Image credit: CMUMC PR
While being VPE of CMU Math Club, I failed to find a speaker for the first week. So, in a blatant abuse of power, I invited myself to speak.
Date: September 7th, 2022
Abstract: Have you ever solved a 15-puzzle? What about a Rubik's cube? Combination puzzles are a lot of fun to solve, and unsurprisingly, there's quite a bit of math behind them too. In this talk we will explore a puzzle that works like a "2D Rubik's cube": You're given a scrambled grid of numbers, and you can take a square subgrid of fixed size and rotate it 90 degrees. When can you unscramble the grid using a sequence of such rotations, and how? Our journey to answering this will involve many surprising connections to very different fields of math.
Powerpoint Slides: (Download)
Google Slides (Not as good; some animations break): (Link)
Video (of a "practice run"): (Youtube)
This was literally my Master's thesis defense.
Date: April 19th, 2023
Abstract: The second-order singularly-perturbed problem concerns the integral functional $\int_\Omega \varepsilon_n^{-1}W(u)+\varepsilon_n^3\|\nabla^2u\|^2\,dx$ for a bounded open set $\Omega \subseteq \mathbb{R}^N$, a sequence $\varepsilon_n \to 0^+$ of positive reals, and a function $W:\mathbb{R} \to [0,\infty)$ with exactly two distinct zeroes. This functional is of interest since it models the behavior of phase transitions, and its Gamma limit as $n \to \infty$ was studied by Fonseca and Mantegazza. In this paper, we study an instance of the problem for $N=1$. We find a different form for the Gamma limit, and study the Gamma limit under the addition of boundary data.
Powerpoint Slides: (Download)
Google Slides (Slight imperfections but good enough): (Link)
This was for NYU's annual cSplash event.
Date: April 28th, 2024
Abstract: Our hobbies can make for some unexpectedly interesting settings for doing math! As someone that spends too much time on videogames, I get a questionable amount of delight whenever I find a way to apply math in whatever game I'm playing. In this talk, I will demonstrate that "math is everywhere" by discussing interesting yet surprisingly elementary math problems that arise in videogames including Genshin Impact, Minecraft, and Love Live School Idol Festival.
Powerpoint Slides: (Download)
Google Slides (Animation order definitely broken, please download the Powerpoint for best results): (Link)