MEETINGS: Tuesdays and Thursdays during summer semester at 4:00 pm.
Here is the Zoom link.
The seminar's main goal is to expose culturally ambitious participants to some mathematical notions not taught in standard courses. These topics form an important part of mathematical folklore, and may prove useful for doing research and enhancing teaching.
Lectures will be given mostly by graduate and undergraduate student participants. See the archived topics below.
Title: What is Arrow's Impossibility Theorem?
Abstract: Consider an election where voters are asked to rank each of three candidates. Is there a “good” way to choose a winner? A famous result in social choice theory, Arrow’s impossibility theorem, tells us that the answer is no for a particular definition of “good”: A system satisfying certain conditions will always produce a dictator. Curiously, the generalization of this question to an infinite electorate quickly leads us into the world of ultrafilters. In this talk we will formulate Arrow’s theorem and give an elementary proof before introducing the ultrafilter perspective and investigating if an infinite electorate really eliminates our dictator.
Title: What is the limit of a sequence of graphs?
Abstract: Graph theory finds applications in many areas of mathematics, as well as physics, computer science, and many other disciplines. But what happens when the graphs under consideration get very large? Within the past 20 years, a few limit theories have been developed, with the aim of approximating features of very large graphs. We will discuss two of these theories, going into more detail about one of them: the bounded-degree random weak limit theory of Benjamini and Schramm.
Title: What is the Lovasz conjecture on Hamiltonian cycles?
Abstract: One version of the Lovasz conjecture on Hamiltonian cycles is that any connected Cayley graph of a finite group has a Hamiltonian cycle. We will review some known results pertaining to the Lovasz conjecture as well as state 2 of its variants. If time permits, we will also discuss the 1-2-3 conjecture, which is about inducing a proper vertex coloring of a graph from a coloring of its edges. After reviewing the results that support the 1-2-3 conjecture, we will discuss its analogue for directed graphs.
Title: What is the Thompson Group?
[pdf] - Some links on this page are to .pdf files. If you need these files in a more accessible format, please contact email@example.com . PDF files require the use of Adobe Acrobat Reader software to open them. If you do not have Reader, you may use the following link to Adobe to download it for free at: Adobe Acrobat Reader.