Giorgio Genovesi on Characterizing Regular Countable Second Countable Spaces in Second Order Arithmetic

Today's seminar talk is by Giorgio Genovesi from Leeds, who will be talking about countable second countable topological spaces in the context of reverse mathematics. 

Title: Characterizing Regular Countable Second Countable Spaces in Second Order Arithmetic

Abstract: Regular countable second countable (CSC) spaces admit rather nice characterizations and can easily be formalized in second order arithmetic. It is natural to ask what set existence axioms are needed to ensure regular CSC spaces remain nice. It turns out many theorems which characterize regular CSC are equivalent to one of the big five subsystems of second order arithmetic.

Hideki Tsuiki visiting Swansea

Professor Hideki Tsuiki from Kyoto University is visiting Swansea University from 22nd to 24th of January. Yesterday, he gave a talk on Coinductive View of Shadows of 3D Fractals. 

The talk did not only give insight into a fascinating area of research, but was also entertaining. You may want to check out some of Prof. Tsuiki's videos, e.g. https://www.youtube.com/watch?v=VsFD37f-2ck  

Elvira Mayordomo visiting Swansea

Elvira Mayordomo is visiting us this week. Today she gave a talk as a part of our seminar series.

Title: On information theory in geometric measure theory

Abstract

Effective and resource-bounded dimensions were defined by Lutz in 2003 and have proven to be useful and meaningful for quantitative analysis in the contexts of algorithmic randomness, computational complexity and fractal geometry.

The point-to-set principle (PSP) of J. Lutz and N. Lutz (2018) fully characterizes Hausdorff and packing dimensions in terms of effective dimensions in the Euclidean space, enabling effective dimensions to be used to answer open questions about fractal geometry, with already an interesting list of geometric measure theory results.

In this talk I will review the point-to-set principles focusing on recent applications and extensions and presenting open questions as well as further application opportunities.

Theory Away Day

Our Theory Research Group kicked off the year with an inspiring away day, providing the perfect opportunity to reconnect as a team after the festive break. It was a chance to reflect on past successes, align our goals, and spark fresh ideas to drive our work forward in 2025. Here's to an exciting year of collaboration and innovation!

 

Oliver Kullmann's talk

Today Oliver Kullmann will give a talk on Automated search for special Latin squares as a part of our Seminar series.

Abstract: 

Latin squares have been studied since the days of Euler. After some overview on the history and background, an effort for a complete enumeration of special types of Latin squares of order 13, by as completely automated means as possible (which is currently actually not possible), will be presented and evaluated. The main method here is Cube-and-Conquer, a kind of 2-stage SAT-solving (as invented by the presenter). Quite some fine-tuning of representation and choice of solver was needed, and will be discussed (at some high level)

Matteo Acclavio visiting Swansea

Next week's theory seminar will be given by Matteo Acclavio from the University of Sussex, who is visiting us for a few days. The topic will be a new logical framework for concurrent programs, abstract below.

Title: A new logical framework for concurrent programs

Abstract:
Designing logical frameworks to reason about the properties of concurrent programs while accurately capturing the essence of concurrency is a challenging task.
The main difficulties can be traced back to the syntactic constraints of the languages used for this purpose.

In this talk, I will present my ongoing line of research, which aims to provide a new computation-as-deduction paradigm for the study of concurrent programs.
In particular, I will show you a non-commutative logic where we can interpret proofs as computation trees for the pi-calculus, and use proof nets to provide canonical representations of these trees modulo interleaving concurrency.

This work is based on joint works with Giulia Manara and Fabrizio Montesi

Next week's Theory Seminar Series

Next week Troy will give a talk on Conceptualising Programming Language Semantics as a part of our seminar series.

Abstract:

Research on the semantics of programming language has tended towards formalisation. Following the successful deployment and myriad uses of formal syntax, many of those working on semantics assumed similar successes would be realised with formal semantics. 

The reality was different, and the resultant language specifications were large, complicated, technical artefacts. My previous historical research has studied those from a technical perspective. 

In this talk, I will explore the conceptual surroundings of the semantics, examining the use of metaphors, analogies, and illustrative language used to accompany or explain the formal documents.

It is early stage research and will focus primarily on picking examples from the history of semantics for deeper analysis in the future.

I will also present some philosophical frameworks I am considering for use in this analysis and begin to discuss how they might help us understand the topic.

This research will ultimately lead to a conference presentation and journal article next year, as well as forming a pilot study for a research grant proposal.