Abstract: I will take a careful look at some of our most primitive images of random phenomena; tossing a coin, shuffling cards and throwing a dart at the wall. Analysis and practical experiments show that, while approximate randomness is possible, usually we are lazy and things are quite far from random. This reflects on the use (and misuse) of "statistical models" and the basic philosophy of randomness.
Note: This talk will be accessible to undergraduates.
NB: A PDF version of this announcement (suitable for posting) is also available.
Abstract: When several large numbers are added in the usual way, carries accrue along the way. It turns out that the carries of "typical numbers" form a Markov Chain (Holte) with an "amazing" transition matrix. This in turn is intimately related to the usual method of shuffling cards and several other areas of mathematics. All of this is joint work with Jason Fulman.
Note: This talk will be accessible to undergraduate students.
Abstract: There is mathematics to be found in the analysis of adding even a single column of numbers. The carries along the way form a random process with fascinating properties. This makes a nice introduction to processes that occur in random matrix theory. The results extend to group extensions, Koszul algebras and many other areas. This is joint work with Alexi Borodin and Jason Fulman.
Note: This talk will be accessible to graduate students.