Algebra

Abstract: We will discuss the basics of quantum computing and quantum algorithms with the (perhaps aspirational) goal of presenting the quantum algorithm for solving the abelian hidden subgroup problem. Time permitting, we will also discuss some connections to cryptography. Familiarity with linear algebra will be assumed; while some basic group theory knowledge will be helpful, I will do my best to adjust the content and pacing of the talk to suit the audience.

Abstract: Category theory is a great tool for understanding structural similarities between different classes of mathematical objects (sets, vector spaces, groups, etc.). This talk is an accessible introduction to category theory with a focus on two important constructions: limits (no relation to calculus) and colimits. The null space of a linear map is an example of a limit. The direct sum of vector spaces is an example of a colimit. We’ll get our hands dirty with lots of examples. No algebra background is assumed (but it would make some things easier).

Abstract: The goal of this talk is to give an introduction to Lie Groups. We will cover the definition of a Lie group and give lots of examples. We will examine algebraic, geometric, and topological perspectives.