Alexei Kovalev
a.g.kovalev at dpmms.cam.ac.uk
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge

Information for potential PhD students


I may take a PhD student for 2018.

Research

My general research area is differential geometry and global analysis; occasionally it includes topics in algebraic geometry or topology. I am interested in `special' differential-geometric structures and their moduli spaces. These structures are often expressed as solutions of partial differential equations, typically non-linear and elliptic, on manifolds or vector bundles. Examples of `special geometries' that I studied include Ricci-flat 7- and 8-dimensional manifolds of holonomy G2 and Spin(7), their calibrated minimal submanifolds, and Calabi–Yau and hyper-Kähler manifolds. Projects that I offer may include applications of Analysis (the PDE methods). Familiarity with Algebraic Geometry and Topology is an advantage. Some of the results might be of interest also to Theoretical Physicists, especially String Theorists.


2017–2018 Part III courses. If you are a Part III student considering doing a PhD with me, then I recommend taking (many of) these courses:

Differential Geometry and Algebraic Topology — lectured in Michaelmas Term,
Complex manifolds and Elliptic Partial Differential Equations — lectured in Lent Term.

I strongly recommend that you do a Part III essay on a geometry topic, preferably related to the above.


PhD student(s) finished to date

2008   Johannes Nordström,   "Deformations and gluing of asymptotically cylindrical manifolds with exceptional holonomy"

2015   Matthias Ohst,   "Deformations of Cayley submanifolds"

2017   Kimberley Moore (supervised jointly with Jason Lotay, Unversity College London),   "Deformation theory of Cayley submanifolds"

2017   Timothy Talbot,   "Asymptotically cylindrical Calabi–Yau and special Lagrangian geometry"