103 KAM Mathematical Colloquium

Abstract

Finding real roots of a polynomial is among the oldest and most fundamental problems in mathematics. The study of the average case (when the polynomial is chosen randomly from some ensemble) was already considered by Waring in the 17 century, and became a central topic in both probability and analysis following breakthrough works of Littlewood-Offord and Kac in the earlier 1940s.

In this talk, we first give a survey on this topic, discussing some central results and ideas. Next, we focus on recent developments (obtained jointly with Tao and many others) which shed new lights on several old problems and also raise new open questions.

O přednášejícím

Professor Van Vu se narodil v Hanoji. Studoval v Budapesti a Ph.D. ziskal na Yaleove univerzite (kde jeho skolitelem byl Laszlo Lovasz). Pak byl zamestnan v Microsoft Research, na University of California v San Diegu a na Rutgers University. Od roku 2011 je Percey F. Smith profesorem matematiky na Yaleove univerzite. Profesor Vu je prednim svetovym odbornikem v nekolika matematickych oborech: v kombinatorice, v pravdepodobnostnich metodach a v aditivni kombinatorice, se sirokym zaberem technik, ktere presahuji hranice jednotlivych oboru. S Terry Taem napsal knihu Additive Combinatorics a v roce 2007 vedl program na toto tema na IAS v Princetonu. Za svuj vyzkum Van Vu ziskal mnoha oceneni. Uvedeme jen Polyovu cenu (2008) a Fulkersonovu cenu (v roce 2012, spolu s A. Johanssonem a J. Kahnem). Prof. Vu prednesl zvanou prednasku na Mezinarodnim kongresu matematiku v Soulu (2014) a byl take "Medallion lecturer" na Svetovem kongresu matematiky a statistiky (2012). Jeho prazske kolokvium je dokladem sire a kvality jeho zajmu.