Wednesday, September 29, 2021
09/29/2021 - 4:00pm
The Putnam seminar meets every Wednesday from 4 to 5:30 in LOM 214. As always, everyone is warmly welcomed to come to hang out, learn more cool math, and meet folks. The seminar is casual, and folks can come and go as they like. See Pat Devlin’s webpage (and/or contact him) for more information. Folks can sign up for the mailing list here: https://forms.gle/nYPx72KVJxJcgLha8
09/29/2021 - 4:15pm
Abstract: There is a long history in number theory of finiteness theorems for Diophantine equations, assertions that a certain equation has only finitely many solutions. Even further, one can ask for effective finiteness theorems; a theorem is effective when it gives an upper bound for the size of any solution, reducing the problem of listing all solutions to a finite (in principle!) computation. Effective finiteness theorems, unfortunately, are very hard to come by. But there is an interesting interrmediate goal: theorems which give upper bounds for the number of solutions, or for the number of solutions subject to some conditions. I will give a general talk about the recent history of results of this kind, avoiding the technical guts of things and trying to give some general idea of strategies, finishing with a recent result of mine with Lawrence and Venkatesh, and a theorem of (2017 Yale Ph.D.) Vesselin Dimitrov with Gao and Habegger.