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ICMS - International Centre for Mathematical Sciences

The past several years have seen landmark progress in the interplay between representation theory, geometry and mathematical physics. Particularly notable have been Braverman, Finkelberg and Nakajima's definition of the Coulomb branch of an N=4 supersymmetric (SUSY) 3d gauge theory, and Mellit's proof of the Hausel-Letellier-Rodriguez-Villegas conjecture on the Poincar\'e polynomials of character varieties. The area has also seen exciting connections to other fields, such as significant progress on the conjectures of Gorsky, Negut and Rasmussen relating coherent sheaves on Hilbert schemes to Khovanov-Rozansky homology. The goal of this conference is to push forward research in areas at the nexus between these results: affine Springer theory, double affine Hecke algebras and Coulomb branches, creating new connections between experts, and exposing young mathematicians to this fast-progressing and exciting research area.

Isaac Newton Institute for Mathematical Sciences (INI)

Waves propagating in complex and random media are key to many areas of physics and engineering. These media include gases, emulsions, powders, porous and polycrystalline materials, to name just a few. The theoretical tools to understand wave phenomena can be applied to all linear waves, such as elastic and electromagnetic. Yet, the community and the tools used are quite disconnected. This workshop aims to bridge the gaps between us, better understand our connections, and share recent advances.

ICMS - International Centre for Mathematical Sciences

Quantum technology is a vibrant discipline of research with numerous applications in all areas of science. The particular interest for this workshop lies in the area of quantum information and the control of quantum systems. While traditionally these disciplines have worked with finite-dimensional mathematical models for the sake of simplicity and since it has appeared sufficient, ever-growing physical systems and progress in experimental realisations make it natural to ask what happens in infinite dimensions: in the end, for large systems, infinite-dimensional approximations can often simplify the description of the finite-dimensional system; moreover, many systems are simply not finite-dimensional and hence a reliable mathematical description is needed. In this research workshop we would like to look at a number of current research themes in the wider area of quantum information such as robust quantum control, long-term stability of quantum systems, entanglement breaking channels and the divisibility of channels. By gathering experts from these areas, this workshop will stimulate discussions and cross-pollination, to look at common structures and frameworks, and to study the transition from finite to infinite dimensions and convergence properties in all of them.

Quantum Mechanics and Quantum Information Theory,    Quantum Information Theory and Quantum Computing

ICMS - International Centre for Mathematical Sciences

This workshop aims to bring together experts on singularity formation from mathematical general relativity as well as from dispersive PDE to map out the current frontiers of the fields, stimulate the transfer of ideas, foster discussions and new collaborations, and to inspire the new generation of researchers to take up the challenges this field holds. On the side of general relativity the workshop focuses on the topics of naked singularities, singularities inside black holes, as well as cosmological singularities. On the side of dispersive PDE the workshop aims to discuss the characterisation of general singularities and blow-up dynamics.

Astronomy, Astrophysics and Cosmology,    Calculus, Differential Equations and Integration

Durham University (UK)

There has been significant recent progress in understanding deformations of integrable string sigma models, their relation to non-abelian and Poisson-Lie duality, and their possible AdS/CFT interpretation in terms of non-commutative field theory. These models can also be naturally recast in terms of double and exceptional field theory. Numerous interesting connections between these research areas are developing, promising to shed light on important open questions.

The International Symposium on Lattice Field Theory is an annual conference that attracts scientists from around the world. Originally started as a place for physicists to discuss recent developments in lattice gauge theory, the conference is now the largest of its type and has grown to cover strongly interacting phenomena in many contexts such as particle physics phenomenology and nuclear theory, as well as algorithms, code development and machine architectures.