Analysis and PDE seminar: Spring 2025
This is the page for the current semester of the seminars in Analysis and PDE at the University of Bergen. This semester seminars are held on Thursdays in the room Sigma or 贬箩酶谤苍别迟 at 12.15 until 14.00.
Main content
| Date | Speaker | Institution | Room | Title |
| 06.02.25 | UiB | A Fourier Basis听for the听Klein Bottle, with Examples | ||
| 13.02.25 | UiB | Canonical sub-Riemannian connections | ||
| 27.02.25 | UiB | Automorphisms of H-type Lie algebras and how they can be useful | ||
| 13.03.25 | UiB | Geometric Deep Learning and Building SO(3)-Equivariant Neural Networks for Learning Vector Fields on Spheres | ||
| 03.04.25 | University of W眉rzburg | Mean-Field Spin Glasses: From Parisi PDE to Machine Learning Landscapes | ||
| 10.04.25 | UiB | 听 | 听 |
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Detailed entries with abstracts
February 6th, Ren茅 Lang酶en
Date and time: Thursday, February 6, at 12.15
Place: 贬箩酶谤苍别迟
Speaker:听Ren茅 Lang酶en, Phd. student @ Department of Mathematics, UiB
Title: A Fourier Basis听for the听Klein Bottle, with Examples
Abstract:听TBA
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February 13th, Erlend Grong
Date and time: Thursday, February 13, at 12.15
Place: Sigma
Speaker:听Erlend Grong, Associate Professor @ Department of Mathematics, UiB
Title:听Canonical sub-Riemannian connections听
Abstract:听
The topic is sub-Riemannian manifold; manifolds where there we only have inner products defined in some of the directions.听
The objective is to be able to determine if two such manifolds are the same, i.e. does or does there not exist an isometry between two different sub-Riemannian manifolds
Similar to the Levi-Civita connection, we discuss a canonical way of defining a Cartan connection on sub-Riemannian manifolds, which gives us a canonical choice of complement and affine connections. We present a new construction, which, unlike the earlier normalization condition of Morimoto, these new connections do not generate extra holonomy when considering general loops compared to horizontal loops.听
These results are part of a preliminary work with Jan Slovak. Results are based on a previous work on chain complexes with Francesca Tripaldi.
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February 27th, Irina Markina
Date and time: Thursday, February 27, at 12.15
Place: Sigma
Speaker:听Irina Markina, Professor @ Department of Mathematics, UiB
Title:听Automorphisms of H-type Lie algebras and how they can be useful
Abstract:听H-type Lie algebras is a family of two-step (pseudo) metric Lie algebras with additional symmetries inherited from the Clifford algebras. We will describe the structure of the group of automorphisms of two-step Lie algebras and determine it precisely for H-type Lie algebras. Then, we outline two ongoing projects where the group of automorphisms and their subgroups of isometric automorphisms will be useful.听
This is a joint project with K.Furutani, Yu.Nikonorov, and I.Kath
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March 13th, Francesco Ballerin
Date and time: Thursday, March 13, at 12.15
Place: Sigma
Speaker:听Francesco Ballerin, PhD. student @ Department of Mathematics, UiB
Title:听Geometric Deep Learning and Building SO(3)-Equivariant Neural Networks for Learning Vector Fields on Spheres
Abstract:听
Geometric deep learning is the field of deep learning which studies how to encode symmetries in a neural network in order to guarantee that certain type of transformations (symmetries) do not impact the result of a neural network. In particular we are interested in vector fields on the sphere.
Analyzing vector fields on the sphere, such as wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector fields. In this work, we introduce a deep learning architecture that respects both symmetry types using novel techniques based on group convolutions in the 3-dimensional rotation group. This architecture is suitable for scalar and vector fields on the sphere as they can be described as equivariant signals on the 3-dimensional rotation group. Experiments show that our architecture achieves lower prediction and reconstruction error when tested on rotated data compared to both standard CNNs and spherical CNNs.
In this talk we introduce the field of geometric deep learning, with applications to sets, graphs, images, and manifolds, and then focus on the specific problem of how to treat vector fields on spheres.
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April 3rd, Anton Klimovsky
Date and time: Thursday, April 3., at 12.15
Place: Aud. 4, RFB
Speaker:听Anton Klimovsky, Senior Lecturer @ W眉rzburg University, Germany
Title:听Mean-Field Spin Glasses: From Parisi PDE to Machine Learning Landscapes
Abstract:听
Mean-field spin glasses, often epitomized by the Sherrington-Kirkpatrick(SK) model, are paradigmatic disordered systems characterized by complexenergy landscapes and non-trivial phase transitions. This presentationelucidates the theoretical framework pioneered by Giorgio Parisi --recipient of the 2021 Nobel Prize in Physics for his revolutionaryreplica symmetry breaking ansatz. We examine the Parisi variationalformula for the limiting free energy and its profound analyticalimplications, focusing on the Hamilton-Jacobi-Bellman equation (the"Parisi PDE") and its stochastic control interpretations. Themathematical rigour underlying these developments is furthered by MichelTalagrand鈥檚 seminal contributions to probability theory and functionalanalysis, recognized by the 2024 Abel Prize.Furthermore, we explore the remarkable connections between spin glasstheory and contemporary machine learning. Drawing inspiration from JohnHopfield鈥檚 influential neural network models and the foundational workof Geoffrey Hinton on Boltzmann machines -- both of whom were honouredwith the 2024 Nobel Prize in Physics -- we discuss how spin glassconcepts inform energy-based models and the challenges of optimizingnon-convex, high-dimensional landscapes.听This presentation underscoresthe interdisciplinary nature of mean-field spin glass theory and itsenduring relevance to rigorous mathematical analysis of complex systemsacross diverse scientific domains.
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Information
The seminars for the Analysis and PDE group at the University of Bergen are currently organized under the direction of Professor Irina Markina (irina.markina@uib.no).
