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Combinatorial Number Theory: Dr. Philip Wood, University of Wisconsin-Madison

Low-degree factors of random polynomials

Wednesday, September 27, 2017
  11:10 a.m.–Noon


Location: Surge Building 277*
  Parking Information

Category: Seminar

Description:

When can a random polynomial with integer coefficients be factored over the integers?  We all know that x^2 5x 6 = (x 3)(x 2), but is that kind of factoring the typical behavior, or is it instead very unusual?  Interestingly, though this question comes from algebra and number theory, this talk will discus how to study the question using tools from combinatorics and probability theory. We prove for a variety of models that it is very unlikely for a random polynomial with integer coefficients to have a low-degree factor—suggesting that, in fact, most integer polynomials do not factor.   The talk will discuss joint work with Sean O’Rourke and with Melanie Matchett Wood and also with undergraduates Christian Borst, Evan Boyd, Claire Brekken, and Samantha Solberg.



Additional Information: Math Seminars

Open to: General Public
Admission: Free
Sponsor: Mathematics

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