* Dates within the next 7 days are marked by a star.
Timo Takala
Preserving uniformity and doubling measure in sphericalization
* Wednesday 05 March 2025, 10:15, M2 (M233)
Note that the seminar is in M2 in this period!
Seminar on analysis and geometry
Duc Khuat (Aalto)
Midterm review: Optimality of Adaptive Sparse Grid Interpolation for Higher Order Uncertain Parameter PDEs
* Wednesday 05 March 2025, 13:30, M240
Numerical Analysis seminar
Thomas Karam (University of Oxford)
Adaptations of basic matrix rank properties to the ranks of tensors
* Thursday 06 March 2025, 14:15, Zoom and M2
This Zoom seminar is also watchable in M2!
Tensors are higher-dimensional generalisations of matrices, and likewise the main notion of complexity on matrices - their rank - may be extended to tensors. Unlike in the matrix case however, there is no single canonical notion of rank for tensors, and the most suitable notion often depends on the application that one has in mind. The most frequently used notion so far has been the tensor rank (hence its name), but several other notions and their applications have blossomed in recent years, such as the slice rank, partition rank, analytic rank, subrank, and geometric rank. Unlike their counterparts for the rank of matrices, many of the basic properties of the ranks of tensors are still not well understood. After reviewing the definitions of several of these rank notions, I will present a number of results of a type that arises in many cases when one attempts to generalise a basic property of the rank of matrices to these ranks of tensors: the naive extension of the original property fails, but it admits a rectification which is simultaneously not too complicated to state and in a spirit that is very close to that of the original property from the matrix case.
Link to Zoom: https://aalto.zoom.us/j/66860024175
Algebra & Discrete Mathematics (ADM) Seminar
Håkan Hedenmalm (KTH Stockholm)
Conformally invariant Gaussian analytic functions, holomorphic correlations, and operator symbols of contractions (FMS Colloquium)
* Thursday 06 March 2025, 16:15,
Further information
The classical Dirichlet space of holomorphic functions on the unit disk is invariant under Möbius transformations, except that it is equipped with a marked point where the functions vanish. Associated with such a Dirichlet space with a marked point, we get a Gaussian analytic function in a canonical fashion. Then, if we take two such Gaussian analytic functions, say with the same marked point at the origin, we consider the holomorphic correlation function of the two. It turns out to be given in terms a contraction on the area-L2 space on the disk. More precisely, we obtain the operator symbol of the contraction. Some contractions on L2 are perhaps more natural than others. For instance, we can consider the multiplication operator associated with a Beltrami coefficient μ. But we can also consider Grunsky operators, which are prominent in the theory of conformal mapping. We obtain a characterization of the operator symbols of Grunsky operators as solutions to a nonlinear wave equation. We also study the average growth of the L2 means of the operator of a general contraction.
Finnish Mathematical Society colloquium
Jinwoo Sung (Chicago)
A quasi-invariant group action on SLE loops
Monday 10 March 2025, 14:15, Y405
Conformal welding is an operation that encodes Jordan curves on the Riemann sphere in terms of circle homeomorphisms. Thus, composition defines a natural group action of circle homeomorphisms on Jordan curves. In this talk, I will discuss a CameronMartin type quasi-invariance result for the SLE loop measure under the right group action by WeilPetersson homeomorphisms. While this result was hinted by Carfagnini and Wang's identification of Loewner energy as the OnsagerMachlup action functional of the SLE loop measure, the group structure of SLE welding has been little understood previously.
Our proof is based on the characterization of the composition operator associated with WeilPetersson circle homeomorphisms using HilbertSchmidt operators and the description of the SLE loop measure in terms of the welding of two independent quantum disks by Ang, Holden, and Sun. This is joint work with Shuo Fan (Tsinghua University and IHES).
Dr. Ozgur Ceyhan (University of Luxembourg)
Byzantine Fault Tolerance and Mean Field Theory
Tuesday 11 March 2025, 15:15, A1 (A123)
The "Byzantine generals problem" is an allegory describing a distributed system aiming for consensus in the presence of unreliable/malicious elements. A widely known classical approach to Byzantine fault tolerance shows the impossibility of dealing with one-third or more faulty elements, i.e., only f-faulty elements are enough to corrupt a system with 3f or fewer components.
In this talk, I will overview fault tolerance in a toy model and examine it as a spin glass model, a magnetic state characterized by randomness in interactions in spin systems. Finally, I will discuss the threshold for faulty elements through a mean-field solution.
Giacomo Maletto (KTH)
TBA
Thursday 13 March 2025, 14:15, M2 (M233)
Algebra & Discrete Mathematics (ADM) Seminar
Prof. Marcus Greferath (University College Dublin/Aalto)
Some old and new ideas on noiseless and noisy group testing
Thursday 13 March 2025, 16:15, M3 (M234)
Group Testing is an area in information and communication sciences that is as well-established as Coding Theory and Cryptography. The author of this talk stumbled over this amazingly interesting topic during the recent COVID-19 pandemic and came to the moderately surprising observation that (non-adaptive) group testing in both the noiseless and the noisy (=error-correcting) case, may be considered as coding theory over the Boolean semi-field (1+1=1). Following this path, he discovered new and re-discovered known results of the theory that now allow for a presentation in a new skin. This talk will delve into the topic and show how Noiseless and Noisy Group Testing can be connected to Partially Ordered Sets, Residuation, Partial Linear Spaces, Configurations, Barbilian Spaces, and Block Designs, which gives raise to further applications of Finite Geometry and Order Theory.
ANTA Seminar / Hollanti et al.
Tuomas Kelomäki (Aalto)
TBA
Friday 21 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
Estibalitz Durand Cartagena (UNED, Madrid)
TBA
Wednesday 02 April 2025, 10:15, M2 (M233)
Seminar on analysis and geometry
Hana Ephremidze (Universität Bonn)
TBA
Thursday 03 April 2025, 14:15, M2 (M233)
Algebra & Discrete Mathematics (ADM) Seminar
Yoh Tanimoto (University of Rome Tor Vergata)
TBA
Tuesday 08 April 2025, 10:15, M3 (M234)
Jiasheng Lin (Institut de Mathématiques de Jussieu-Paris Rive Gauche)
TBA
Tuesday 15 April 2025, 10:15, M3 (M234)
Aleksis Koski
TBA
Wednesday 16 April 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
Aapo Pulkkinen
TBA
Wednesday 07 May 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
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