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A bi-Hamiltonian nature of the Gaudin algebras

Let h be a direct sum of n copies of a simple Lie algebra g. In 1994, Feigin, Frenkel, and Reshetikhin constructed a large commutative subalgbera of the enveloping algebra U(h). This subalgebra, whic...

Diffusion of knowledge and the lottery society

Diffusion of knowledge models in macroeconomics describe the evolution of an interacting system of agents who perform individual Brownian motions (this is internal innovation) but also can jump on top...

Classical W-algebras, Drinfeld-Sokolov hierarchies and tau functions

Abstract:  Classical W-algebras W(g,O) are a family of Poisson vertex algebras associated to a simple Lie algebra g and a nilpotent orbit O. For (almost) every W(g,O) it is possible to construct ...

A win-win interaction between conformal geometry and PDEs

Abstract:  In this talk I will present, in a very general way, some of my most recent works. I will show examples of how to use conformal geometry to prove some properties, including uniqueness, ...

Modified Patankar-Runge-Kutta Methods: Introduction, Analysis and Numerical Applications

Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta schemes in a way to ens...

Solid Math 2024

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Adapting Boundary Conditions to Fit the Science

Dynamic boundary conditions play an essential role in acurately modeling complex physical interactions on the boundary. In this lecture we explain the role of dynamic boundary conditions in modeling d...