FRIAS Junior Fellowship "McKay correspondence for vanishing cohomology"

A popular question in complex and algebraic geometry is whether a given topological, cohomological, categorical etc. invariant of a resolution of a singular space is independent of the specific shape of the resolution and, thus, reflects properties of the singular space itself. Questions of this sort are the focus of the area of geometry known as Mckay correspondence. The subject emerged in the early 1980's and its further development has been greatly influenced by the needs of Mirror Symmetry which entered mathematics soon afertwards. Mirror symmetry, in its original form, compares holomorphic and symplectic invariants of mirror pairs of Calabi-Yau manifolds which quite often arise as resolutions of singular spaces. The primary goal of the project is to establish a Mckay correspondence for basic Hodge theoretic invariants of the so-called Landau-Ginzburg models. The latter form the basis of modern versions of Mirror Symmetry.

Additional information: http://www.frias.uni-freiburg.de/en/people/fellows/current-fellows/shklyarov?set_language=en
contact person: Dr. Dmytro Shklyarov
Phone: +49 761 203-5568
Email: dmytro.shklyarov@math.uni-freiburg.de

Start of project: 01.01.2014
End of project: 31.10.2014

Albert-Ludwigs-University Freiburg
Dr. Dmytro Shklyarov
Abteilung für Reine Mathematik
Prof. Dr. Katrin Wendland
Ernst-Zermelo-Str. 1
79104 Freiburg
Germany

Phone: +49 761-203-5563
Fax: +49 761 203-5541
Email: katrin.wendland@math.uni-freiburg.de
http://home.mathematik.uni-freiburg.de/mathphys/mitarbeiter/wendland
Actual Research Report