The pullback equation for differential forms

{\bf This seminar is at ground floor!}

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An important question in geometry and analysis is to know when two $k-$forms

$f$ and $g$ are equivalent. The problem is therefore to find a map $\varphi$

such that%

\[

\varphi^{\ast}\left( g\right) =f.

\]

We will mostly discuss the symplectic case $k=2$ and the case of volume forms

$k=n.$ We will give some results when $3\leq k\leq n-2,$ the case $k=n-1$ will

also be considered.

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The results have been obtained in collaboration with S. Bandyopadhyay, G.

Csato and O. Kneuss and can be found, in part, in the book below.\bigskip

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Csato G., Dacorogna B. et Kneuss O., \emph{The pullback equation for

differential forms}, Birkha\"{u}ser, PNLDE Series, New York, \textbf{83} (2012).