About Me

I am currently a third year Ph.D. Student in Mathematics at UC Davis!

I graduated from High School in 2021 and Received a B.S. in Math from UC Davis in 2023.

I enjoy studying complex algebraic geometry, integrable systems, PDE's, modular forms, and combinatorics applied to various mathematics and theoretical physics problems! My current advisor is Professor Motohicho Mulase and I am doing research pertaining to Gromov-Witten invariants of Fano Varieties and Mirror Symmetry.

My Notes

I slowly (but surely) will update my notes section with various collections of notes I have taken on various textbooks and topics. You will notice a sizable introductory couple of pages which preempt each note that involves "key questions", "preliminary facts", "overarching questions for the entire chapter", and "what's in this chapter?" sections. 

"Key Questions" are those which motivate the content of the chapter and are the underlying fundamental questions which led to the development of the content in the first place. "Preliminary Facts" will list relevant topics which are meant to be known by the reader before starting certain sections/problems in the text. Though these won't be reviewed in the text, mentioning them for the reader so they vaguely know what kinds of things they should remember may be helpful. "Overarching Questions" will be those which help solidify the "natural flow" of the material. "What's in this Chapter" will be a short blurb of the key concepts and takeaways one should get from each section in the chapter. This will help to review the material in a much more condensed manner.

"Walk With Me" Podcast

I am starting a "podcast" series both on youtube (@zachybara) which accompanies notes on mathematics I upload here. The series is called "Walk With Me" and the goal is to provide some nice audio/visual companion to make reading and understanding not just my notes, but the content the notes are based on, much easier and more humanized. 

The title "Walk With Me" is simultaneously figurative (in that I'd like to invite the listener to "walk through" the labyrinth-like structure of the material with me and gain some nice intuition for not just what the material contains, but why its a natural thing to care about) and literal (I will literaly be on a walk)! I've enjoyed many of these mathematical "walk with me" moments with my advisor and other mentor professors and I hold the lessons and insights I learn from them very near and dear to my heart. I try as much as I can to pass down this culture of "walking and talking" to students I encounter and find it an amazingly fun activity.

I've heard plenty of people say "mathematics is the language of the universe" - implying that its existence is somehow independent of the human experience. In my opinion, the reason math exists at all is BECAUSE humans are there to invent it! It's not intrinsic to anything other than the human curiosity to know why. Though, in many textbooks and in many courses the "human" part of the mathematics seems to take a backseat (for good reasons). I hope this podcast can be a medium to "humanize" mathematics in my own unique way.