Geometric Hydrodynamics
This course consists of two parts.
In the first part I introduce the geometric approach to fluid mechanics. This approach is based on description of fluid as a Hamiltonian mechanics on the manifold of the group of diffeomorphisms (Arnold,1966). I further discuss a spacetime covariant approach developed by Lichnerowitz (1941) and Carter (1979) and variational approach to (Hamilton principle) fluid mechanics.
In the second part I address applications of geometric approach to conservation laws and introduce a notion of anomalies.
Anomalies were initially discovered in quantum field theories in late 1960s. They soon became a foundational principle of quantum field theory. Very recent development has revealed that, quit remarkably, the anomalies of quantum field theory are integral part of fluid dynamics.
The course intended for graduate students and researchers with a background in mathematical physics and interest in geometry.
In the first part I introduce the geometric approach to fluid mechanics. This approach is based on description of fluid as a Hamiltonian mechanics on the manifold of the group of diffeomorphisms (Arnold,1966). I further discuss a spacetime covariant approach developed by Lichnerowitz (1941) and Carter (1979) and variational approach to (Hamilton principle) fluid mechanics.
In the second part I address applications of geometric approach to conservation laws and introduce a notion of anomalies.
Anomalies were initially discovered in quantum field theories in late 1960s. They soon became a foundational principle of quantum field theory. Very recent development has revealed that, quit remarkably, the anomalies of quantum field theory are integral part of fluid dynamics.
The course intended for graduate students and researchers with a background in mathematical physics and interest in geometry.
Lecturer
Date
19th September ~ 28th November, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Wednesday | 15:20 - 17:50 | A3-2-303 | ZOOM 05 | 293 812 9202 | BIMSA |
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Pavel Wiegmann received his PhD and Habilitation from the Landau Institute of Theoretical Physics in Moscow, where he worked as a Senior Researcher until 1994. Between 1990 and 1992, he held a similar position at Princeton University and the Institute for Advanced Study before joining the faculty at the University of Chicago, where he currently holds the title of Distinguished Service Professor at the Kadanoff Center for Theoretical Physics.
In 2004, he was an invited speaker at the International Congress of Mathematicians in Madrid. He received the Humboldt Prize (also known as the Humboldt Research Award) in 2002 and became a Fellow of the American Physical Society in 2003. That same year, he held the Kramers Chair at the Spinoza Institute in Utrecht, Netherlands, and in 2006, he held the Chaire Internationale Blaise Pascal in Île-de-France. He was named a Simons Foundation Fellow in 2015 and received the Onsager Prize from the American Physical Society in 2017.
Wiegmann's research interests span a wide range of topics, including: Theoretical Condensed Matter Physics (electronic physics in low dimensions, quantum magnetism, correlated electronic systems, quantum Hall effects, topological aspects of condensed matter, quantum field theories, and quantum liquids);Mathematical Physics (integrable models of quantum field theory and statistical mechanics, quantum groups, and representation theory);Quantum Field Theory (anomalies, conformal field theory, quantum gravity, stochastic geometry, and random matrix theory); Nonlinear Physics (stochastic aspects of pattern formation, interface dynamics, incommensurate systems, integrable aspects of nonlinear physics, and singularities in hydrodynamics and fluid mechanics).