Seminars and Colloquia by Series

Recurrent solutions and dynamics of turbulent flows

Series
Colloquia
Time
Thursday, September 22, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Predrag Cvitanović – School of Physics, Georgia Tech –

In the world of moderate, everyday turbulence of fluids flowing across planes and down pipes, a quiet revolution is taking place. Applied mathematicians can today compute 'exact coherent structures', i.e. numerically precise 3D, fully nonlinear Navier-Stokes solutions: unstable equilibria, traveling waves, and (relative) periodic orbits. Experiments carried out at Georgia Tech today yield measurements as detailed as the numerical simulations; our experimentalists measure 'exact coherent structures' and trace out their unstable manifolds. What emerges is a dynamical systems theory of low-Reynolds turbulence as a walk among sets of weakly unstable invariant solutions.

 

We take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the talk is aimed at anyone who had ever wondered why - if no cloud is ever seen twice - we know a cloud when we see one? And how do we turn that into mathematics?

Topological full groups

Series
Colloquia
Time
Tuesday, November 17, 2015 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Volodymyr Nekrashevych – Department of Mathematics, Texas A&M –

Please Note: This talk should interest people in Algebra, Dynamical Systems and Mathematical Physics in addition to Geometry and Topology. Volodia Nekrashevych will visit Atlanta from Sunday November 15th evening until Tuesday November 17th afternoon. He will be available for private talks on Monday November 14th after noon or on Tueasday morning before 10AM. Contact him directly by email or contact jeanbel@math.gatech.edu to schedule a meeting or to have a dinner with him.

Topological full groups are naturally associated with semigroups of local homeomorphisms: iterations of a single homeomorphism, holonomy groupoids of laminations, groupoids of local isomorphisms of quasiperiodic sets (for example Penrose tilings), etc. Some of these groups have interesting properties from the point of view of group theory. For instance, they provide first examples of amenable infinite simple finitely generated groups (by a result of K. Juschenko and N. Monod) and first examples of simple amenable groups of Burnside type. The full group of the Penrose tiling is another interesting example from the point of view of amenability.

Pages