Centre for Mathematics, University of Coimbra

Seminars

Discrepancy of stratified samples from partitions of the unit cube

2023-11-29

Speaker: Florian Pausinger (Queen's Univ. Belfast, Northern Ireland)

Jittered sampling is a classical way of generating structured random sets in a d-dimensional unit cube. Such sets combine the simplicity of fixed grids with certain probabilistic properties of sets of i.i.d uniformly distributed points and are thus a popular choice in numerical...

On the Dorfman connections of a Courant algebroid

2023-11-29

Speaker: Fani Petalidou (Aristotle Univ. Thessaloniki, Greece)

In this talk, after a short introduction to Courant algebroids and the related algebras defined by them, we will present the notion of Dorfman connection of a Courant algebroid on a vector bundle and some basic results about this. Then, we will present the role of such connections in...

Uniform completions via Cauchy sequences

2023-12-05

Speaker: Graham Manuell (CMUC, Univ. Coimbra)

While the usual approach using Cauchy sequences is not powerful enough to give completions of uniform spaces in general, if handled appropriately Cauchy sequences suffice for completions of uniform locales. We describe the construction and talk about how this approach might be applied more...

Induced congruences in \(\sigma\)-frames

2023-12-05

Speaker: Raquel Bernardes (CMUC, Univ. Coimbra)

Given a \( \sigma \)-space \( X \) and its lattice of open sets \( \mathcal{O}(X) \), we will study congruences on the \( \sigma \)-frame \( \mathcal{O}(X) \) representing the subspaces of \( X \) (referred to as induced congruences). We will show that when \( X \) is a \( T_D \) \(...

On derived functors of semimodule-valued functors

2023-12-06

Speaker: Alex Patchkoria (A. Razmadze Math. Institute of Tbilisi State Univ., Georgia)

A concept of a proper projective semimodule is introduced and proper projective resolutions are used to construct derived functors of additive functors from the category of cancellative semimodules to the category of cancellative semimodules. We investigate exactness of the long sequence of...

A brief introduction to Machine Learning: from the perceptron to large language models

2023-12-15

Speaker: Francisco Pereira (CISUC & Polytechnic Institute of Coimbra)

The field of machine learning has experienced a strong expansion in recent years, mostly driven by the development of new computational methods and the unprecedented surge in the volume of data accessible for processing and analysis. This dynamic has opened up new frontiers for exploration...