The Trinity College Mathematics Colloquium meets periodically throughout the semester, usually on Thursdays from 12:15–1:15 pm in MECC 270. Talks are designed to be engaging and accessible to mathematicians across all fields. Talks are followed by lunch in the mathematics lounge.
Thursday February 12 - Felipe Ramírez (Wesleyan University)
Title: A Century Of Metric Dichotomies In Diophantine Approximation
Abstract:
The basic question of Diophantine approximation is: how well can you approximate irrational numbers by rational numbers? A classical theorem of Dirichlet (c. 1840) says that every real number x can be approximated by infinitely many rationals p/q to within a distance of 1/q^2. Since then, much of the research in Diophantine approximation has been animated by follow-up questions. Can 1/q^2 be replaced by some other function of q? Can we establish similar results if restrictions are placed on p/q, such as coprimality of p and q? Can we prove analogous results in higher-dimensional settings, like x in R^m? Very quickly, answers become metric/probabilistic. In 1924 (m=1) and 1926 (m>1), Khintchine proved the foundational result of metric Diophantine approximation, a zero-one law answering the aforementioned questions in a measure-theoretic way. I will discuss Khintchine's theorem and the follow-up questions to Khintchine's theorem that have animated much research over the last century, including some recent work in the setting where X is an n-by-m system of linear forms.
Thursday February 26 - Ann Trenk (Wellesley College)
Thursday March 12 - Jonathan Lindbloom (Dartmouth College)
Thursday March 26 - Keith Conrad (UConn)
Title: Patterns that don't last
Thursday April 2 - Han-Bom Moon (Fordham University)
If you are interested in giving a talk, please get in touch!