|Date: Friday, February 02, 2018
Location: 3096 East Hall (3:10 PM to 4:00 PM)
Title: Invariant Theory and Hilbert's 14th Problem
Abstract: The 14th of Hilbert's 23 problems asks a simple question: given any subfield of the field of rational functions in n variables, is the subring of polynomials within that subfield finitely generated as a k-algebra? It also has the interesting status of being one of the Hilbert problems for which the answer is known to be "no". In this talk, we'll look at the historical context of invariant theory surrounding this problem, as well as its larger significance in algebraic geometry, and why Hilbert might have thought it was true.Then we'll show a couple of special cases in which it actually is true, and finally outline the counterexample, constructed by prolific counterexample constructor Masayoshi Nagata in 1959. This talk will be accessible to anyone who has taken 631.
Speaker: Will Dana