Splash Biography

Often introduced for purely mundane equation-solving purposes, most people are familiar with some sense of 'algebra.' However, algebra -- in its many forms -- is an incredibly diverse topic whose influence and impact is often underappreciated. In this session, we want to show that analyzing this more abstracted idea of 'algebra' leads to some of the most useful and insightful mathematical and physical objects we have today. This whirlwind tour will guide learners through the foundations of modern algebra, the rigorous study of group theory, algebraic geometry, and representation theory, as well as the essential use of these ideas in physics, namely quantum mechanics and theoretical particle physics.

Often relegated to a secondary role in the standard mathematics curriculum, complex numbers are usually unfortunately presented as a contrived abstraction used to solve certain equations. In this session, we want to show that, ironically, these 'imaginary' entities are some of the most useful and insightful mathematical and physical (!) objects we have today. This whirlwind tour will guide learners through the motivations of complex numbers, the rigorous (and magical) field of complex analysis, as well as the essential use of these ideas in physics, namely quantum mechanics and theoretical particle physics.