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- ItemField Arithmetic(Zürich : EMS Publ. House, 2018) Pop, Florian; Stix, JakobField Arithmetic studies the interrelation between arithmetic properties of fields and their absolute Galois groups. It is an interdisciplinary area that uses methods of algebraic number theory, commutative algebra, algebraic geometry, arithmetic geometry, finite and profinite groups, and nonarchimedean analysis. Some of the results are motivated by questions of model theory and used to establish results in (un-)decidability.
- ItemFlat Surfaces and Algebraic Curves(Zürich : EMS Publ. House, 2018) Möller, Martin; Zorich, AntonThis workshop brought together two distinct communities: “flat” geometers, studying the moduli of flat surfaces, and Teichmüller dynamics, and algebraic geometers studying the moduli space of curves. While both communities study similar or often the same objects, very different viewpoints and toolboxes lead to different questions being addressed, and different progress being made. The workshop sought to educate each community about the techniques of the other, and to foster communication between the two groups. One particular focus was enumerative geometry.
- ItemEmergence of Structures in Particle Systems: Mechanics, Analysis and Computation(Zürich : EMS Publ. House, 2018) Schmidt, Bernd; Stefanelli, Ulisse; Theil, FlorianThe meeting focused on the last advances in particle systems. The talks covered a broad range of topics, ranging from questions in crystallization and atomistic systems to mesoscopic models of defects to machine learning approaches and computational aspects.
- ItemDesign and Analysis of Infectious Disease Studies(Zürich : EMS Publ. House, 2018) Halloran, M. Elizabeth; O'Neill, PhilipThis was the fifth workshop on mathematical and statistical methods on the transmission of infectious diseases. Building on epidemiologic models which were the subject of earlier workshops, this workshop concentrated on disentangling who infected whom by analysing high-resolution genomic data of pathogens which were routinely collected during disease outbreaks. Following the trail of the small mutations which continuously occur in different places of the pathogens’ genomes, mathematical tools and computational algorithms were used to reconstruct transmission trees and contact networks.
- ItemToric Geometry(Zürich : EMS Publ. House, 2019) Maclagan, Diane; Schenck, HalToric geometry is a subfield of algebraic geometry with rich interactions with geometric combinatorics, and many other fields of mathematics. This workshop brought together a broad range of mathematicians interested in toric matters, and their generalizations and applications.
- ItemMini-Workshop: Operator Algebraic Quantum Groups(Zürich : EMS Publ. House, 2019) Caspers, Martijn; Weber, Moritz; Wysoczanska-Kula, AnnaThis mini-workshop brought together a rich and varied cross-section of young and active researchers working on operator algebraic aspects of quantum group theory. The primary goals of this meeting were to highlight the state-of-the-art results on the subject and to trigger new research by advertising some of the main open directions in operator algebraic quantum group theory: classification problems for C$^\ast$- and von Neumann algebras, relations to free/non-commutative probability, applications in quantum information theory, and the creation of new quantum groups and potential classification results for subclasses of quantum groups.
- ItemTopology of Arrangements and Representation Stability(Zürich : EMS Publ. House, 2018) Gaiffi, Giovanni; Jiménez Rolland, Rita; Suciu, AlexanderThe workshop “Topology of arrangements and representation stability” brought together two directions of research: the topology and geometry of hyperplane, toric and elliptic arrangements, and the homological and representation stability of configuration spaces and related families of spaces and discrete groups. The participants were mathematicians working at the interface between several very active areas of research in topology, geometry, algebra, representation theory, and combinatorics. The workshop provided a thorough overview of current developments, highlighted significant progress in the field, and fostered an increasing amount of interaction between specialists in areas of research.
- ItemDifferentialgeometrie im Grossen(Zürich : EMS Publ. House, 2019) Hamenstädt, Ursula; Kapovich, Michael; Weinkove, BenThe topics discussed at the meeting reflected current trends in global differential geometry. These topics included complex geometry, Einstein metrics, geometric flows, metric geometry and manifolds satisfying curvature bounds.
- ItemNon-commutative Geometry, Index Theory and Mathematical Physics(Zürich : EMS Publ. House, 2018) Nest, Ryszard; Schick, Thomas; Yu, GuoliangNon-commutative geometry today is a new but mature branch of mathematics shedding light on many other areas from number theory to operator algebras. In the 2018 meeting two of these connections were highlighted. For once, the applications to mathematical physics, in particular quantum field theory. Indeed, it was quantum theory which told us first that the world on small scales inherently is non-commutative. The second connection was to index theory with its applications in differential geometry. Here, non-commutative geometry provides the fine tools to obtain higher information.
- ItemMini-Workshop: Deep Learning and Inverse Problems(Zürich : EMS Publ. House, 2018) de Hoop, Maarten; Maaß, Peter; Schönlieb, CarolaMachine learning and in particular deep learning offer several data-driven methods to amend the typical shortcomings of purely analytical approaches. The mathematical research on these combined models is presently exploding on the experimental side but still lacking on the theoretical point of view. This workshop addresses the challenge of developing a solid mathematical theory for analyzing deep neural networks for inverse problems.