Maths seminars at HÍ

Mathematical seminars and Mathematical Colloquia at the University of Iceland 🇮🇸.

Announcements are sent on the mailing-list math-seminars 📬. You can subscribe by filling the form there.
The Mathematical Colloquium is usually on Thursday, 13:20 - 14:50. To suggest a speaker, get in touch.

Forthcoming

Past

18-8-2025, 13:20 (note the unusual day!) in room 155, VR-II
Javier Ramos Maravall (Universidad Autónoma de Madrid)
A Survey on Multilinear Kakeya and Restriction Estimates.
We will review certain multilinear estimates in the context of Kakeya and Fourier restriction theory, and explain why these estimates have recently played an important role in resolving some outstanding problems. We will also discuss how transversality can provide valuable insights for refining these estimates.

12-8-2025, 13:20 (note the unusual day!) in room 157, VR-II
David Þorsteinsson (KU Leuven)
Chiselling Algorithms for Computing Block Term Decompositions of Tensors.
Block term decomposition (BTD) is a unifying generalisation of the two most common tensor decompositions, namely canonical polyadic decomposition (CPD) and higher-order singular value decomposition (HOSVD). While BTD has found applications in various fields, including machine learning, optimisation, and blind source separation, all known algorithms for its computation were optimisation-based until recently. We will investigate the relationship between two recently proposed BTD algorithms, identifying both as examples of the general tensor sparsification framework newly presented by Brooksbank, Kassabov, & Wilson. Working from this shared theoretical basis, we show that algebraic and Lie-theoretic methods can be used to better interpret the underlying mechanism of the algorithms, and to derive necessary and sufficient conditions for uniqueness of the decompositions uncovered by these algorithms, improving on the bounds presented by the original authors.

22-7-2025, 10:00 (note the unusual day and time!) in room 158, VR-II
Boumediene Hamzi
Bridging Machine Learning, Dynamical Systems, and Algorithmic Information Theory: Insights from Sparse Kernel Flows, Poincaré Normal Forms and PDE Simplification.

In this talk, we explore how Machine Learning (ML) and Algorithmic Information Theory (AIT), though emerging from different traditions, can mutually inform one another in the following directions:

  • AIT for Kernel Methods: We investigate how AIT concepts inspire the design of kernels that integrate principles such as Kolmogorov complexity and Normalized Compression Distance (NCD). We propose a novel clustering method based on the Minimum Description Length (MDL) principle, implemented via K-means and Kernel Mean Embedding (KME). Additionally, we employ the Loss Rank Principle (LoRP) to learn optimal kernel parameters for Kernel Density Estimation (KDE), extending AIT-inspired techniques to flexible, nonparametric models.

  • Kernel Methods for AIT: We also demonstrate how kernel methods can approximate AIT measures such as NCD and Algorithmic Mutual Information (AMI), offering new tools for compression-based analysis. In particular, we show that the Hilbert-Schmidt Independence Criterion (HSIC) can be interpreted as an approximation to AMI, providing a robust theoretical basis for clustering and dependence measurement. Finally, we illustrate how techniques from ML and Dynamical Systems (DS)—including Sparse Kernel Flows, Poincaré Normal Forms, and PDE Simplification— can be reformulated through the lens of AIT.

Our results suggest that kernel methods are not just flexible tools in ML— they can serve as conceptual bridges across AIT, ML, and DS, leading to more unified and interpretable approaches to unsupervised learning, the analysis of dynamical systems, and model discovery.



