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Isaac Newton Institute for Mathematical Sciences (INI)

A large collection of inverse problems involve using waves scattered or emitted from an object to image its interior or to determine some of its material properties. Applications including radar and microwave imaging, astronomy, sonar, ultrasound, and geophysics, may share many characteristics. These applications also cover a spectrum of problems and length scales from low to high frequency, near to far field, static to highly dynamic, and from imaging discrete isolated objects to the interior of a continuously varying medium. Through this spectrum, different computational and theoretical challenges in inverse problems will arise – and understanding the transition through regimes can also provide new insights in and of itself.

This workshop will put a spotlight on the mathematical similarities of Rich and Non-linear Tomography across these applications in order to catalyse rapid development of new tomographic methods. As part of a highly interdisciplinary programme, the aim is for real-world problems in these applications to motivate a breadth of theoretical and practical mathematical research challenges – from microlocal analysis through to Bayesian methods. It will also help to break down communication barriers between disciplines and applications.

Isaac Newton Institute for Mathematical Sciences (INI)

This workshop aims to showcase the most up-to-date developments in the theoretical and numerical treatment of wave scattering. The word canonical refers to wave scattering by simple obstacles. These include, but are not restricted to, infinite scatterers with a distinct geometric feature (half-planes, wedges, etc.) or simple smooth scatterers (cylinders, spheres, etc.). Canonical problems are excellent for developing innovative mathematical and numerical approaches and illustrating their strengths. The purpose of the workshop is to inspire participants to apply the advanced theoretical techniques presented to significant practical problems. It will bring together recognised international leaders and early career researchers to maximise the visibility of this theoretical work to the more applied community.

ICMS - International Centre for Mathematical Sciences

There is a history of fruitful links between low-dimensional topology and number theory, going back at least to Mazur's observation that primes in number rings can be viewed as analogues of knots in a 3-manifold. More recently, the introduction of arithmetic gauge theory by M. Kim and collaborators paves the way to further bring ideas from theoretical physics to bear on fundamental problems in number theory and arithmetic geometry. This conference aims to explore this exciting new direction, and the links between number theory, topology and physics in general, with a particular focus on the role played by gauge fields as a unifying framework.

Zahlentheorie, Arithmetik,    Geometrie und Topologie

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.

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.

Astronomie, Astrophysik und Kosmologie,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

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.