Hello, I'm August.


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Hi, my name is August Liu. My official (legal) name is Mengzhen Liu, but I've found people having difficulty pronouncing and remembering it so I simply go by "August".*

A Picture of MeI am an undergrad at University of Cambridge reading Mathematics. I am currently in Part II of the mathematical tripos, the third year of the mathematics course at Cambridge. I previously studied International Baccalaureate Diploma Program at International Dept. of Beijing National Day School. I also participated in Ross Mathematics Program at Ohio, United States in summer 2018 for six weeks of number theory.

Contact and Curriculum Vitae

You can Email me at ml868 at cam dot ac dot uk.

My CV can be accessed here. (Last Update August 2021)

Recent Work/Publications

Tiling of Rectangles with Squares via Diophantine Approximation
Preprint. With Tamás Keleti, Stephen Lacina, Changshuo Liu, José Ramón Tuirán Rangel [arxiv]

Laplacian Fractional Revival on Graphs
Accepted by Electronic Journal of Combinatorics. Volume 28, Issue 3 (2021), P3.22. With Ada Chan, Bobae Johnson, Malena Schmidt, Zhanghan Yin, Hanmeng Zhan [doi]

Laplacian Pretty Good Fractional Revival
Accepted by Discrete Mathematics. Volume 345, Issue 10 (2022). With Ada Chan, Bobae Johnson, Malena Schmidt, Zhanghan Yin, Hanmeng Zhan [doi]

Explicit Burgess Bound for Composite Moduli
Accepted by International Journal of Number Theory. Volume No. 17, Issue No. 10, pp. 2207 - 2219, Year 2021. With Niraek Jain-Sharma, Tanmay Khale [doi]

Expository Writings

Here are some expository writings inspired by some math texts/materials/lectures that I came across. I try to produce these as often as possible recently to help myself, but also to help you make some subtle observations.

Number Theory

  1. Farey Sequences pdf
  2. Structure of Units of Integers Modulo n pdf

Group Theory

  1. Product Formula pdf
  2. Cosets and Hall's Marriage Theorem pdf
  3. Index of a Coset pdf



* I got asked a lot about this name; honestly I enjoy these questions and how often they come up, with great repetitiveness. So here are some preemptive answers:
- I was born in January, not August.
- I picked out this name by myself at 5.
- I don't know why I picked this out, but I knew very few English words back then so it's either this or name of shapes or fruits. "August" is probably one of the top choices if I was making it with rationality.