Ramblings of an Aspiring Mathematician

Hello, my name is Logan Hyslop, and I am currently a rising third year undergraduate at UCLA, where I am studying math. Some facts about me: I enjoy sailing and doing math, lately I seem to be listening to a lot of Kid Cudi, and I have ADHD.

UCLA doesn’t really have undergraduate theses/advisors, but I suppose my “pseudo-advisor” (which is something I made up while writing this) is Paul Balmer.

Interests

I am primarily interested in homotopy theory, and its applications- in particular algebraic K-theory and trace methods.

Everyone likes the Mumford quote, “[Algebraic geometry] seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.”
This description I believe also applies quite aptly to homotopy theory these days, and I’d like to further the plot.

Resources I like

Here’s a (somewhat unorganized) selection of some of the books/lecture notes that I have come across, and recommend for certain topics

• Notes on Algebraic K-theory, these have a particularly nice introduction to spectra and higher algebra that I generally recommend to people who ask for resources for starting out with higher algebra.
• Lectures on Condensed Math
• Lectures in Analytic Geometry
• Categorical Homotopy Theory
• Elements of Infinity Category Theory
• Lecture notes for learning E_n algebras
• Homological Theory of Representations
• Differential Cohomology
• Equivariant Homotopy Theory Notes

To insert a shameless plug, here are slides from a talk I gave entitled You Could’ve Condensed Mathematics. The talk was designed for undergraduates, meant to be a very non-technicaly introduction to some of the ideas of condensed math.

For a more technical introduction, here is a video of a talk I gave introducing condensed math and analytic geometry, starting from the beginning and ending with the definition of analytic spaces. (See my CV for more details and more of my talks).