Welcome to the seminar page for the Vanderbilt number theory group. We have a vibrant group, currently consisting of Larry Rolen<\/a>, Andreas Mono<\/a>, \u00a0Michael Griffin<\/a>, \u00a0and\u00a0Eleanor McSpirit<\/a>.<\/p>\n During the pandemic, many previous talks were held on zoom, and many recordings of previous talks can be found on the seminar Youtube page:\u00a0https:\/\/www.youtube.com\/@vanderbiltnumbertheory6986\/videos<\/p>\n Info on talks from prior semesters can be found on the tabs above.<\/p>\n
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| <\/td>\n | \u00a0Upcoming Talks Fall 2024:<\/p>\n Date: October 18, 2024, 12:10 PM Central time (Stevenson 1310)<\/p>\n Speaker: Walter Bridges<\/strong> (University of North Texas)<\/p>\n The first problem concerns secondary terms in asymptotic equidistribution.\u00a0 For example, if $p(a,b,n)$ denotes the number of partitions of $n$ with parts congruent to $a$ modulo $b$, then it is easy to show that $p(a_1,b,n) \\sim p(a_2,b,n)$ as $n \\to \\infty$ for all $0\\leq a_1,a_2 < b$.\u00a0 On the other hand, the difference $p(a_1,b,n)-p(a_2,b,n)$ oscillates as $n \\to \\infty$ for any $a_1 \\neq a_2$.\u00a0 A new technique allows us to predict the oscillation for this and similar problems.<\/p>\n The second problem concerns zero attractors for sequences of partition polynomials.\u00a0 If the coefficients of the polynomial $P_n(\\zeta)$ count the number of partitions of $n$ into $m$ parts, then R. Stanley asked to identify the zero attractor of the sequence $P_n(\\zeta)$ as $n \\to \\infty$ – that is, the set of limit points of the zero sets of the $P_n(\\zeta)$.\u00a0 It was shown by Boyer and Goh that the zero attractor of $P_n(\\zeta)$ is a “Pac-Man” shaped curve in the unit disk.\u00a0 We prove a zero attractor for partition polynomials that count hook lengths; somewhat surprisingly, the zero attractor features isolated points.<\/p>\n This is joint work\u00a0with W. Craig, A. Folsom, J. Franke, T. Garnowski, J. Males and L. Rolen.<\/p>\n Date: October 21, 12 PM Central time (Buttrick- Room<\/span> 206)<\/p>\n Speaker: Hui Xue<\/strong> (Clemson University)<\/p>\n Date: November 5<\/p>\n Speaker: Eleanor McSpirit<\/strong> (Vanderbilt University)<\/p>\n Title\/Abstract: TBA<\/p>\n Date: November 21<\/p>\n Speaker:\u00a0Gene Kopp\u00a0<\/strong>(LSU)<\/p>\n Date:<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Welcome to the seminar page for the Vanderbilt number theory group. We have a vibrant group, currently consisting of Larry Rolen, Andreas Mono, \u00a0Michael Griffin, \u00a0and\u00a0Eleanor McSpirit. During the pandemic, many previous talks were held on zoom, and many recordings … Continue reading |