Tel Aviv University Several lectures by Professor Fedor Nazarov, Kent State University --------------------- Dear Colleagues, 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: <http://www.math.technion.ac.il/~techm/temp/20121228NAZA.pdf> ) 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! M.S. See also: <http://www.math.tau.ac.il/~ostrover/colloquium/colloq_31122012.html> 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 Abstract: 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 Sodin. Longer seminar! Note special time! Schreiber Building Room 309 from 14:30 to 16:00! --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> To see today's activities and other future and past activities go to <http://www.math.technion.ac.il/~techm/today.html> Announcement from: Misha Sodin <sodin@post.tau.ac.il> ----------