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Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

In 2009 a new direction in variational calculus was proposed, called Lagrangian multiform theory (also referred to as pluri-Lagrangian systems), which breaks with the conventional approach in a fundamental way: in this new theory the Lagrangian is no longer a simple function of the fields, but an extended object (a differential or difference p-form). Furthermore, the Lagrangian is not put in by hand, i.e. chosen on the basis of secondary considerations (such as requiring certain symmetries), but emerges itself as a solution of the principal variational equations. These equations come from varying both the fields (as in the conventional theory) as well as the hyper-surfaces over which the action is integrated in the space of independent variables. The theory forms unique departure from the standard picture, in that it forms the first least-action principle that merges variational calculus with the key integrability notion of 'multidimensional consistency' (which is the key property of integrable systems, comprising the class of remarkable model equations which allow for the coexistence of infinite families of equations on one and the same mathematical functions). The fast development of the theory in the last decade, establishing the basic principles of the classical theory, demonstrating the applications to integrable systems and making the first steps towards a quantum theory, make it very timely to have a meeting on this new subject. The ambition of this novel viewpoint on the least-action principle, possibly as a candidate for a new foundational principle of physics, compel to branch out to researchers working in fundamental physics.

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

The Langlands Programme as we now know it was framed as a research agenda in the late 1960s. At the same time that the Nobel Prize was being awarded to Murray Gell-Mann "for his contributions and discoveries concerning the classification of elementary particles and their interactions," the Langlands Program predicted that the elementary particles of arithmetic -- L-functions -- should be classified by automorphic representations of algebraic groups. One of the pillars of the Langlands Programme is a conjecture, known as the local Langlands Correspondence, which is crucial to attaching complete L-functions to automorphic representations. The local Langlands Correspondence is now a theorem for automorphic representations of quasisplit classical groups by the work of James Arthur, relying on the work of many mathematicians. Arthur packets play a key role in this recent work. This conference gathers together experts on Arthur packets over global and local fields to cross-pollinate ideas and work on open problems.

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

Vortex dynamics is at the heart of many unresolved problems in fluid mechanics and is also central to numerous applications in science and engineering. The goal of the proposed meeting is to survey the recent progress in this field focusing on applied mathematics aspects of both classical and emerging problems. We are planning to bring together about 40 researchers at different career stages working on various aspects of vortex dynamics, spanning applied mathematical analysis, scientific computing, physical modeling as well as scientific and engineering applications. A highlight of the workshop will be events designed to foster cross-fertilization between applied mathematics and different application areas.