복소기하학연구단
Speaker Gil Bor CIMAT At first sight, the pair of front and back wheel tracks left by a passing bike on a sandy or muddy terrain seems like a random pair of curves. This is not the case. For example, one can usually distinguish between the front and back wheel tracks, and even …
Speaker Youngju Kim Konkuk University The collar lemma says that a closed geodesic in a real hyperbolic 2-manifold has an embedded tubular neighborhood whose width only depends on the length of the geodesic. The width of the collar does not depend on the underlying hyperbolic 2-manifold. On the other hand, a totally geodesic …
Speaker Boris Doubrov Belarusian State University, Minsk We introduce the notion of a bifiltered manifold and generalizing the constructions of the symbol and Tanaka prolongation from nilpotent differential geometry. Next, we consider bifiltered manifolds modeled by bigradings of simple Lie algebras and show how this generalizes known constructions in the parabolic geometries such …
Speaker Dennis The The Artic University of Norway, Tromso In their 2013 article, An & Nurowski considered two surfaces rolling on each other without twisting or slipping, and defined a twistor distribution (on the space of all real totally null self-dual 2-planes) for the associated 4D split-signature conformal structure. If this split-conformal structure …
Speaker Michel Brion U. Grenoble This is an introductory lecture on symmetric spaces in algebraic geometry.
Speaker Michel Brion U. Grenoble This is an introductory lecture on compactifications of symmetric spaces in algebraic geometry.
Speaker In-Kyun Kim KIAS In algebraic geometry, constructing moduli spaces that parametrize families of algebraic varieties with certain properties is an important problem. In the case of Fano varieties, the construction of moduli spaces is a challenging problem. K-stability provides a criterion for selecting nice representatives within the moduli space, which helps create …
Speaker Chuyu Zhou Yonsei University We will present various criterion for K-stability for Fano varieties, including viewpoints from test configurations, valuations, and filtrations.
Speaker Chuyu Zhou Yonsei University We will present the construction of moduli space of Fano varieties with K-stability, including defining the moduli functor, showing various good properties of the functor, and introducing Alper-Halpern Leistner-Heinloth criterion for the existence of good moduli space.
Speaker Chuyu Zhou Yonsei University We will introduce a novel characteristic of K-stability, i.e. wall crossing phenomenon, and present a comparison between K-stability and GIT-stability. Time permitting, we will survey some open problems.
Speaker Benjamin Bakker Univ. Illinois Chicago Compact hyperkahler manifolds X are higher-dimensional generalizations of K3 surfaces; their geometry is tightly constrained by the existence of a holomorphic symplectic form. For example, a result of Matsushita says the only nontrivial fibration structures f:X→B they admit are fibrations by Lagrangian tori. In this talk, I …
Speaker Benjamin Bakker Univ. Illinois Chicago Matsushita conjectured that for any Lagrangian fibration f:X→B of a compact hyperkahler manifold X, the fibers deform either maximally or trivially in moduli. In this talk I'll explain how to prove this conjecture via Hodge theory. I will also discuss some other features of the topology of …