Master's and PhD student applications
I am interested in finding quality Master's and PhD students (both international and Chinese).
What prospective international students need to know:
Please understand that I receive a lot of spam applications which I ordinarily don't reply to (or I direct them to this webpage). At the very least, please ensure that you: (a) do not ask for a letter of acceptance in your first email [I'm not committing to supervising you for 2+ years after one email!], (b) do not write your email as if it could be copy/pasted to 100+ other academics, and (c) do not plagiarize material into your application. It is clear that many of these spam applications are from people seeking a free holiday in China and are not serious about research.
So that I can distinguish your application from the spam applications, please state what topic you're interested in researching (see the examples below), and please include a reference to one of my papers where I discuss that topic (or something related). I'm asking for a small amount of research for someone who is applying to undertake years worth of research.
International students in our college need to learn Chinese and obtain HSK4 before starting their coursework (which is mostly in Chinese). PhD students need to also obtain HSK5 before graduation. Learning Chinese will probably add an extra year to your postgraduate degree. This is a significant challenge for international students, and it's not in either of our interests for me to take on students who will likely fail at Chinese before even starting research. Realistically, I need to see a strong commitment to learning Chinese (and not just "promises" to learn Chinese), because otherwise the student would not succeed.
Applications are due around March, and go through the International Student Service System. The academic year starts in September. Government scholarships are announced late, around August.
I'm now in computer science, so your research topic needs to involve some amount of computer science, and your degree will be in computer science.
In China, rules and regulations often change: the lab's rules, the department's rules, the university's rules, and the government's rules. I don't get informed when rules change, and the regulations are written mostly in Chinese. As such, it's often a surprise to me to find out about changes.
Example research topics:
1. Sade's algorithm is the best method for computing the number of Latin squares (McKay and Wanless, 2005 used it to compute the number of Latin squares of order 11). I'm interested in adapting Sade's algorithms to enumerate Latin squares (or partial Latin rectangles) which have specific properties (e.g., no 2×2 subsquares).
2. Determining when two Latin squares are inequivalent is facilitated by using invariants. I'm interested in enumerating substructures of Latin squares and using them to generate a "Latin square fingerprint". There are also computational methods (canonical labeling), and the usual approach is by McKay, Meynert, and Myrvold, 2006. It would be interesting to modify their approach, using different graphs and different invariants, to see if we can improve on the "worst case" scenarios (which tend to be extraordinarily slow).
3. Xu and Tian, 2018 describe an image encryption method using self-orthogonal Latin squares. I think their idea of treating self-orthogonal Latin squares as a kind of "2D permutation" can be treated as a strong type of "orthogonality" among Latin squares. I would like to search for such "strongly" orthogonal Latin squares (and partial Latin rectangles), and see if they can be used to solve the long-standing open problem of the existence of 3-MOLS(10).
4. The standard process of generating random Latin squares is by Jacobson and Matthews, 1996 (although there's a new method by DeSalvo 2016). I'm wondering if there is any experimentally measurable differences between these randomly generated Latin squares, and random Latin squares generated (non-uniformly) one-row at a time, then being acted upon by a random isotopism. Maybe there's practically no difference (or maybe there is).
5. For which finite groups H1 and H2, and dimension parameters r, s, n, and m, does there exist an r×s partial Latin rectangle with symbols from {1,...,n} and m entries in total with autotopism group isomorphic to H1 and autoparatopism isomorphic to H2? This is a very general combinatorial question; it would be interesting to resolve small instances of this problem computationally, and to find minimum examples. Progress on this problem was made by Stones 2013, and Stones and Falcón, 2017.
6. I'm interested in enumeration and symmetry problems related to equi-n-squares, e.g. applying Burnside's Lemma to compute the number of non-isotopic equi-n-squares, and determining which isotopisms θ=(α,β,γ) are autotopisms of some equi-n-square. Much of the techniques used in Stones, Vojtěchovský, and Wanless 2012 apply here.
7. Stones, Su, Liu, Wang, and Lin 2015 proposed a Latin square autotopism secret sharing scheme. I'm interested in developing real-world cryptographic applications that involve this secret sharing scheme.
8. I'm interested in analyzing certain types of networks, e.g.: 1. networks that arise in proofs generated by automated theorem provers, and 2. networks that arise between entities in incremental games. One paper on the topic of networks is Li, Stones, Wang, Deng, Liu, Wang, 2012.
9. I'm developing an interest in using web data (e.g., webpages, comments on articles) to gauge public attitudes (part of quantitative psychology). This research tends to require a fair amount of careful manual inspection, which is a bit tedious. I have one paper on this topic (Stones 2016).
Other topics are probably suitable as long as they involve "combinatorics" and "computation" in some way.