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- ItemAlgebraische Zahlentheorie(Zürich : EMS Publ. House, 2018) Sujatha, Ramdorai; Urban, Eric; Venjakob, OtmarThe origins of Algebraic Number Theory can be traced to over two centuries ago, wherein algebraic techniques are used to glean information about integers and rational numbers. It continues to be at the forefront of
- ItemAlgebraic K-theory(Zürich : EMS Publ. House, 2019) Hesselholt, Lars; Huber-Klawitter, Annette; Kerz, MoritzAlgebraic $K$-theory has seen a fruitful development during the last three years. Part of this recent progress was driven by the use of $\infty$-categories and related techniques originally developed in algebraic topology. On the other hand we have seen continuing progress based on motivic homotopy theory which has been an important theme in relation to algebraic $K$-theory for twenty years.
- 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.
- ItemAnalytic Number Theory(Zürich : EMS Publ. House, 2019) Matomäki, Kaisa; Vaughan, Robert C.; Wooley, Trevor D.Analytic number theory is a subject which is central to modern mathematics. There are many important unsolved problems which have stimulated a large amount of activity by many talented researchers. At least two of the Millennium Problems can be considered to be in this area. Moreover in recent years there has been very substantial progress on a number of these questions.
- ItemAlgebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (hybrid meeting)(Zürich : EMS Publ. House, 2020) Huybrechts, Daniel; Thomas, Richard; Xu, ChenyangThe talks at the workshop and the research done during the week focused on aspects of algebraic geometry in the broad sense. Special emphasis was put on hyperkähler manifolds and derived categories.
- ItemMini-Workshop: Degeneration Techniques in Representation Theory(Zürich : EMS Publ. House, 2019) Fourier, Ghislain; Lanini, MartinaModern Representation Theory has numerous applications in many mathematical areas such as algebraic geometry, combinatorics, convex geometry, mathematical physics, probability. Many of the object and problems of interest show up in a family. Degeneration techniques allow to study the properties of the whole family instead of concentrating on a single member. This idea has many incarnations in modern mathematics, including Newton-Okounkov bodies, tropical geometry, PBW degenerations, Hessenberg varieties. During the mini-workshop Degeneration Techniques in Representation Theory various sides of the existing applications of the degenerations techniques were discussed and several new possible directions were reported.
- ItemMini-Workshop: Asymptotic Invariants of Homogeneous Ideals(Zürich : EMS Publ. House, 2018) Cooper, Susan; Harbourne, Brian; Szpond, JustynaRecent decades have witnessed a shift in interest from isolated objects to families of objects and their limit behavior, both in algebraic geometry and in commutative algebra. A series of various invariants have been introduced in order to measure and capture asymptotic properties of various algebraic objects motivated by geometrical ideas. The major goals of this workshop were to refine these asymptotic ideas, to articulate unifying themes, and to identify the most promising new directions for study in the near future. We expect the ideas discussed and originated during this workshop to be poised to have a broad impact beyond the areas of algebraic geometry and commutative algebra.
- ItemMini-Workshop: (Anosov)$^3$ (hybrid meeting)(Zürich : EMS Publ. House, 2021) Delarue, Benjamin; Pozzetti, Beatrice; Weich, TobiasThree different active fields are subsumed under the keyword Anosov theory: Spectral theory of Anosov flows, dynamical rigidity of Anosov actions, and Anosov representations. In all three fields there have been dynamic developments and substantial breakthroughs in recent years. The mini-workshop brought together researchers from the three different communities and sparked a joint discussion of current ideas, common interests, and open problems.
- ItemMini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory(Zürich : EMS Publ. House, 2018) Manon, Christopher; Mixon, Dustin G.; Vinzant, CynthiaFrames are collections of vectors in a Hilbert space which have reconstruction properties similar to orthonormal bases and applications in areas such as signal and image processing, quantum information theory, quantization, compressed sensing, and phase retrieval. Further desirable properties of frames for robustness in these applications coincide with structures that have appeared independently in other areas of mathematics, such as special matroids, Gel’Fand-Zetlin polytopes, and combinatorial designs. Within the past few years, the desire to understand these structures has led to many new fruitful interactions between frame theory and fields in pure mathematics, such as algebraic and symplectic geometry, discrete geometry, algebraic combinatorics, combinatorial design theory, and algebraic number theory. These connections have led to the solutions of several open problems and are ripe for further exploration. The central goal of our mini-workshop was to attack open problems that were amenable to an interdisciplinary approach combining certain subfields of frame theory, geometry, and combinatorics.
- ItemMini-Workshop: Computational Optimization on Manifolds (online meeting)(Zürich : EMS Publ. House, 2020) Herzog, Roland; Steidl, GabrieleThe goal of the mini-workshop was to study the geometry, algorithms and applications of unconstrained and constrained optimization problems posed on Riemannian manifolds. Focus topics included the geometry of particular manifolds, the formulation and analysis of a number of application problems, as well as novel algorithms and their implementation.