My doctoral research was in the field of symplectic geometry. I spent most of my time thinking about the topology and intersection patterns of Lagrangian submanifolds of complex projective space. I was particularly interested in so called "twistor Lagrangians" - ones which are mapped to maximal totally complex submanifolds of quaternionic projective space under the twistor fibration. You can find out more about these in my
thesis (this version of my thesis differs slightly from the official one and might change as I discover and correct typos; you can find the official version at UCL discovery).
- M. Konstantinov,   Remarks on monotone Lagrangians in CP3, in preparation
- 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
The results of this paper have been improved and expanded upon in chapters 2 and 5 of my PhD thesis. You can also find the relevant Mathematica code here.
- G.Fuchsbauer, M.Konstantinov, K.Pietrzak, V.Rao,  Adaptive Security For Constrained PRF's, Advances in Cryptology – ASIACRYPT 2014 pp 82-101
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.