Hi! My name is Kam Chuen Tung (I usually go by Alex) and I am from Hong Kong. I am currently a PhD student in the University of Waterloo, advised by Prof. Lap Chi Lau. My research involves studying expansion properties of graphs from the perspectives of spectral graph theory, convex optimization, random walks, and metric embedding. Prior to my PhD studies, I obtained a BSc in Mathematics (minor in French) in the Chinese University of Hong Kong. I am known as alex20030190 on Codeforces. Some of my socially acceptable hobbies are writing, solving puzzles, and choir singing.
We study spectral sparsification of hypergraphs when the hyperedges arrive one by one, using chaining to obtain a bound on the number of hyperedges using only $O(n^2)$ space.
We obtain almost linear-time algorithms for partitioning directed graphs and hypergraphs using the reweighted eigenvalues SDP relaxation plus $\ell_2^2$ triangle inequalities.
We further extend the concept of reweighted eigenvalues to derive Cheeger’s inequalities for directed graphs and hypergraphs.