Monday, June 10
Monday, 8:30am-9:50am
Simon Thomas (Rutgers University),
Title: Measuring the relative complexity of mathematical problems
Abstract: In 1937, Reinhold Baer solved the classification problem for the additive subgroups of the rational numbers Q. Since then, despite the efforts of many mathematicians, no satisfactory classification has been found for the additive subgroups of Q ⊕ Q and it is natural to ask whether this problem is “genuinely more difficult”. In these talks, I will discuss a recently developed method for measuring the relative complexity of mathematical problems and will illustrate this approach with concrete problems from algebra and topology. In particular, I will explain why it would be a very bad idea to assign the classification problem for subgroups of Q⊕Q as the PhD thesis problem of a graduate student.
CurrentTrends-Thomas-2024.pdfCoffee break
Monday, 10:20am-11:40am
Sarah Peluse (University of Michigan),
Title: Tic-tac-toe and additive combinatorics
Abstract: I'll introduce some of the most important problems and results in additive combinatorics. We will begin by discussing the Hales--Jewett theorem, which has implications for the game of tic-tac-toe, as well as its density variant and various famous theorems implied by these results. The second talk will focus on open problems.
Lunch break
Monday, 2:00pm-3:20pm
Sarah Peluse (University of Michigan),
Title: Tic-tac-toe and additive combinatorics
Abstract: I'll introduce some of the most important problems and results in additive combinatorics. We will begin by discussing the Hales--Jewett theorem, which has implications for the game of tic-tac-toe, as well as its density variant and various famous theorems implied by these results. The second talk will focus on open problems.