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- ItemLow-dimensional Topology(Zürich : EMS Publ. House, 2020) Moriah, Yoav; Purcell, Jessica; Schleimer, SaulThe workshop brought together experts from across all areas of low-dimensional topology, including knot theory, mapping class groups, three-manifolds and four-manifolds. In addition to the standard research talks we had five survey talks by Burton, Minsky, Powell, Reid, and Roberts leading to discussions of open problems. Furthermore we had three sessions of five-minute talks by a total of thirty-five participants.
- ItemMechanics of Materials: Towards Predictive Methods for Kinetics in Plasticity, Fracture, and Damage(Zürich : EMS Publ. House, 2020) McDowell, David L.; Müller, Stefan; Werner, Ewald A.The workshop dealt with current advances of computational methods, mathematics and continuum mechanics directed at thermodynamically consistent forms of constitutive equations for complex evolutionary phenomena in modern materials such as plasticity, fracture and damage. The main aspects addressed in presentations and discussions were multiphysical description of new materials, (visco)plasticity, fracture, damage, structural mechanics, mechanics of materials and dislocation dynamics.
- ItemComputational Inverse Problems for Partial Differential Equations (hybrid meeting)(Zürich : EMS Publ. House, 2020) Hohage, Thorsten; Kaltenbacher, BarbaraInverse problems in partial differential equations (PDEs) consist in reconstructing some part of a PDE such as a coefficient, a boundary condition, an initial condition, the shape of a domain, or a singularity from partial knowledge of solutions to the PDE. This has numerous applications in nondestructive testing, medical imaging, seismology, and optical imaging. Whereas classically mostly boundary or far field data of solutions to deterministic PDEs were considered, more recently also statistical properties of solutions to random PDEs have been studied. The study of numerical reconstruction methods of inverse problems in PDEs is at the interface of numerical analysis, PDE theory, functional analysis, statistics, optimization, and differential geometry. This workshop has mainly addressed five related topics of current interest: model reduction, control-based techniques in inverse problems, imaging with correlation data of waves, fractional diffusion, and model-based approaches using machine learning.
- ItemStochastic Processes under Constraints (hybrid meeting)(Zürich : EMS Publ. House, 2020) Kolb, Martin; Pène, Francoise; Wachtel, VitaliThe analysis of random processes under various constraints and conditions has been a central theme in the theory of stochastic processes, which links together several mathematical subdisciplines. The connection between potential theory and a certain type of conditioning of Markov processes via Doob's h-transform can be seen as a classical highlight. The last decades have seen further exciting and highly interesting developments which are related to the title of the workshop such as the analysis of persistence exponents for various classes of processes and various types of penalization problems. Many of these problems are rooted in questions from statistical mechanics. The workshop aims to investigate the topic stochastic processes under constraints from all these different perspectives.
- ItemEnveloping Algebras and Geometric Representation Theory (hybrid meeting)(Zürich : EMS Publ. House, 2021) Leclerc, Bernard; Varagnolo, MichaelaThe workshop brought together experts investigating algebraic Lie theory from the geometric and categorical viewpoints.
- ItemMATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations (hybrid meeting)(Zürich : EMS Publ. House, 2021) Guo, Zihua; Hassell, Andrew; Portal, Pierre; Po Lam Yung, CanberraThe consideration of wave propagation in inhomogeneous media or the modelling of nonlinear waves often requires the study of wave equations with low regularity data and/or coefficients. Several Australian-European collaborations have recently led to deeper analytical understanding of rough wave equations. This tandem workshop provided a platform for such collaborations and brought together early career researchers and leading experts in harmonic analysis, microlocal analysis and spectral theory. The workshop focused on collaboration and technical knowledge exchange on topics such as local smoothing, spectral multipliers, restriction estimates, Hardy spaces for Fourier integral operators, and nonlinear partial differential equations.
- ItemMathematical Advances in Geophysical Fluid Dynamics (online meeting)(Zürich : EMS Publ. House, 2020) Hieber, Matthias; Korn, Peter; Titi, Edriss S.This workshop on "Mathematical Advances in Geophysical Fluid Dynamics" was organized as an online seminar and addressed recent advances in analytical, modeling and computational studies of geophysical fluid models. Of particular interest were the contributions concerning modeling and computation of sea-ice models, well-posedness results for the primitive equations, internal waves for stratified flows and models for moist atmospheric dynamics including phase transitions.
- ItemDiscrete Geometry (hybrid meeting)(Zürich : EMS Publ. House, 2020) Goaoc, Xavier; Rote, GünterA number of important recent developments in various branches of discrete geometry were presented at the workshop, which took place in hybrid format due to a pandemic situation. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as topology, combinatorics, algebraic geometry or functional analysis. The open questions abound and many of the results presented were obtained by young researchers, confirming the great vitality of discrete geometry.
- ItemMini-Workshop: Superpotentials in Algebra and Geometry(Zürich : EMS Publ. House, 2020) González, Eduardo; Rietsch, Konstanze; Williams, LaurenMirror symmetry has been at the epicenter of many mathematical discoveries in the past twenty years. It was discovered by physicists in the setting of super conformal field theories (SCFTs) associated to closed string theory, mathematically described by $\sigma$-models. These $\sigma$-models turn out in two different ways: the A-model and the B-model. Physical considerations predict that deformations of the SCFT of either $\sigma$-model should be isomorphic. Thus the mirror symmetry conjecture states that the A-model of a particular Calabi-Yau space $X$ must be isomorphic to the B-model of its mirror $\check{X}$. Mirror symmetry has been extended beyond the Calabi-Yau setting, in particular to Fano varieties, using the so called Landau-Ginzburg models. That is a non-compact manifold equipped with a complex valued function called the \emph{superpotential}. In general, there is no clear recipe to construct the mirror for a given variety which demonstrates the need of joining mathematical forces from a wide range. The main aim of this Mini-Workshop was to bring together experts from the different communities (such as symplectic geometry and topology, the theory of cluster varieties, Lie theory and algebraic combinatorics) and to share the state of the art on superpotentials and explore connections between different constructions.
- ItemHomotopical Algebra and Higher Structures (hybrid meeting)(Zürich : EMS Publ. House, 2021) Lazarev, Andrey; Livernet, Muriel; Markl, MartinHomotopical algebra and higher category theory play an increasingly important role in pure mathematics, and higher methods have seen tremendous development in the last couple of decades. The talks delivered at the workshop described some of the latest progress in this area and applications to various problems of algebra, geometry, and combinatorics.