Speaker: Robbie Robinson, George Washington University

Title: Number theory and maps of the interval

Abstract: In 1924 Soichi Kakeya published a paper describing a far reaching generalization of both the decimal and continued fraction expansions of real numbers in the unit interval, but this work was largely forgotten in the chaos surrounding WWII. Similar results were later independently obtained by Bissinger (1944), Everett (1946), Renyi (1957) and Parry (1964). In particular, Renyi and Parry introduced dynamics to the subject, in the form of maps of the interval. This dynamical point of view unified the subject, which remains active to this day. In this talk we survey the area, mentioning (in addition to those names above) contributions of Lagrange (1798), Gauss (c 1800), Gelfond (1959), Rohlin (1961), Schmidt (1980), Adler & Flatto (1984) and others.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491