Evening sunset one the western side of Oia in Santorini, Greece

Math




'But I don’t want to go among mad people," Alice remarked.

"Oh, you can’t help that," said the Cat: "we’re all mad here. I’m mad. You’re mad."

"How do you know I’m mad?" said Alice.

"You must be," said the Cat, "or you wouldn’t have come here."' (Lewis Carroll, Alice in Wonderland)

DERIVED GEOMETRY OF FANOS

SEPT 7, 2022

A compilation of my notes and studies on Derived Categories in the setting of Fano varieties.


MANIFOLDS APPLICATION II: EINSTEIN'S EQUATIONS

AUG 12, 2019
Representation of the four regions in Kruskal-Szekeres Spacetime

This blog post gives an in depth discussion on the mathematical background leading up to Einstein's famous Field Equations. In order for the reader to understand all the material covered, it is strongly suggested that all of my previous blog posts be read prior to this one.

Topics such as Ricci curvature, vacuum solutions, Schwarzschild De Sitter metrics, and more are covered!

MANIFOLDS APPLICATION: MAXWELL'S EQUATIONS

Jun 15, 2019
Minkowski Cone

Using everything we've learned about manifolds from the past three posts, this post delves into an alternate approach to electromagnetism and Maxwell's famous equations. Moreover, this post covers all background material on Minkowski spacetime and the Hodge dual, so that we have a good understanding of the intersection between electromagnetism and theoretical physics.

About Me

Personal Headshot taken at the Manbeck-Hoxter Wedding

My name is Chris and I'm a mathematics Ph.D. student at University of California, Santa Barbara (UCSB) studying Algebraic Geometry with a focus towards stability conditions (as occuring in String theory, etc).

Prior to my focus on pure mathematics, I completed my masters in applied computational topology, which itself was a bit of an abstraction from my undergrad in computer science engineering. Oddly enough, it all started with my love of Latin and classical Greek — but that's getting a bit off track.

Nowadays I spend the majority of my free time either woodworking like my father, or downhill / slalom longboarding (see homepage video). If you're ever in the central California area for the latter, give me a hollar. Thanks for visiting!