Sergei Yakovenko's blog: on Math and Teaching

Sunday, December 16, 2007

Seminar on Khovanskii-Varchenko theorem (II)

Topological properties of Abelian integrals

The second “learning in groups” meeting will be devoted to the study of the Gauss–Manin connexion in homology, which will ultimately result in a local representation of Abelian integrals as linear combinations of real powers and logarithms with analytic coefficients analytically depending on parameters.

This representation already suffices to produce local uniform bounds for the number of isolated zeros, as was explained on the previous Tuesday.

Recommended reading: Section 26 from the book (printing disabled), esp., subsections F and I-K.

Time and location: Tuesday Dec. 18, 2007, 14:00 (in place of the usual Geometry & Topology seminar time), Pekeris Room.

What it will be about:   😉
Katz formula

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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