75 results
Search Results
Now showing 1 - 10 of 75
- ItemAlgebraic K-theory and Motivic Cohomology(Zürich : EMS Publ. House, 2016) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, MarcAlgebraic $K$-theory and motivic cohomology have developed together over the last thirty years. Both of these theories rely on a mix of algebraic geometry and homotopy theory for their construction and development, and both have had particularly fruitful applications to problems of algebraic geometry, number theory and quadratic forms. The homotopy-theory aspect has been expanded significantly in recent years with the development of motivic homotopy theory and triangulated categories of motives, and $K$-theory has provided a guiding light for the development of non-homotopy invariant theories. 19 one-hour talks presented a wide range of latest results on many aspects of the theory and its applications.
- ItemMini-Workshop: Fast Solvers for Highly Oscillatory Problems(Zürich : EMS Publ. House, 2016) Börm, Steffen; Le Borne, Sabine; Martinsson, Per-GunnarThe efficient numerical solution of highly oscillatory problems is one of the grand challenges of Applied Mathematics with diverse applications across the natural sciences and engineering. This workshop brings together experts in domain based methods and integral equation methods to share novel ideas and to discuss challenges on the way to developing efficient solvers at high frequencies.
- ItemMini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations(Zürich : EMS Publ. House, 2016) Ehrlich, Philip; Kuhlmann, SalmaNew striking analogies between H. Hahn’s fields of generalised series with real coefficients, G. H. Hardy’s field of germs of real valued functions, and J. H. Conway’s field No of surreal numbers, have been lately discovered and exploited. The aim of the workshop was to bring quickly together experts and young researchers, to articulate and investigate current key questions and conjectures regarding these fields, and to explore emerging applications of this recent discovery.
- ItemAlgebraic Cobordism and Projective Homogeneous Varieties(Zürich : EMS Publ. House, 2016) Levine, Marc; Panin, Ivan; Vishik, AlexanderThe aim of this workshop was to bring together researchers in the theory of projective homogeneous varieties with researchers working on cohomology theories of algebraic varieties, so that the latter can learn about the needs in an area of successful applications of these abstract theories and the former can see the latest tools.
- ItemMini-Workshop: Topological Complexity and Related Topics(Zürich : EMS Publ. House, 2016) Lupton, Gregory; Vandembroucq, LucileTopological complexity is a numerical homotopy invariant of topological spaces, of Lusternik-Schnirelmann type, introduced by Farber and motivated by the motion planning problem from topological robotics. This mini-workshop assembled researchers interested in calculating the topological complexity and its many variants, with the aim of providing a snapshot of the current state of knowledge, and shaping directions of future research.
- ItemAnalytic Number Theory(Zürich : EMS Publ. House, 2016) Montgomery, Hugh L.; Vaughan, Robert C.; Wooley, Trevor D.Analytic number theory has flourished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject
- ItemMini-Workshop: Computations in the Cohomology of Arithmetic Groups(Zürich : EMS Publ. House, 2016) Elbaz-Vincent, Philippe; Ellis, GrahamExplicit calculations play an important role in the theoretical development of the cohomology of groups and its applications. It is becoming more common for such calculations to be derived with the aid of a computer. This mini-workshop assembled together experts on a diverse range of computational techniques relevant to calculations in the cohomology of arithmetic groups and applications in algebraic $K$-theory and number theory with a view to extending the scope of computer aided calculations in this area.
- ItemMini-Workshop: Applied Koopmanism(Zürich : EMS Publ. House, 2016) Mezic, Igor; Putinar, MihaiKoopman and Perron–Frobenius operators are linear operators that encapsulate dynamics of nonlinear dynamical systems without loss of information. This is accomplished by embedding the dynamics into a larger infinite-dimensional space where the focus of study is shifted from trajectory curves to measurement functions evaluated along trajectories and densities of trajectories evolving in time. Operator-theoretic approach to dynamics shares many features with an optimization technique: the Lasserre moment–sums-of-squares (SOS) hierarchies, which was developed for numerically solving non-convex optimization problems with semialgebraic data. This technique embeds the optimization problem into a larger primal semidefinite programming (SDP) problem consisting of measure optimization over the set of globally optimal solutions, where measures are manipulated through their truncated moment sequences. The dual SDP problem uses SOS representations to certify bounds on the global optimum. This workshop highlighted the common threads between the operator-theoretic dynamical systems and moment–SOS hierarchies in optimization and explored the future directions where the synergy of the two techniques could yield results in fluid dynamics, control theory, optimization, and spectral theory.
- ItemMini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry(Zürich : EMS Publ. House, 2016) Di Rocco, Sandra; Harbourne, Brian; Szemberg, TomaszWhile arrangements of hyperplanes have been studied in algebra, combinatorics and geometry for a long time, recent discoveries suggest that they (and more generally arrangements of nonlinear subvarieties) play an even more fundamental role in major problems in algebraic geometry than has yet been understood. The workshop brought into contact experts from commutative algebra and algebraic geometry working on these problems – it provided opportunities to get updated on the latest developments through talks of the participants, but also reserved time for working groups in which participants brainstormed ideas and insights in the context of high-intensity discussions aimed at initiating immediate progress on proposed problems, thereby setting the stage for on-going collaborations after the workshop.
- ItemArbeitsgemeinschaft: The Geometric Langlands Conjecture(Zürich : EMS Publ. House, 2016) Gaitsgory, Dennis; Scholze, Peter; Vilonen, KariThe Langlands program is a vast, loosely connected, collection of theorems and conjectures. At quite different ends, there is the geometric Langlands program, which deals with perverse sheaves on the stack of $G$-bundles on a smooth projective curve, and the local Langlands program over $p$-adic fields, which deals with the representation theory of $p$-adic groups. Recently, inspired by applications to p-adic Hodge theory, Fargues and Fontaine have associated with any $p$-adic field an object that behaves like a smooth projective curve. Fargues then suggested that one can interpret the geometric Langlands conjecture on this curve, to give a new approach towards the local Langlands program over $p$-adic fields.