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BEGIN:VEVENT
UID:news1413@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20221014T114957
DTSTART;TZID=Europe/Zurich:20221109T141500
SUMMARY:Seminar Analysis and Mathematical Physics: Paolo Bonicatto (Univers
 ity of Warwick)
DESCRIPTION:In the classical theory\, given a vector field $b$ on $\\mathbb
  R^d$\, one usually studies the transport/continuity equation drifted by $
 b$ looking for solutions in the class of functions (with certain integrabi
 lity) or at most in the class of measures. In this seminar I will talk abo
 ut recent efforts\, motivated by the modelling of defects in plastic mater
 ials\, aimed at extending the previous theory to the case when the unknown
  is instead a family of k-currents in $\\mathbb R^d$\, i.e. generalised $k
 $-dimensional surfaces. The resulting equation involves the Lie derivative
  $L_b$ of currents in direction $b$ and reads $\\partial_t T_t + L_b T_t =
  0$. In the first part of the talk I will briefly introduce this equation\
 , with special attention to its space-time formulation. I will then shift 
 the focus to some rectifiability questions and Rademacher-type results: gi
 ven a Lipschitz path of integral currents\, I will discuss the existence o
 f a “geometric derivative”\, namely a vector field advecting the curre
 nts. Joint work with G. Del Nin and F. Rindler (Warwick).
X-ALT-DESC:<p>In the classical theory\, given a vector field $b$ on $\\math
 bb R^d$\, one usually studies the transport/continuity equation drifted by
  $b$ looking for solutions in the class of functions (with certain integra
 bility) or at most in the class of measures. In this seminar I will talk a
 bout recent efforts\, motivated by the modelling of defects in plastic mat
 erials\, aimed at extending the previous theory to the case when the unkno
 wn is instead a family of k-currents in $\\mathbb R^d$\, i.e. generalised 
 $k$-dimensional surfaces. The resulting equation involves the Lie derivati
 ve $L_b$ of currents in direction $b$ and reads $\\partial_t T_t + L_b T_t
  = 0$. In the first part of the talk I will briefly introduce this equatio
 n\, with special attention to its space-time formulation. I will then shif
 t the focus to some rectifiability questions and Rademacher-type results: 
 given a Lipschitz path of integral currents\, I will discuss the existence
  of a “geometric derivative”\, namely a vector field advecting the cur
 rents. Joint work with G. Del Nin and F. Rindler (Warwick).</p>
DTEND;TZID=Europe/Zurich:20221109T160000
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