Sergei Yakovenko's blog: on Math and Teaching

Thursday, December 6, 2007

Seminar on Khovanskii-Varchenko theorem (I)

Filed under: research seminar — Sergei Yakovenko @ 5:54
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Alexandre N. (”Sasha”) Varchenko and Askold G. (”Asik”) Khovanskii, Moscow, August 2007, photo by D. Novikov We (D. Novikov and S.Y.)  launch a campaign “Learn Khovanskii–Varchenko Theorem“. A few (2-4) next weeks we will discuss in detail the proof of this remarkably simple but powerful result with a view to have a number of generalizations.

The two manuscripts (one in Russian, another in English) are available:

Time and location: Tuesdays, 16:00-18:00, Room 261 (unless otherwise announced).

The first meeting: Dec 11, 2007.

Fewnomial theory (S.Y.). This purely geometric theory starts with a multidimensional generalization of the Rolle theorem for several variables and allows to prove infinitely many both classical and new results starting from the Descartes’ rule.

If somebody has a scanned copy of the English original by Khovanskii, please post a link in comments.

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“Auxiliary Lesson” שעור עזר) #7) December 6, 2007

Invariant manifolds for hyperbolic maps. Complex hyperbolicity.

  1. Formal theory: cross-resonances.
  2. Hadamard-Perron theorem for holomorphisms. Contracting map principle reactivated.
  3. Hadamard-Perron theorem for vector fields. Complex hyperbolicity.
  4. Invariant hypernolic curve for saddle-nodes.
  5. Poincare resonances.
  6. Center manifolds: formal but non-analytic.

Reading: Section 7 from the book (printing disabled), Section 27 (parts A-C) from the book (printing disabled)

Disclaimer is as sadly relevant as before…

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