29/10/2024

Dmitrii Korshunov defends doctoral thesis this Wednesday (30)

IMPA PhD student Dmitrii Korshunov defends his doctoral thesis this Wednesday (30), at 10 am, in room 232 of IMPA. The defense will be broadcast on the institute's YouTube channel . Originally from Astrakhan, Russia, the student talks “about the geometry of polyhedral spaces and hyperkahler manifolds”.

The thesis, supervised by researcher Mikhail Verbitskiy, consists of three parts. The first solves a problem by Richard Kenyon on piecewise extension domes of linear curves in three-dimensional Euclidean space. The solution is obtained as a consequence of a general result on the symplectic geometry of Kapovich-Millson polygon space.

The second part is a contribution to node theory focusing on network nodes. "Alan Turing considered a set of elementary operations defined combinatorially on network nodes, which turned out to be equivalent to node isotopes. The main result is the proof that the list of Turing operations can be reduced to just one operation," the work highlights.

The third part deals with the geometry of the period space of an irreducible hyperkahler manifold. “This space has a natural class of immersed spheres called twistor lines. There is an internal metric associated with this class, defined in the spirit of subriemannian geometry. We establish that this metric is Finsler and investigate some of its properties. These questions were motivated by the proof of Torelli's global theorem for hyperkahler manifolds,” the abstract states.