The presentations will be Thursday 8/27 in SEO 636 from 10-11am.
(mentored by Dane Meade)
I will talk about differential forms, this includes closed and exact forms, and computations with the wedge product. I will also talk about the exterior derivative, the de Rham complex, and de Rham groups. Finally I will break down the Meyer Vietoris Sequence and show what short and long exact sequences are!
(mentored by Xiaotong Dawson Yang)
Fourier analysis allows us to take a signal and break it up into its constituent frequencies. This talk will introduce Fourier series in the context of finite Abelian groups and expand on its many applications and uses including image filters, sound processing, compression, and solving differential equations.
(mentored by Andre de Moura)
The Sylow theorems are a powerful tool for the classification of finite groups, seeing what the possible structure of the group may be. I am going to introduce some terminology on p-groups, direct, and semidirect products and go through an example of classifying groups of small order.
(mentored by Clay Mizgerd)
This presentation provides an overview of how the notions of matrix diagonalization are generalized to an infinite-dimensional case. We will begin by recalling symmetric operators, defining the notion of a Hilbert Space, and extending finite-dimensional definitions to their infinite-dimensional counterparts. We will then state the spectral theorem for bounded self-adjoint compact operators and examine a sketch of the proof. Finally, we’ll go through a motivating example.