SCU Mathematics Colloquium Series Schedule
Unless noted otherwise, talks will be at 4:00pm Tuesdays. Room 103 O'Connor. There will be refreshments before all talks in O'Connor 31 starting around 3:45pm.
Title: Quadratic Forms that Represent Almost the Same Primes
Abstract: A prime p can be written as p = x^2 + 9y^2 for integers x,y if and only if it can be written p = x^2 + 12y^2. The primes that can be written this way are those of the form 12k+1 (for k a positive integer), e.g. 13 = 2^2 + 9(1^2) = 1^2 + 12(1^2). Are there any other examples of such pairs of quadratic forms? How often does this occur? We give an answer to this question, and in the process we introduce the algebraic number theory which explains the existence of such pairs.
Title: Untangling the 2-Dog Group
The speaker will discuss the solution of a problem suggested by his two research assistants, the dachshunds Fritz and Sasha. To wit, in what ways can two dogs entangle themselves and their walker during a stroll around the block? And, furthermore, how much of that entanglement can be resolved by countermoves on the part of the walker? The answer involves an infinite, nonabelian group--reminiscent of s Braid Groups--and an index-two subgroup. The speaker will give a complete description of these groups in terms of generators and relations; give a minimal presentation of the main group--with two generators and one relation; and show by group-theoretic means that the right hand t know what the left hand is doing.
Title:Complexity, Embodiment, and Language Learning
The question of how children learn the grammar of their native language(s) remains a hot topic. Forty years ago, Gold 's Theorem implied that it was impossible to learn grammar from only correct examples. Subsequent formal work involving complexity considerations suggests otherwise, but provides no plausible mechanism. Very recent research based on the explicit coupling of linguistic form and meaning does yield a theory of child language learning that appears to be consistent with all the known facts.
Title: Adventures of a would-be Enthernet Interface Programmer
This talk will recount several anecdotes (i.e., cautionary tales) describing what happened when an intrepid instructor offered an undergraduate course on programming a network-card. A few unsolved problems will be mentioned.
Title: Message Passing Algorithms for Marginalization
Last Updated: 7 November 2004