Lectures, seminars and dissertations
* Dates within the next 7 days are marked by a star.
Augustin Lafay (Aalto)
Coulomb Gas representation of loop and web models
* Today * Tuesday 29 October 2024, 10:15, M3 (M234)
In this talk, I will present a non-rigorous method known in the physics litterature as Coulomb Gas. I will focus on the O(N) loop models and, if time permits, I will discuss its higher rank counterpart, the A_2 web models. The Coulomb Gas method identifies scaling limit of partition and correlation functions of the lattice models with quantities obtained from the compactified imaginary Liouville, and A_2 Toda, conformal field theories. From a mathematician point of view, it can be seen as a tool to obtain conjectures on, for instance, conformal weights of (the scaling limit of) lattice observables.
Petteri Kaski
A universal sequence of tensors for the asymptotic rank conjecture
* Today * Tuesday 29 October 2024, 15:15, M2 (M233)
The exponent $\sigma(T)$ of a tensor $T\in\mathbb{F}^d\otimes\mathbb{F}^d\otimes\mathbb{F}^d$ over a field $\mathbb{F}$ captures the base of the exponential growth rate of the tensor rank of $T$ under Kronecker powers. Tensor exponents are fundamental from the standpoint of algorithms and computational complexity theory; for example, the exponent $\omega$ of matrix multiplication can be characterized as $\omega=2\sigma(\mathrm{MM}_2)$, where $\mathrm{MM}_2\in\mathbb{F}^4\otimes\mathbb{F}^4\otimes\mathbb{F}^4$ is the tensor that represents $2\times 2$ matrix multiplication.
Our main result is an explicit construction of a sequence $\mathcal{U}_d$ of zero-one-valued tensors that is universal for the worst-case tensor exponent; more precisely, we show that $\sigma(\mathcal{U}_d)=\sigma(d)$ where $\sigma(d)=\sup_{T\in\mathbb{F}^d\otimes\mathbb{F}^d\otimes\mathbb{F}^d}\sigma(T)$. We also supply an explicit universal sequence $\mathcal{U}_\Delta$ localised to capture the worst-case exponent $\sigma(\Delta)$ of tensors with support contained in $\Delta\subseteq [d]\times[d]\times [d]$; by combining such sequences, we obtain a universal sequence $\mathcal{T}_d$ such that $\sigma(\mathcal{T}_d)=1$ holds if and only if Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)] holds for $d$. Finally, we show that the limit $\lim_{d\rightarrow\infty}\sigma(d)$ exists and can be captured as $\lim_{d\rightarrow\infty} \sigma(D_d)$ for an explicit sequence $(D_d)_{d=1}^\infty$ of tensors obtained by diagonalisation of the sequences $\mathcal{U}_d$. As our second result we relate the absence of polynomials of fixed degree vanishing on tensors of low rank, or more generally asymptotic rank, with upper bounds on the exponent $\sigma(d)$. Using this technique, one may bound asymptotic rank for all tensors of a given format, knowing enough specific tensors of low asymptotic rank.
Joint work with Mateusz Michałek (U. Konstanz).
arXiv: https://arxiv.org/abs/2404.06427
ADM seminar
Henri Lahdelma
Parabolic techniques for reverse Hölder classes (diploma thesis talk)
* Wednesday 30 October 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Prof. Raimo Hämäläinen (Aalto University)
Taking stock of behavioural OR: A review of behavioural studies with an intervention focus
* Monday 04 November 2024, 15:15, Riihi (Y225a)
Further information
We surveyed the relevant OR literature covering a 30-year period and developed a typology to organise the reviewed studies. The typology is comprised of four types of studies, each type representing a distinctive approach in terms of its assumptions about behaviour (determinist or voluntarist) and the research methodologies they use (variance or process). By categorising studies in this way, and drawing on research in associated cognate areas where relevant, eight empirically-generated knowledge themes emerge: intervention configurations, individual differences, model-driven support impacts, (un)intended use, model building process, engagement paths and strategies, facilitated modelling practice, and social dynamics. Each of these knowledge themes provides important insights into the behavioural factors that affect, or are affected by, OR-supported activity.
SAL Weekly Seminar
Julien Roussillon (Aalto)
TBA
Tuesday 05 November 2024, 10:15, M3 (M234)
Alex Takeda
TBA
Tuesday 05 November 2024, 15:15, M2 (M233)
TBA
ADM seminar
Jan van Neerven (Delft University of Technology)
Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices
Wednesday 06 November 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Mark Veraar (Delft University of Technology)
Stochastic PDEs in critical spaces
Wednesday 06 November 2024, 11:15, M3 (M234)
Seminar on analysis and geometry
Andrew Granville (Université de Montréal)
Extremal problems for multiplicative functions (Finnish Mathematical Society remote colloquium)
Wednesday 06 November 2024, 16:15, U6 (U149)
Nowadays there are two prominent approaches to questions about the distribution of prime numbers: Riemann's classical methods using zeros of zeta functions, and the recent pretentious theory of multiplicative functions (which is mostly a combination of older "ad hoc" techniques). In this talk we present the basics of this newer theory, how it relates closely to the theory of integral-delay equations and then focus on some recent work on extremal problems (in joint work of the speaker with Kevin Church, Kaisa Matomaki, Kannan Soundararajan and Daodao Yang).
Finnish Mathematical Society colloquium
Joona Oikarinen (Aalto)
TBA
Tuesday 12 November 2024, 10:15, M3 (M234)
Prof. Hiroshi Kawabi (Keio University/University of Oxford)
A graph discretized approximation of diffusions with drift and killing on a complete Riemannian manifold
Tuesday 12 November 2024, 15:15, M1 (M232)
In this talk, we present a graph discretized approximation scheme for diffusions with drift and killing on a complete Riemannian manifold M. More precisely, for a given Schrödinger operator with drift on M having the form A = −∆ − b + V, we introduce a family of discrete time random walks in the flow generated by the drift b with killing on a sequence of proximity graphs, which are constructed by partitions cutting M into small pieces. As a main result, we prove that the drifted Schrödinger semigroup {e^{−tA}}_{t≥0} is approximated by discrete semigroups generated by the family of random walks with a suitable scale change. This result gives a finite dimensional summation approximation of a Feynman-Kac type functional integral over M. Furthermore, when M is compact, we also obtain a quantitative error estimate of the convergence.
This talk is based on a joint work with Satoshi Ishiwata (Yamagata University) and the full paper can be found on https://doi.org/10.1007/s00208-024-02809-9 (online-first article in Mathematische Annalen).
Leah Schätzler
Existence of variational solutions for doubly nonlinear equations in noncylindrical domains
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)
Wednesday 13 November 2024, 13:00, M3 (M234)
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 15 November 2024, 09:00, M3 (M234)
Further information
Milo Orlich
TBA
Tuesday 19 November 2024, 15:15, M2 (M233)
TBA
ADM seminar
Olavi Nevanlinna
TBA
Wednesday 20 November 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Lizao Ye
TBA
Tuesday 26 November 2024, 15:15, M2 (M233)
TBA
ADM seminar
Theo Elenius
TBA
Wednesday 27 November 2024, 10:15, M3 (M234)
Seminar on analysis and geometry
Anna-Mariya Otsetova
TBA
Wednesday 11 December 2024, 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
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.
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.
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