev space W^1,p? Such a question is of basic interest in Nonlinear Elasticity, where Sobolev homeomorphisms describe an acceptable class of deformations between two elastic bodies. In a recent but important development, we have discovered an if and only if condition called the Internal Douglas Condition which gives a pleasingly complete answer to this problem in the planar case. In this talk, we will discuss this result and the related works leading up to it. This talk is based on joint work with Jani Onninen and Haiqing Xu.
Seminar on analysis and geometry
Hana Ephremidze (Universität Bonn)
TBA
Thursday 10 April 2025, 14:15, M2 (M233)
Algebra & Discrete Mathematics (ADM) Seminar
Prof. Iván Blanco Chacón (U. Alcalá)
TBA
Thursday 10 April 2025, 16:15, M3 (M234)
ANTA Seminar / Hollanti et al.
Jiasheng Lin (Institut de Mathématiques de Jussieu-Paris Rive Gauche)
TBA
Tuesday 15 April 2025, 10:15, M3 (M234)
Anna-Mariya Otsetova (Midterm review)
TBA
Friday 25 April 2025, 11:15, M3 (M234)
Aapo Pulkkinen
TBA
Wednesday 07 May 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
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