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- 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.
- 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.
- 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: Algebraic Tools for Solving the Yang–Baxter Equation(Zürich : EMS Publ. House, 2019) Lebed, Victoria; Rump, Wolfgang; Vendramin, LeandroThe workshop was focused on three facets of the interplay between set-theoretic solutions to the Yang--Baxter equation and classical algebraic structures (groups, monoids, algebras, lattices, racks etc.): structures used to construct new solutions; structures as invariants of solutions; and YBE as a source of structures with interesting properties.
- ItemMini-Workshop: Cohomology of Hopf Algebras and Tensor Categories(Zürich : EMS Publ. House, 2019) Witherspoon, Sarah; Zhang, JamesThe mini-workshop featured some open questions about the cohomology of Hopf algebras and tensor categories. Questions included whether the cohomology ring of a finite dimensional Hopf algebra or a finite tensor category is finitely generated, questions about corresponding geometric methods in representation theory, and questions about noetherian Hopf algebras. The workshop brought together mathematicians currently working on these and other open problems.
- ItemComputational Multiscale Methods(Zürich : EMS Publ. House, 2019) Peterseim, DanielMany physical processes in material sciences or geophysics are characterized by inherently complex interactions across a large range of non-separable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources by multiple orders of magnitude. The observation and prediction of physical phenomena from multiscale models, hence, requires insightful numerical multiscale techniques to adaptively select relevant scales and effectively represent unresolved scales. This workshop enhanced the development of such methods and the mathematics behind them so that the reliable and efficient numerical simulation of some challenging multiscale problems eventually becomes feasible in high performance computing environments.
- ItemArbeitsgemeinschaft: Elliptic Cohomology according to Lurie(Zürich : EMS Publ. House, 2019) Lurie, Jacob; Nikolaus, ThomasIn this collection we give an overview of Jacob Lurie's construction of elliptic cohomology and Lubin Tate theory. As opposed to the original construction by Goerss-Hopkins-Miller, which uses heavy obstruction theory, Lurie constructs these objects by a moduli problem in spectral algebraic geometry. A major part of this text is devoted to the foundations and background in higher algebra needed to set up this moduli problem (in the case of Lubin Tate theory) and prove that it is representable.
- ItemMini-Workshop: Seshadri Constants(Zürich : EMS Publ. House, 2019) Farnik, Lucja; Hanumanthu, Krishna; Huizenga, JackSeshadri constants were defined by Demailly around 30 years ago using the ampleness criterion of Seshadri. Demailly was interested in studying problems related to separation of jets of line bundles on projective varieties, specifically in the context of the well-known Fujita Conjecture. However, Seshadri constants turned out to be objects of fundamental importance in the study of positivity of linear series and many other areas. Consequently, in the past three decades, they have become a central object of study in numerous directions in algebraic geometry and commutative algebra. In this mini-workshop, we studied some of the most interesting current research problems concerning Seshadri constants. We expect that this exploration will help focus research on some of the most important questions in this area in the years to come.
- ItemTropical Geometry: new directions(Zürich : EMS Publ. House, 2019) Markwig, Hannah; Mikhalkin, Grigory; Shustin, EugeniiThe workshop "Tropical Geometry: New Directions" was devoted to a wide discussion and exchange of ideas between the leading experts representing various points of view on the subject, notably, to new phenomena that have opened themselves in the course of the last 4 years. This includes, in particular, refined enumerative geometry (using positive integer q-numbers instead of positive integer numbers), unexpected appearance of tropical curves in scaling limits of Abelian sandpile models, as well as a significant progress in more traditional areas of tropical research, such as tropical moduli spaces, tropical homology and tropical correspondence theorems.
- ItemNew Developments in Representation Theory of p-adic Groups(Zürich : EMS Publ. House, 2019) Gan, Wee Teck; Takeda, ShuichiroThe representation theory of $p$-adic groups has played an important role in the Langlands program. It has seen significant progress in the past two decades, including various instances of the local Langlands correspondences, construction of supercuspidal representations and questions on periods and distinction. This workshop explored new ideas and further developments in this subject.