* Seuraavan viikon tapahtumat merkitty tähdellä
Konstantin Izyurov (University of Helsinki)
Bosonization of the critical Ising correlations
* Tuesday 19 November 2024, 10:15, M3 (M234)
I will explain an identity between scaling limits of the Ising correlations in arbitrary finitely connected planar domains, and correlations of a suitable version of a Gaussian free field, yielding explicit formulae for the former. The proof is based on (rigorously established) operator product expansions for the Ising and GFF correlation, and a limiting version of a classical identity between Szegö and Bergman kernel on Riemann surfaces. Joint work with Baran Bayraktaroglu, Tuomas Virtanen and Christian Webb.
Olavi Nevanlinna
Extracts from metric functional analysis
* Wednesday 20 November 2024, 10:15, M3 (M234)
We shall concentrate on metric compactification of Banach spaces, in order to highlight differences and similarities between metric and linear functional analysis.
We discuss weak convergences via metric functionals, indicate connections to invariant subspace problem, present a metric version of Eberlein-Shmulian theorem. As an example related to fixed point theorems we show a metric version of Markov-Kakutani theorem. The talk is based on discussions and work with Armando Gutiérrez.
Recommended non-technical reading:
Anders Karlsson, From linear to metric functional analysis, PNAS July 9, 2021.
Seminar on analysis and geometry
Vanni Noferini
What is a tropical root and what can it do for you?
* Thursday 21 November 2024, 11:00, M2 (M233)
Xavier Poncini (Aalto)
Transformer mechanistic interpretability
* Friday 22 November 2024, 14:30, M2 (M233)
The transformer architecture is the key algorithmic ingredient underlying modern large language models. Scaling laws suggest more capable models can be achieved by simply "stacking more layers", with resource limitations projected to bite only around 2030. Unfortunately, our understanding of these models is limited and is not scaling appropriately. Mechanistic interpretability is a nascent field that addresses this concern by reverse engineering algorithms and internal representations of neural networks. After giving a mathematical treatment of the transformer architecture, I will present an early success of the mechanistic interpretability approach -- the identification of so-called induction heads, which are responsible for a type of in-context learning exhibited by such models.
Dr. Olli Herrala (Aalto University)
A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development
Monday 25 November 2024, 15:15, Riihi (Y225a)
Further information
We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed approach, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio.
SAL Weekly Seminar
Lizao Ye
TBA
Tuesday 26 November 2024, 15:15, M2 (M233)
TBA
ADM seminar
Stanislav Hencl (Charles University, Prague)
Ball Evans approximation problem: Recent progress and open problems
Wednesday 27 November 2024, 10:15, M3 (M234)
In this talk we give a short overview about the Ball-Evans approximation problem, i.e. about the approximation of Sobolev homeomorphism by a sequence of diffeomorphisms (or piecewise affine homeomorphisms) and we recall the motivation for this problem. We show some recent planar results and counterexamples in higher dimensions, and we give a number of open problems connected to this problem and related fields. We concentrate in detail on the joint result with A. Pratelli [1] about the approximation on planar W1,1-homeomorphisms by a sequence of piecewise affine homeomorphisms.
Seminar on analysis and geometry
Hanz Cheng
Recovery of material parameters in induction motor rotors
Thursday 28 November 2024, 11:00, M2 (M233)
We discuss some numerical algorithms for recovering parameters in eigenvalue problems for linear elasticity of transversely isotropic materials. Specifically, the algorithms are used to recover the elastic constants of a rotor core. Numerical tests show that in the noiseless setup, two pairs of bending modes are sufficient for recovering one to four parameters accurately. To recover all five parameters that govern the elastic properties of induction motors accurately, we require three pairs of bending modes and one torsional mode. Moreover, we study the stability of the inversion method against multiplicative noise; for tests in which the data contained multiplicative noise of at most 1\%, we find that all parameters can be recovered with an error less than $10\%$.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Monday 09 December 2024, 09:15, M3 (M234)
Further information
Eric Schippers (University of Manitoba)
TBA
Tuesday 10 December 2024, 10:15, M3 (M234)
Anna-Mariya Otsetova
TBA
Wednesday 11 December 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Theo Elenius
TBA
Thursday 12 December 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
MSc (Tech) Leevi Olander
Mid-term review presentation
Wednesday 18 December 2024, 14:00, M2 (M233)
Mid-term review presentation by Leevi Olander
(exact title will be confirmed nearer the date)
Stochastic Sauna 2024
Workshop on Probability and Statistics
Thursday 19 December 2024, 09:45, M1 (M232)
Further information
See workshop homepage:
https://math.aalto.fi/en/research/stochastics/sauna2024/
Jonas Tölle
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Tuesday 07 January 2025, 10:15, M3 (M234)
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
ANTA Seminar / Hollanti et al.
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Thursday 09 January 2025, 10:15, M3 (M234)
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
ANTA Seminar / Hollanti et al.
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Monday 13 January 2025, 10:15, M3 (M234)
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
ANTA Seminar / Hollanti et al.
Andreas Rosen (University of Gothenburg)
TBA
Wednesday 15 January 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Wednesday 15 January 2025, 10:15, M134
We will begin this course by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
ANTA Seminar / Hollanti et al.
Prof. Guillermo Mantilla-Soler (National U. Colombia Medellin)
Seminar course (7.-17.1.): An introduction to Dirichlet's L-functions and a proof of Dirichlet's theorem of primes in arithmetic progressions
Friday 17 January 2025, 10:15, M3 (M234)
We will begin this course (MS-EV0030) by reviewing Euler's change of paradigm, with respect to Euclid, and his proof on infinitude of primes. Then, we will study the generalization made by Dirichlet, and will prove Dirichlet's theorem on arithmetic progression. Through the course we will learn about the development of L-functions, character theory and the beginning of the relation between Galois representations and certain complex functions.
There will be 5 sessions during 2 weeks. For students interested in credits: attendance gives 2 cr and more can be obtained (upon request) by completing further assignments. Sessions take place on Tue, Thu on the first week and Mon, Wed, Fri the second week, all at 10:15-12.
ANTA Seminar / Hollanti et al.
Prof Joni Virta (University of Turku)
Unsupervised linear discrimination using skewness
Wednesday 12 February 2025, 10:15, M237
It is known that, in Gaussian two-group separation, the optimally discriminating projection direction can be estimated without any knowledge on the group labels. In this presentation, we (a) motivate this estimation problem, and (b) gather several unsupervised estimators based on skewness and derive their limiting distributions. As one of our main results, we show that all affine equivariant estimators of the optimal direction have proportional asymptotic covariance matrices, making their comparison straightforward. We use simulations to verify our results and to inspect the finite-sample behaviors of the estimators.
Aalto Stochastics and Statistics Seminar / Leskelä
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Sivusta vastaa: webmaster-math [at] list [dot] aalto [dot] fi