# Lectures, seminars and dissertations

* Dates within the next 7 days are marked by a star.

Leah Schätzler

**Existence of variational solutions for doubly nonlinear equations in noncylindrical domains**

*** Today * ** Wednesday 13 November 2024, 10:15, M3 (M234)

I will talk about the existence of variational solutions to doubly nonlinear parabolic PDEs in noncylindrical domains $E \subset \mathds{R}^n \times [0,\infty)$.
This setting arises from models where the underlying domain $E^t := \{ x \in \mathds{R}^n : (x,t) \in E \}$ changes in time.
The prototype of the considered PDEs is
$$
\partial_t \big( |u|^{q-1} u \big) - \operatorname{div}\big( |Du|^{p-2} Du \big) = 0
\quad\text{in } E
$$
with parameters $q \in (0,\infty)$ and $p \in (1,\infty)$, which combines the porous medium equation and the parabolic $p$-Laplacian.
The talk is based on joint work (in progress) with Christoph Scheven, Jarkko Siltakoski and Calvin Stanko.

Seminar on analysis and geometry

Yu Liu (Aalto University)

**Optimisation with neural network surrogate models embedded (Midterm review)**

*** Today * ** Wednesday 13 November 2024, 13:00, M3 (M234)

Aino Weckman

**Optimising emission reduction actions in organisations' climate work (MSc thesis presentation)**

*** ** Thursday 14 November 2024, 10:00, M2 (M233)

Joanna Bisch

**Model order reduction for parametric generalised EVPs**

*** ** Thursday 14 November 2024, 11:00, M2 (M233)

We look for approximate eigensolutions of the pencil $( A(\sigma),M)$ for several values of the $d$-dimensional parameter vector $\sigma$. We are interested in few of the smallest eigenvalues that lie in the spectral interval of interest $(0,\Lambda)$. Both matrices are assumed to be s.p.d for any admissible parameter vector. In addition, the matrix $A(\sigma)$ is assumed to be spectrally equivalent to an s.p.d. average matrix $\overline{A}$.
For this purpose we develop a Ritz method that uses the same subspace for any parameter value. The subspace is designed using the observation that any eigenvector can be split into two components. The first component belongs to an easily computable subspace. The second component is defined by a correction formula that is a $d+1$ dimensional analytic function. Accordingly, the Ritz space is defined using this splitting and polynomial interpolation of the second component.
We give estimates for the approximation error and illustrate the method by numerical examples. The advantage of our approach is that the analysis easily treats eigenvalue crossings that typically have posed technical challenges.

Numerical Analysis seminar

**Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)**

*** ** Friday 15 November 2024, 09:00, M3 (M234)

Further information

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

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

**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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