I am a graduate student in the MIT Mathematics Department. I am very fortunate to be advised by Michel Goemans. Before that, I obtained my B.Sc. in Computer Science and Mathematics (Combined Honours) with Distinction at the University of British Columbia, where I was advised by Bruce Shepherd. Even before that, I attended Shaoxing No. 1 High School, where I participated in competitive programming.
My research interests include algorithms, combinatorics and optimization, in particular designing discrete algorithms and analyzing discrete structures. I am also broadly interested in theoretical computer science, operations research and graph theory.
While not doing mathematics, I enjoy hiking, backpacking, kayaking and skiing. Check out photos on my Instagram!
I will be back in Vancouver from May 18 to May 23! I will give a talk titled Planarity via Spanning Tree Number: A Linear-Algebraic Criterion at 3-4 PM on May 23. Location: Room X836, ICICS Building, UBC. 🇨🇦
Apr 11, 2024
I will be in Miami on April 12 to attend the Citadel Securities PhD Summit. Stop by my poster (on my work with Alan) if you are around! 🏝
Oct 11, 2023
Tomorrow (October 12) in 2-132, I will give a talk titled Fantastic Spanning Trees in Planar Graphs and Where to Find Them, based on my joint work with my RSI student Alan, at the Simple Person’s Applied Math Seminar (SPAMS). Food from 醉杭州 (including 酒酿圆子) will be provided! 🥘
Aug 4, 2023
My RSI mentorship has now ended. Congratulations to my students Alan and Deyan for completing their projects, and additional congratulations to Alan for making it into the top 5 presentations! We plan to expand our results into a paper. Stay tuned! 🎉
We introduce a novel linear-algebraic planarity criterion based on the number of spanning trees. We call a matrix an incidence submatrix if each row has at most one 1, at most one -1, and all other entries zero. Given a connected graph G with m edges, we consider the maximum determinant \mathsf{maxdet}(G) of an m \times m matrix [M|N], where M is the incidence matrix of G with one column removed, over all incidence submatrices N of appropriate size, and define its excess to be the number of spanning trees in G minus \mathsf{maxdet}(G). Given a disconnected graph, we define its excess to be the sum of the excesses of its connected components. We show that the excess of a graph is 0 if it is planar, and at least 18 otherwise. This provides a “certificate of planarity” of a planar graph that can be verified by computing the determinant of a sparse matrix and counting spanning trees. Furthermore, we derive an upper bound on the maximum determinant of an m \times m matrix [M|N], where M and N are incidence submatrices. Motivated by this bound and numerical evidence, we conjecture that this maximum determinant is equal to the maximum number of spanning trees in a planar graph with m edges. We present partial progress towards this conjecture. In particular, we prove that the \mathsf{maxdet}(⋅) value of any subdivision of K_{3, 3} or K_5 is at most that of the best planar graph with the same number of edges.
2021
Optimization Problems on Network Flows with Degree Constraints
In a vertex-capacitated directed graph with sources and sinks, we would like to concurrently route demands from the sources to the sinks. This model has many applications in the real world. However, conditions in the reality usually incur new side constraints to this general model. For instance, the next-hop routing in Internet protocol (IP) networks requires each router to have one single next destination, called the next hop, for each incoming packet destined to an IP address. A flow with this property is said to be confluent. If this constraint is relaxed to allow d next destinations at each vertex, then such a flow is said to be d-furcated. In general, side constraints concerning bounded out-degree of each vertex give rise to network flows with degree constraints. Such constraints contribute to simplicity of resulting network flow models. Given a network flow model, several optimization problems can be asked. For instance, how the demands can be routed so that the flow does not exceed the capacity at each vertex too much? Another natural question is to find a subset of the demands with the maximum amount which can be routed subject to the vertex capacities. In this thesis, we survey algorithms that find approximate solutions close to optimum values within theoretically guaranteed factors.