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## Seminars, Colloquia, and Conferences
Seminars |
## Seminars, Colloquia, and Conferences## 2012 Norbert Wiener Lectures## Jordan S. EllenbergProfessor of Mathematics, University of Wisconsin - MadisonNumber theorist, Novelist, Blogger, Political Columnist HOW TO COUNTPublic LectureThere Is No Such Thing As Public Opinion: Polls, Hanging Chads, and
Slime MoldsTuesday March 27, 6-7pm, Cabot Auditorium, Cabot Intercultural CenterReception: 7-8pm, Hall of Flags, Cabot Intercultural Center Abstract: Public opinion polls routinely show that large majorities of Americans support cutting spending and oppose raising taxes. But when lists of government programs are presented one by one, cuts in each program face majority opposition. What's going on here? A typical account is that Americans are irrational thinkers who want a free lunch, with low taxes and big government programs for all. The truth is more complicated. In fact, trying to put together the opinions of a heterogeneous population can lead to paradoxical results, even when the individuals involved are perfectly rational. The math that explains the puzzling polling on the budget -- first discovered by Condorcet in the midst of the French Revolution, and culminating in the Nobel-winning work of Kenneth Arrow -- also explains the vexingness of the Bush-Gore-Nader clash in Florida, and the apparently irrational decisions made by slime molds, primitive brainless creatures who biologists believe to be similar in certain respects to electorates. Undergraduate LecturePolynomials as NumbersWednesday March 28, 4:30-5:30pm, Braker 1 Abstract: It has been understood for a long time that there are deep analogies between polynomials and integers. By now, the study of that analogy has become a subject of its own. Ideas of number theory (like "prime numbers" and "zeta functions") carry over to polynomials, and ideas of polynomials (like "evaluating a polynomial \(P(x)\) at a value \(x\)" carry over to integers, and as a result our understanding of both areas is enriched and improved. I'll give an overview of this story, centering on counting questions: how many squarefree integers are there? How many squarefree polynomials are there? In what sense is the answer "the same"? ColloquiumArithmetic Counting Problems: The Topology of Numbers Thursday March 29, 4:30-5:30pm, Bromfield-Pearson 101 Preceded by tea in the Mathematics Conference Room. Abstract: The study of class groups of number fields is one of the oldest parts of algebraic number theory, and is still almost entirely mysterious. The Cohen-Lenstra conjectures propose to understand the probability distribution obeyed by the class group of a "random" number field. These conjectures are not quite what you might expect: for instance, the probability that the class group has order not divisible by \(3\) is not supposed to be \(2/3\), as you might expect, but rather the infinite product \((1-\frac 13)(1-\frac 19)(1-\frac 1{27})\)..... I will explain recent work of myself, Akshay Venkatesh, and Craig Westerland which proves a version of the Cohen-Lenstra conjecture over the ring of polynomials over a finite field. In this case, it turns out that the Cohen-Lenstra conjecture in number theory is in fact reflecting a beautiful conjecture about topology -- in particular, the topology of certain moduli spaces called Hurwitz spaces. I'll explain our progress towards this conjecture and speak more generally about the relationship between topology and counting problems coming from arithmetic. The Norbert Wiener Lectures were initially funded by an anonymous gift to the Department of Mathematics. All talks are free and open to the public. Directions to Bromfield-Pearson > Interactive Campus Maps > Previous Wiener Lectures > |
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