April 29 (Monday) 4:00-6:00 pm Special event: Admission to candidacy
Speaker: Mithun Veettil (Binghamton)
Talk 1 (4:00-4:55)
Title: Hilbert's Irreducibility Theorem
Abstract: Hilbert's irreducibility theorem deals with the following problem: Let
f(t,x) be an irreducible polynomial in
K[t,x]. Then for which field
K is it true that there are infinitely many specializations
t↦t0∈K such that
f(t0,x) is irreducible in
K[x]? Surprisingly, it turns out that
Q and function fields have this property.
Talk 2 (5:00-5:55)
Title: Golomb Topology on a Domain
Abstract: Golomb topology on a domain is a generalization of arithmetic topology on
Z+, appearing in Furstenberg's proof of the infinitude of primes. This paves way for the otherwise rare examples of countably infinite connected Hausdorff spaces. Following this, I shall conclude with a homeomorphism problem of Golomb topology on Dedekind domains. This talk is based on the 2019 paper by Pete Clark, Noah Lebowitz-Lockard, and Paul Pollack
http://alpha.math.uga.edu/~pete/CLLP_November_30_2017.pdf