# Jerusalem Mathematics Colloquium

Thursday, 5th January 2006, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Alexandre Eremenko

(Purdue University)

"Polya's conjecture on zeros of successive
derivatives of real entire functions"

** Abstract: **
This talk is based on a joint work with Walter Bergweiler.
We prove Polya's conjecture of 1943:
For a real entire function of order greater than 2,
with finitely many non-real zeros, the number of non-real
zeros of the n-th derivative tends to infinity as n tends to
infinity.
We use the saddle point method and potential theory,
combined with the theory
of analytic functions with positive imaginary part
in the upper half-plane.

Light refreshments will be served in the faculty lounge at 3:30.

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