Konferenzservice Mandl

Zusammenfassung: Probability theory and communications have developed hand in hand for about a century. The research challenges in the latter field (from telephone networks to wireless communications and the Internet) have spurred the development of the mathematical theory of stochastic processes, particularly in the theory of Markov processes, point processes, stochastic networks, stochastic geometry, stochastic calculus, information theory, and ergodic theory. Conversely, a large number of applications in communications would not have been possible without the development of stochastics. This program aims at the exposition of the latest developments in mathematical sciences lying on the boundary between stochastics and communications. Several workshops will take place during the program.

Zusammenfassung: The workshop organisers will gather about 40 mathematicians and physicists, and the scientific goal is to pursue an in-depth understanding of the interactions between Hodge theory on the one hand and QFT and string theory on the other. This includes work relating to supersymmetric gauge theories with the geometric Langlands conjecture, the use of mixed Hodge theory to study the renormalization group flow, and the noncommutative Hodge structure uncovered in the theory of charges in boundary TQFTs. In addition, there are plans to have a series of expository lectures on scale in QFT.

Zusammenfassung: In the last 25 years, a new mathematical approach, gyrokinetics, has been developed to treat low-frequency fluctuations in plasmas. In this approach, the fast orbital 'gyromotion' is averaged to produce kinetic equations for rings of charge. This is a mathematically rigorous description that is far more tractable than the full kinetic theory. Despite some practical successes in code-building and simulations, the mathematical properties and physical implications of gyrokinetics are insufficiently well understood. In space and astrophysics, the wide applicability and power of the gyrokinetic theory has yet to be fully recognised and exploited. To realise the benefits of this approach, it is essential that gyrokinetics be put on a firm mathematical and physical footing. This program will include several workshops.