Abstracts

10/15 (Harriet Pollatsek): I'm interested in special finite geometries called {\em symmetric designs} because a group contains a difference set if and only if there exists a companion symmetric design. Research on difference sets is mainly on the existence question: given a group, does it contain a difference set? So the existence question for symmetric designs looms large. The Bruck-Ryser-Chowla Theorem says that if a symmetric design with certain parameters exists, then a corresponding diophantine equation has a nontrivial solution. The proof is a nice tour of some number theory along with some matrix algebra (including a version of Witt's theorem). I'll define all these things, give some examples, and outline the proof of the Bruck-Ryser-Chowla Theorem.

10/22 (Eva Curry): Radix representations of numbers, such as base 10 or base 2 representations, can be generalized to higher dimensions, as well as to arbitrary lattices. Studying these representations leads to interesting questions at the intersection of ergodic number theory, fractal topology, wavelet theory, and analysis on fractals.

Details

We meet in Room 422, Clapp Laboratory

The Monday meetings are 12:20--1:10 unless otherwise stated.

Other possible times are: Monday after 4:05; Tuesday after 2:30 (though Math 140-2 goes to 3:55, also the number theory seminar meets 4:00 at Amherst); Wednesday after 2:30 (depending on department/faculty meetings); Thursday after 4:05 (depending on Umass colloquia).

(Website maintained by Alan Durfee)

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