Daniel Chen
I am a third year Mathematics undergraduate at the University of Cambridge.
I maintain some interactive lecture notes and explanations at theoremtown.com.
Please feel free to give me anonymous feedback, suggestions, thoughts, jokes etc. via my admonymous page.
Research
Denoising the Result of Monte Carlo Ion Implantation
Daniel Chen, Silvaco TCAD
Presentation slides will be uploaded soon
Eight-week research project at Silvaco. One of the important processes during semiconductor manufacturing is implantation, in which a wafer is bombarded with ions to modify its electrical properties. Computer simulations of this process produce noisy results; in this project, a novel smoothing algorithm is developed that halves the mean-squared error compared to previous methods.
Associated Permutations of Complete Non-Ambiguous Trees
Daniel Chen, Sebastian Ohlig
Discrete Mathematics & Theoretical Computer Science, vol 25:2 (April 2024)
As part of PROMYS Europe 2022, I worked in a pair on a six-week research project in combinatorics, culminating in proving an open conjecture at age 17. We established a new bijection from upper-diagonal CNMs to tree-like tableaux, and after the program we continued to discover new ideas, defining a novel row-and-column swapping operation.
arXiv e-prints
Alternative Proof of the Determinant of Complete Non-Ambiguous Trees (April 2024)
Expected Number of Dice Rolls Until an Increasing Run of Three (October 2023)