This study introduces a novel suite of historical large language models (LLMs) pre-trained specifically for accounting and finance, utilising a diverse set of major textual resources. The models are unique in that they are year-specific, spanning from 2007 to 2023, effectively eliminating look-ahead bias, a limitation present in other LLMs. Empirical analysis reveals that, in trading, these specialised models outperform much larger models, including the state-of-the-art LLaMA 1, 2, and 3, which are approximately 50 times their size. The findings are further validated through a range of robustness checks, confirming the superior performance of these LLMs.

The celebrated Splitting Theorem by Cheeger-Gromoll states that a manifold with non-negative Ricci curvature which contains a line is isometric to a product, where one of the factors is the real line. A related result was later proved by Kasue. He showed that a manifold with non-negative Ricci curvature and two mean convex boundary components, one of which is compact, is also isometric to a product. In this talk, I will present a variant of Kasue’s result based on joint work with Andrea Mondino. We consider manifolds with non-negative Ricci curvature and disconnected mean convex boundary. We show that if one boundary component is parabolic and convex, then the manifold is a product, where one of the factors is an interval of the real line. The result is an application of recently developed tools in synthetic geometry and exploits the interplay between Ricci curvature and optimal transport.

Jochen Koenigsmann’s Habilitation introduced a classification of fields elementarily characterised by their absolute Galois groups, including two conjecturally empty families. The emptiness of one of these families would follow from a Galois cohomological conjecture concerning radically closed fields formulated by Koenigsmann. A promising approach to resolving this conjecture involves the use of local-global principles in Galois cohomology. This talk examines the conceptual foundations of this method, highlights its relevance to Koenigsmann’s classification, and evaluates existing local-global principles with regard to their applicability to this conjecture.

Topological Quantum Field Theories (TQFTs) have been studied as mathematical toy models for quantum field theories in physics and are described by a functor out of some bordism category. In dimension 2, TQFTs are fully classified by Frobenius algebras. Homotopy Quantum Field Theories (HQFTs), introduced by Turaev, consider additional homotopy data to some target space X on the bordism categories. For homotopy 1-types Turaev also gives a classification via crossed G-Frobenius algebras, where G denotes the fundamental group of X.
In this talk we will introduce a multi-object generalization of Frobenius algebras called Frobenius categories and give a version of this classification theorem involving the fundamental groupoid. Further, we will give a classification theorem for HQFTs with target homotopy 2-types by considering crossed modules (joint work with Alexis Virelizier).