I work in the field of symplectic geometry. I spend most of my time thinking about the topology of Lagrangian submanifolds. Studying these usually involves understanding some invariants defined using holomorphic curves. These are also interesting in themselves and I quite enjoy finding out more about them.
- M. Konstantinov, J. Smith,   Monotone Lagrangians in CPn of minimal Maslov number n + 1,
- M. Konstantinov,   Higher rank local systems in Lagrangian Floer Theory, preprint, 2017
To obtain some of the results in this paper I used Wolfram Mathematica 10.3. Here is the relevant code:
- A programme for visualising the boundaries of Maslov 2 discs on the Chiang Lagrangian, lifted to the universal cover S3 (if your browser has the Wolfram CDF player, you can access an interactive version
- A programme which does the linear algebra in the computation of Floer cohomology with local coefficients for the Chiang Lagrangian (for the entire notebook in CDF format click here).
- G.Fuchsbauer, M.Konstantinov, K.Pietrzak, V.Rao,  Adaptive Security For Constrained PRF's, Advances in Cryptology – ASIACRYPT 2014 pp 82-101
In the Autumn of 2018 I am teaching tutorials at King's College for the Linear Algebra, Real Analysis 2 and Probability and Stats 2 modules. You can find some materials for Prob and Stats here .
Whenever I get the time I quite like talking about maths. Below are some past activities of mine along these lines.
- "Meet your researcher" programme, UCL, 07 Feb 2017
Here are some slides from that talk giving a glimpse of symlectic topology. And here is an extended version with pictures of holomorphic curves.
- Lecturer, mini-project supervisor; Uni-Link Summer Showcase in Mathematics, UCL, 25-27 Jul 2016
- Lecturer, project supervisor; Summer Research School 2014, HSSIMI
- An open book decomposition of the 3 sphere with some Dehn twists: here.