On the generalized Ramanujan and Arthur conjectures over function fields
Ciubotaru, D
Harris, M
Annals of Mathematics
Thu, 20 Nov 2025
12:00 -
12:30
Lecture Room 4
Thu, 27 Nov 2025
12:00 -
13:00
L3
Thu, 06 Nov 2025
17:00
17:00
L3
Composition of transseries, monotonicity, and analyticity
Vincenzo Mantova
(University of Leeds)
Abstract
Transseries generalise power series by including exponential and logarithmic
terms, if not more, and can be interpreted as germs of a non-standard Hardy
field by composition (for instance, on surreal numbers). I'll discuss a few
results that must 'obviously' be true, yet their proofs are not obvious: that
composition is monotonic in both arguments, once claimed but not proved by
Edgar for LE-series, that it satisfies a suitable Taylor theorem and that in
fact composition is 'analytic with large radius of convergence' (joint with V.
Bagayoko), something which appeared before in various special forms, but not
in full generality. I'll show how monotonicity and Taylor can be used to prove
some fairly general normalisation results for hyperbolic transseries (joint
with D. Peran, J.-P. Rolin, T. Servi).
Thu, 04 Dec 2025
17:00
17:00
L3
Sharply k-homogeneous actions on Fraïssé structures
Robert Sullivan
(Charles University, Prague)
Abstract
Given an action of a group G on a relational Fraïssé structure M, we call this action *sharply k-homogeneous* if, for each isomorphism f : A -> B of substructures of M of size k, there is exactly one element of G whose action extends f. This generalises the well-known notion of a sharply k-transitive action on a set, and was previously investigated by Cameron, Macpherson and Cherlin. I will discuss recent results with J. de la Nuez González which show that a wide variety of Fraïssé structures admit sharply k-homogeneous actions for k ≤ 3 by finitely generated virtually free groups. Our results also specialise to the case of sets, giving the first examples of finitely presented non-split infinite groups with sharply 2-transitive/sharply 3-transitive actions.
Thu, 27 Nov 2025
12:00 -
12:30
Lecture Room 4
Thu, 13 Nov 2025
12:00 -
12:30
Lecture Room 4
Thu, 06 Nov 2025
12:00 -
12:30
Lecture Room 4
Lanczos with compression for symmetric eigenvalue problems
Nian Shao
(École Polytechnique Fédérale de Lausanne - EPFL)
Abstract
The Lanczos method with implicit restarting is one of the most successful algorithms for computing a few eigenpairs of large-scale symmetric matrices.Despite its widespread use, the core idea of employing polynomial filtering for restarting has remained essentially unchanged for over two decades. In this talk, we introduce a novel compression strategy, termed Lanczos with compression, as an alternative to restarting. Unlike traditional restarting, Lanczos with compression sacrifices the Krylov subspace structure but preserves the subsequent Lanczos sequence. Our theoretical analysis shows that the compression introduces only a small error compared to the standard Lanczos method. This talk is based on joint work with Angelo A. Casulli (GSSI) and Daniel Kressner (EPFL).
Thu, 30 Oct 2025
12:00 -
12:30
Lecture Room 4
On the symmetry constraint and angular momentum conservation in mixed stress formulations
Umberto Zerbinati
(Mathematical Institute (University of Oxford))
Abstract
In the numerical simulation of incompressible flows and elastic materials, it is often desirable to design discretisation schemes that preserve key structural properties of the underlying physical model. In particular, the conservation of angular momentum plays a critical role in accurately capturing rotational effects, and is closely tied to the symmetry of the stress tensor. Classical formulations such as the Stokes equations or linear elasticity can exhibit significant discrepancies when this symmetry is weakly enforced or violated at the discrete level.
This work focuses on mixed finite element methods that impose the symmetry of the stress tensor strongly, thereby ensuring exact conservation of angular momentum in the absence of body torques and couple stresses. We systematically study the effect of this constraint in both incompressible Stokes flow and linear elasticity, including anisotropic settings inspired by liquid crystal polymer networks. Through a series of benchmark problems—ranging from rigid body motions to transversely isotropic materials—we demonstrate the advantages of angular-momentum-preserving discretisations, and contrast their performance with classical elements.
Our findings reveal that strong symmetry enforcement not only leads to more robust a priori error estimates and pressure-independent velocity approximations, but also more reliable physical predictions in scenarios where angular momentum conservation is critical.
These insights advocate for the broader adoption of structure-preserving methods in computational continuum mechanics, especially in applications sensitive to rotational invariants.
Mon, 10 Nov 2025
14:00 -
15:00
Lecture Room 3
From reinforcement learning to transfer learning and diffusion models, a (rough) differential equation perspective
Prof Xin Guo
(Berkeley, USA)
Abstract
Transfer learning is a machine learning technique that leverages knowledge acquired in one domain to improve learning in another, related task. It is a foundational method underlying the success of large language models (LLMs) such as GPT and BERT, which were initially trained for specific tasks. In this talk, I will demonstrate how reinforcement learning (RL), particularly continuous time RL, can benefit from incorporating transfer learning techniques, especially with respect to convergence analysis. I will also show how this analysis naturally yields a simple corollary concerning the stability of score-based generative diffusion models.
Based on joint work with Zijiu Lyu of UC Berkeley.