22-7-2025, 11:00 (note the unusual day and time!) in room 158, VR-II
Jonghyeon Lee
Kernels Simplify Differential Equations.
Many nonlinear ordinary and partial differential equations are difficult or time-consuming to solve and analyse. It is unsurprising that transforming them to equations with ‘simpler’ behaviour is an active field of research; this includes mapping them to linear differential equations either locally or globally or approximating the solution with a relatively small number of basis functions that capture the essential elements of the behaviour. Kernel methods have considerable value in learning such transformations because they are typically linearity in time complexity as a function of the collocation points and have strong theoretical convergence results. In the first part of the talk, we introduce the idea of generalized kernel regression to learn the Cole-Hopf transformation, which maps the nonlinear Burgers equation to the linear equation, and a Poincare normal form of the Hopf bifurcation of the Brusselator. We then move on to discussing the applications of kernels to recover the eigenfunctions of the Koopman operator, which maps a nonlinear ODE to a dynamical system in infinite dimensions, and applications including Lyapunov functions and quasi-potential functions of stochastic systems. Finally, we conclude by proposing a new kernelized reduced order model (KROM) which uses an empirical kernel matrix to quickly solve nonlinear PDEs.

20-5-2025, 14:00 (note the unusual day and time!) in room 157, VR-II
Finnur Lárusson
Reconciling dichotomies in holomorphic dynamics.
I will describe recent joint work with Leandro Arosio (University of Rome, Tor Vergata) in holomorphic dynamics. We study the iteration of endomorphisms of complex manifolds of a fairly general kind, as well as the iteration of automorphisms for a class that is somewhat smaller, but still includes almost all linear algebraic groups.  The main goal of our work is to reconcile two fundamental dynamical dichotomies in these settings, “attracted vs. recurrent” and “calm vs. wild”.

15-5-2025, 13:20 in room 157, VR-II
Joseph Stanley Smith (RU)
Interactive theorem provers and mathematics.
Interactive theorem provers are gaining popularity and becoming increasingly powerful. In this talk, I will introduce what interactive theorem provers are and explain how they are being used in mathematics. I will also discuss the future of interactive theorem provers and the potential role artificial intelligence may play in their story.

10-4-2025, 13:20 in room 157, VR-II
Daniel Amankwah - HÍ
Scaling Limits of Random Series-Parallel Maps.
A finite graph embedded in the plane is called a series-parallel map if it can be constructed from a tree by iteratively subdividing and doubling edges. In this talk, we investigate the scaling limits of weighted random two-connected series-parallel maps with $n$ edges. Under suitable integrability conditions on the weights, we show that when distances are rescaled by a factor of $n^{-1/2}$, these maps converge in the Gromov–Hausdorff sense to a constant multiple of Aldous’ continuum random tree (CRT). The proof relies on a bijection between certain families of trees and series-parallel maps, allowing us to analyze geodesics using a Markov chain argument introduced by Curien, Haas, and Kortchemski (2015).

3-4-2025, 13:20 in room 157, VR-II
Eggert Briem - HÍ
Homomorphisms and isomorphisms of real commutative Banach algebras into C(X).
We give conditions, either on the dual space of an algebra A or on the norm of the algebra, which garantee the existence of homomorphism or isomorphism into C(X).

20-3-2025, 13:20 in room 158, VR-II
Pierre-Louis Curien
General coherence theorems on CW-complexes and polyhedral complexes.
We formulate and prove a coherence theorem on regular CW-complexes: 1-cells determine so-called cellular paths, and the theorem states that, if each path component of the complex is simply connected, any two such parallel paths (i.e. with the same end 0-cells) are provably equivalent by repeated transformations along 2-cell (this is in fact an « if and only if »). in other words, continuous homotopy agrees with a discrete and cellular version of homotopy.
A number of coherence theorems of the literature of category theory follow as a corollary, via a geometrical reading of the relevant data. For example, for monoidal categories (introduced by Mac Lane), the associated polytopes are called associahedra.
But most of those theorems were originally proved in a quite different way, using techniques now well-established in computer science under the name of rewriting systems.
We give a second strictly less general proof of geometrical coherence, applying to polyhedral complexes satisfying a certain condition (which is in particular satisfied by all polytopes), that relies on an orientation given by some generic vector, and that retains most of the features of Mac Lane’s original proof.
Finally, if we further restrict our attention to a class of polytopes called nestohedra, that have a nice combinatorial description, and to a certain subclass of those, we show that we get even closer to Mac Lane’s original proof. (Joint work with Guillaume Laplante-Anfossi).