Summer Scholarship Projects

Together with more senior researchers, I am offering two (fully funded!) summer projects for undergraduate students. If you are a second or third year undergraduate student in Australia or New Zealand and are interested in either of the projects then do get in contact with me at jonathan(dot)cohen(at)anu(dot)edu(dot)au.

Further details on the research scholarship scheme, including how to apply, are available here.

On the social side, I completed one of these scholarships a few years ago and can attest that you will have a great time with your fellow summer scholars! There are regular social events over the summer and many opportunities to hit the town. Students undertaking a project related to logic will also be able to attend the Logic Summer School. In addition to that, there is the fortnightly NotYASS discussion group, which often covers logic-related topics, as well as a weekly "logic cafe".  With the latter two, you will have the opportunity to socialise with senior researchers from a number of areas - something that is usually not possible as an undergraduate! And, heck, it's all expenses paid!  

Both of the projects listed below have very broad possibilities. The second, in particular, has many possible routes depending on where your main interests lie. To name a few subjects in the vicinity, it incorporates randomised algorithms, computational complexity, logic and even a bit of linguistics!

Don't feel that you need an extensive background in logic or algebra for either of the projects - we can bring you up to speed on what you need to know fairly quickly. After that, the fun can begin!

Project 1 (Joint supervision with Tomasz Kowalski)
GRASS: Group Relation Algebras Systematically Studied

Relation algebras are fundamental mathematical objects, which crop up everywhere from logic to algebra to computer science. While there are powerful tools for computing with other algebraic structures, they are not directly applicable in the relation algebra context.

The initial goal of the project is to design and implement algorithms for generating a large class of relation algebras, related to groups. There are many places to go from there, depending upon the interests and skills of the student. The software would most likely be developed in GAP, a powerful open source system for computational discrete algebra.

The ideal student would not be shy of mathematics and have some experience with abstract algebra (groups, rings, fields or the like) or combinatorics. Some programming skills are needed, but much more important is the ability to design efficient algorithms. In return, you'll learn a lot that is relevant to modern mathematics, logic and computer science, many aspects of which could fruitfully be continued as an honours project.


Project 2 (Joint supervision with Rajeev Goré)
The Structure of Random Proofs

Some theorems are harder than others. For instance, there are mathematical theorems whose proofs run to many hundreds of pages, while others take only a line or two. So, how long is an average proof? Alas, we don't even know the answer to this question in the case of propositional logic!

There are, in fact, a few different ways of proving theorems in propositional logic. For some, we have a pretty good idea of how long a proof will be, while others are still unclear. The goal of this project is to write software for generating random proofs in two distinct, though intimately related, proof systems. Once that is done, it will be possible to examine how much the length of a proof increases on average when passing from the stronger system to the weaker one.

This project sits on the intersection of many topics in logic and computer science. If you have a background in programming, enjoy designing algorithms and want a taste of research in theoretical computer science then this is a perfect way to spend the summer! Successful completion of the project will also give you a good start on many possible topics for honours projects.