Tel Aviv University
Several lectures by
Professor Fedor Nazarov,
Kent State University
Prof. Fedor Nazarov will be visiting our School
from December 27 till January 4. During his stay
he will give a series of lectures.
Mini-course: Cauchy Integral and Rectifiability
Friday 28.12.2012, 10-13, Schreiber 106
Friday 04.01.2013, 10-13, Schreiber 106
A tentative plan of his lectures is accessible here:
Colloquium lecture: The ball is a local minimizer
of the optimal lattice packing density in $R^3$
Monday, 31.12.2012, 12:15-13:15, Schreiber 106
Horowitz seminar: Littlewood-Offord-Turan
estimate for the number of real zeroes of a random
polynomial with i.i.d. coefficients
Monday, 31.12.2012, 14:30-16:00, Schreiber 309
The abstract is appended below.
Analysis seminar: The Hormander-type proof of
the Bourgain-Milman theorem
Tuesday, 01.01.2013, 14-16, Schreiber 209
You are welcome!
Abstract for December 31.
Monday, December 31
Fedor Nazarov, Kent State University
Littlewood-Offord-Turan estimate for the number of real zeroes of a
random polynomial with i.i.d. coefficients
We show that the average number of real zeroes of any random polynomial
of degree $n$ with independent identically distributed coefficients does
not exceed $C\log^4 n$ with some absolute $C>0$. The proof follows
closely the paper by Littlewood and Offord published in 1942, where the
case of $\pm 1$ coefficients was considered. Our main deviation from
their scheme is using the Turan lemma from Turan's 1953 book in place of
the pointwise "anticoncentration" estimate used by Littlewood and
Offord. The result is on par with the original Littlewood-Offord bound
$C\log^2 n$ but still short of the would be optimal estimate $C\log n$,
which is widely believed to hold and whose validity is known for all
sufficiently regular distributions. This is a joint work with Mikhail
Longer seminar! Note special time!
Schreiber Building Room 309 from 14:30 to 16:00!
Technion Math Net-2 (TECHMATH2)
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