School of Mathematics

As first observed by Mazur and Mumford, there exists a deep analogy between 3-manifolds and number fields. In the 90s, Morishita expanded upon and delved deeper into these connections between low-dimensional topology and number fields. More recently, Minhyong Kim proposed that, in line with the aforementioned analogy, one should develop “arithmetic field theories” for number fields. Kim’s proposal invigorated interest in this area of study, leading to a plethora of new research directions. Examples include the work of Kim and collaborators, as well as connections to the Langlands program explored by Ben-Zvi—Sakellaridis—Venkatesh. The once-unexpected comparison between 3-manifolds and number fields is now proving fruitful, and it promises to illuminate number theory, potentially leading to significant breakthroughs.

This workshop will bring together experts and young researchers to further explore a field that is still largely unexplored. While the analogies are striking, we believe that the field has not yet seen its full potential. One of the goals of the workshop is to find new problems which can be attacked with ideas stemming from the analogy between number fields and 3-manifolds.

In recent years, the field of machine learning (ML) has seen tremendous progress, with many breakthroughs directly connected to the well-studied mathematical theory of Stochastic Differential Equations (SDEs). This increasingly fruitful relationship between SDEs and ML has produced several state-of-the-art innovations, ranging from Langevin algorithms in Bayesian learning to score-based diffusion models in computer vision.

This workshop aims to bring the SDE and ML communities closer together and “sow the seeds” for future interdisciplinary and impactful research. For example, we anticipate the following general themes will be explored:

•     SDE-inspired learning algorithms and architectures

•     Computational or learning-based algorithms for SDEs

•     Theoretical connections between SDEs and machine learning

•     Applications and areas of opportunity between disciplines

 Mathematicians and computer scientists (both established and early career) are encouraged to attend and, by embracing researchers with diverse interests, we hope to inspire new collaborations and directions for SDEs and ML.

The field of population genomics is one of the fastest growing areas of interdisciplinary research. It is the culmination of the developing relationship between big data, mathematics and biological understanding. The conference aims to address every facet of this emerging field through interdisciplinary collaboration. There is much recognition that the field of population genomics is multidisciplinary, and that many research groups are sparsely distributed throughout the UK. This conference aims to be a formal and structured setting, for postgraduate researchers, in which research can be discussed without the pressure of an overwhelming number of late stage career researchers being present.

This workshop aims to provide an opportunity for PhD students and postdocs to form new collaborations and generate new research in the areas of Extremal and Probabilistic, Geometric, and Structural Combinatorics.

Rewilding is a radical and sometimes controversial approach to ecosystem management which focuses on renewing ecosystem processes and enriching food webs of degraded ecosystems. It is distinguished from more traditional ecosystem restoration in a number of ways, including less predictable ecosystem dynamics, minimal human intervention in the long term, a willingness to embrace the emergence of novel ecosystems and a more inclusive relationship between people and nature.  In the context of rapidly changing environmental conditions, rewilding may often be the most pragmatic and powerful approach to restoring biodiversity and delivering improved ecosystem services (for example water purification, pollination, soil improvement, flood protection). The delivery of such services at large scale is seen as a key tool in adaptation to climate change and thus of direct benefit to humanity.
Rewilding is rapidly developing a scientifically grounded conceptual framework and it is crucial that mathematical and statistical concepts and applications are integrated at this early stage.  Despite the launching of a number of rewilding projects around the world, there has been a lack of quantitative protocols and therefore analytical rigour in testing for significant improvements in ecosystem service delivery and biodiversity gain.
The aim of ‘rewilding mathematics’ is to explore these issues by building new partnerships between the mathematical sciences and ecologists with expertise in rewilding. We hope that it will be a landmark in the formation of a scientific basis for rewilding.

HiGHS Workshop 2024

Kinetic theory is an area of mathematics which investigates systems that involve many elements using tools from Analysis of PDEs, Probability, and Numerical Analysis and Modelling. While originating in physical systems such as dilute gases, Kinetic Theory’s reach has expanded dramatically in recent decades to include biological, chemical, and even societal phenomena.

This ICMS workshop aims to bring together experts from various facets of Kinetic Theory to share their recent advances and discuss the future of the field. The workshop will also provide ample opportunities for early career researchers to present their research and engage with world renown experts in the field. 

The Many Facets of Kinetic Theory follows on the momentum generated by the INI-supported network, KineticNet which aims to facilitate cohesion, collaboration, and generate a sense of community between the different people working in the field of Kinetic Theory in the UK.

Please see induvial webpage links for further information.

SSBF 2024  - https://www.icms.org.uk/SSBF2024

SMC 2024 - https://www.icms.org.uk/SMC2024

A Mathematics for Humanity Workshop. This workshop will be centred on topics that lie in the intersection of mathematics and democracy. See webpage for full details and application form.

The aim of this workshop is to gather together experts from different subfields of additive combinatorics, to foster in-depth discussion of the legion of recent advances, and to explore avenues for future research.