School of Mathematics

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1 week postgraduate summer school in mathematical general relativity.

Confirmed workshop topic titles are:

Traditional Research Groups:

Non-commutative (crepant) resolutions of singularities

Polynomial interpolation problems in higher dimensions

Proposed Research Groups:

Markov bases of toric ideals

Homological properties of neural ideals

Algebraic approaches to maximum likelihood thresholds for coloured Gaussian graphical models

Dialogue Groups:

Commutative algebra methods in topological data analysis

Singularity bias in polynomial neural networks

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Recent research has pointed to fundamental underlying relationships between each of three sub-fields of combinatorics: matroid theory, structural graph theory, and topological graph theory. While the connection between matroids and graphs is long-established, newer foundational links with topological graph theory are creating fresh opportunities for cross-disciplinary advances.

The purpose of this workshop is to provide the first dedicated forum to bring together experts in all these three fields to share techniques and approaches, and seed ongoing cross-disciplinary collaboration and advances.

This conference will bring together researchers working in mathematical general relativity, in Newtonian gravity, and on the Newtonian limit of general relativity. The unifying theme is the analysis of partial differential equations involved in those fields. The conference will provide a platform to share analytic methodology pertinent to each field and to learn about recent advances and open problems.

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Collective cell migration and pattern formation are entwined phenomena of immense fascination. Development, tissue repair and disease progression all involve coordination between cell movements, growth, and intercellular signalling processes. A better understanding of their interplay across different spatial and temporal scales will help improve diagnosis and treatment of diseases.

The aim of this workshop is to draw together state of the art techniques within (i) the biological mechanisms that underpin processes of collective cell migration and pattern formation, (ii) the mathematical and computational models used to study these phenomena, and (iii) the analytical tools that can be used to unlock core properties contained within these models.

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This workshop brings together cryptanalysts and designers to study these novel assumptions, aiming to validate or invalidate them.

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