Baohua Fu (Chinese
Academy of Sciences)
Title.
Deformation rigidity of Fano manifolds
Abstract.
A smooth projective variety X is called rigid if any
deformation of X is isomorphic to itself. A first example is the
projective space, but in general it is a subtle and difficult
problem to prove the deformation rigidity. I'll report some recent
progress in this problem. Part of this talk is based on joint works
with Yifei Chen (Chinese Academy of Sciences) and Qifeng Li
(Shandong University).
Alexey
Glutsyuk (HSE, IITP)
Title.
On rationally integrable planar dual multibilliards and projective
billiards
Abstract.
A caustic of a strictly convex planar bounded billiard is
a smooth curve whose tangent lines are reflected from the billiard
boundary to its tangent lines. The famous Birkhoff Conjecture states
that if the billiard boundary has an inner neighborhood foliated by
closed caustics, then the billiard is an ellipse. It was studied by
many mathematicians, including H.Poritsky, M.Bialy, S.Bolotin,
A.Mironov, V.Kaloshin, A.Sorrentino and others.
We present positive results on its dual version stated by
S.Tabachnikov, for so-called dual billiards (curves equipped with a
family of projective involutions acting on tangent lines and fixing
tangency points), under the condition of existence of a rational
function whose restriction to each tangent line is invariant under
its involution. We will discuss a related open problem on
classification of polygonal projective billiards (polygons equipped
with a transversal line field on the boundary, defining reflection
of lines from the boundary) with rationally integrable billiard
flow. It is closely related to a problem on actions of groups of
Cremona transformations generated by de Jonquieres involutions.
Hiromu
Tanaka (University of Tokyo)
Title.
Classification of smooth Fano threefolds in positive characteristic
Abstract.
In the 1980s, Mori-Mukai completed the classification of smooth Fano
threefolds in characteristic zero, based on work by Iskovskih and
Shokurov. In this talk, I will explain an analogous result in
positive characteristic.
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