Status  Tentative 
Seminar Series  SEMCPHT 
Subjects  hepth 
Date  Tuesday 16 June 2020 
Time  11:00 
Institute  CPHT 
Seminar Room  Salle Louis Michel, CPHT, Ecole Polytechnique 
Speaker's Last Name  Oblak 
Speaker's First Name  Blagoje 
Speaker's Email Address  
Speaker's Institution  LPTHE 
Title  Virasoro Berry Phases in the KdV Equation 
Abstract  I consider a model of fluid particle motion given by the reconstructed KdV equation on a circle. For travelling waves that are "uniformizable" in a suitable sense, the map that governs stroboscopic motion can be derived analytically. The particle's drift velocity, then, is essentially the Poincaré rotation number of that map, and has a geometric origin: it is the sum of a dynamical phase, a geometric/Berry phase, and an "anomalous phase". The last two phases are universal, as they follow entirely from the underlying Virasoro group structure. The Berry phase, in particular, is produced by a sequence of adiabatic conformal transformations due to the moving wave profile, and was previously found in twodimensional conformal field theories. 
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