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The International Centre for Mathematical Sciences (ICMS)

The interplay between geometry and physics has been a driving force for new developments in both mathematics and physics for a very long time. In the last two decades, higher category theory has become a fine contributor in this dialogue, providing many invaluable ideas and very useful heuristics. Organised in partnership with the Clay Mathematics Institute, this workshop aims to present the latest results in the application of (higher) geometry to theoretical physics and to foster new collaborations between mathematicians and theoretical physicists.

Isaac Newton Institute for Mathematical Sciences

Isaac Newton Institute for Mathematical Sciences, Cambridge

Automorphic Maass and non-holomorphic Eisenstein forms have (re)emerged recently as exciting tools in the analysis of two dimensional conformal field theories and also of the semiclassical near-singularity dynamics of black holes. These automorphic forms are naturally expressed in terms of L-functions, which brings out their deep connections to number theory. This workshop will bring together experts on automorphic L-functions with researchers interested in the novel applications of this mathematical structure to questions in fundamental physics.

The International Centre for Mathematical Sciences (ICMS)

The UK has always been at the forefront of, and has a reputation in, integrable systems research. It is an area that glues together topics in mathematical physics, analysis, algebra, geometry, applied mathematics and probability. Research in non-commutative integrable hierarchies has had a recent resurgence – they have many applications, including (eg.) in non-commutative nonlinear optics, and have strong links to string theory. The main themes outlined align with, and will be led, by recent research by the invitees. We propose a different than usual workshop format, along the lines of those held at Oberwolfach and the American Institute of Mathematics. Nominated experts give feeder presentations in their areas on successive mornings, outlining the current frontier of research and open problems. In the afternoons, these are followed up by discussion sessions and working groups who report back to the workshop as a whole at the end of the day. The workshop structure develops dynamically throughout the week. The organisers and the Scientific Advisory Group meet daily to set the agenda ahead, using feedback from the end-of-day reports and participants.

(i) Regularity and solutions; (ii) Non-commutativity, both in terms of non-Abelian (eg.\/ matrix) versions of classical integrable systems and in terms of non-commutative independent variables; and (iii) The connections of such systems to random matrix theory.

The International Centre for Mathematical Sciences (ICMS)

The String Math conference has been running annually since 2011, bringing together mathematicians and physicists who work at the interface between string theory, quantum field theory, and mathematics.

LHC physics, dark matter and dark energy, string theory, neutrino physics, precision measurements, non-accelerator probes of new physics, inflation, gravitational waves, cosmic tensions, and modified gravity.

Astronomy, Astrophysics and Cosmology,    High Energy Physics, Particles and Fields

Isaac Newton Institute for Mathematical Sciences, Cambridge

During the 20th century, interactions between geometers and theoretical physicists were revolutionary in both areas, leading to such unexpected developments as mirror symmetry and the impact of topological field theory on invariants of 4-manifolds. Another momentum is now developing around new connections between number theory and physics, mainly but not exclusively through the theory of automorphic forms. We have reached a time when contacts between number theorists and physicists have the potential for another revolution.

Number Theory, Arithmetic,    Geometry and Topology