Author s : Justin Malestein, Louis Theran. Author s : Theran, Louis.
Author s : Pavle V. Author s : Grande, Francesco,Sanyal, Raman. Author s : Friedl, Tobias. Author s : Netzer, Tim,Sanyal, Raman.
Author s : Blythe, Duncan A. Author s : E. Author s : Adiprasito, Karim,Sanyal, Raman.
Lie Algebraic Methods in Integrable Systems
Author s : Dochtermann, Anton,Sanyal, Raman. Author s : Adiprasito, Karim,Benedetti, Bruno.
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Objective "Discrete structures appear throughout mathematics not only as approximations to continuous objects, but also as mathematical objects of their own right. The ""right"" discrete models should have analogous theory to the continuous limit, but often more transparent, more interesting structure, it ""tells you more"". The proposed project has the agenda to connect, and make substantial progress in, a number of interesting, but rather diverse instances for this, including - Convex Polytopes as models for linear, semi-definite and non-linear optimization problems, - Polyhedral Surfaces as models for differential geometry, including questions of discrete integrability, - Structured meshes as the ""right"" discrete structures for solving systems of partial differential equations with quality guarantees, - Triangulation models as they appear as models for space in quantum gravity.
In this simultaneous treatment of these topics we hope to capture connections and identify analogous and parallel structures in different parts of mathematics. This is a theory proposal, but a number of the core topics are suggested by applied research, as done e. In collaboration between individuals and groups with diverse mathematical expertise in Berlin, throughout Europe and beyond we are set to establish an additional ""theory backbone""; for applied research in Berlin.
Field of Science partial differential equations differential equations mathematics numerical analysis geometry. Activity type Higher or Secondary Education Establishments. Website Contact the organisation. Administrative Contact Sindy Kretschmer Ms. Status Closed project. Start date 1 July End date 30 June By combining methods from rigidity with intricate geometric constructions, Adiprasito and Ziegler proved that this is completely wrong for polyhedra in a very high-dimensional space.
This gives completely new insights into a problem first posed in by the famous geometer Jakob Steiner: Can all combinatorial types of polyhedra be realized such that all vertices lie on a sphere? In Focus Area III: Topological connectivity the point of view is more global — one looks, for example, at the space of all realizations of a combinatorial structure, or for coincidences that must always occur when complicated and highly-connected structures are drawn in the plane.
In this talk we shall discuss recently discovered algebraic structures of an operadic nature underlying stochastic calculus. This development nicely ties in with previous and upcoming results related to the algebraic structure stochastic calculus and stochastic differential equations have.
Volker Genz University of Cologne , "Crystal combinatorics and mirror symmetry of cluster varieties". We study the spectral measure of a geometric graph obtained from random points taken in a compact Riemannian manifold. In the special case of rank one manifolds, we compute the exact asymptotics of this spectrum, by using the spherical functions of the space.
In recent work with Schumann we have proven a conjecture of Naito-Sagaki giving a branching rule for the decomposition of the restriction of an irreducible representation of the special linear Lie algebra to the symplectic Lie algebra, therein embedded as the fixed-point set of the involution obtained by the folding of the corresponding Dyinkin diagram. This conjecture had been open for over ten years, and provides a new approach to branching rules for non-Levi subalgebras in terms of Littelmann paths. In this talk I will introduce the path model, explain the setting of the problem, our proof, and provide some examples of other non-Levi branching situations.
Skip to main content. Sunday, 22 January, to Friday, 27 January, This workshop will take place in Les Diablerets on January , Confirmed speakers: Minicourses: Reda Chhaibi Toulouse , "From random dynamics to combinatorial and geometric crystals" 1.
Sergey Fomin University of Michigan , "Quivers, clusters, and beyond" This mini-course will provide an elementary introduction to the basic theory of quiver mutations and cluster transformations, and review some of its applications. Roland Friedrich Saarland University , "Operadic Aspects of Stochastic Calculus" In this talk we shall discuss recently discovered algebraic structures of an operadic nature underlying stochastic calculus. Les Diablerets Switzerland. See map: Google Maps.
Related Integrable systems on Lie algebras and symmetric spaces
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