복소기하학연구단
Speaker Hoseob Seo IBS CCG In L2 extension theorems from an irreducible singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure, which determines when a given function can be extended. In this talk, we show that the singularity of the Ohsawa measure can be …
Speaker Guolei Zhong IBS-CCG As a fundamental building block of the equivariant minimal model program, the rationally connected variety plays a significant role in the classification of projective varieties admitting non-isomorphic endomorphisms. Twenty years ago, Nakayama confirmed Sato’s conjecture that, a smooth projective rational surface is toric if and only if it admits …
Speaker Benjamin McMillan IBS-CCG The Killing operator in (semi) Riemannian geometry has well understood kernel: the infinitesimal symmetries of a given metric. At the next level, the range of the Killing operator can be interpreted as those perturbations of the metric that result from a mere change of coordinates---in contexts like general relativity, …
Speaker Jinhyun Park KAIST The classical reciprocity theorem, also called the residue theorem, states that the sum of the residues of a rational (meromorphic) differential form on a compact Riemann surface is zero. Its generalization to smooth projective curves over a field is often called the Tate reciprocity theorem. There is a different …
Speaker Jaewoo Jeong IBS CCG The Hankel index of a real variety is a semi-algebraic invariant that quantifies the (structural) difference between nonnegative quadrics and sums of squares on the variety. Note that the Hankel index of a variety is difficult to compute and was computed for just few cases. In 2017, …
Speaker Dennis The UiT The Arctic University of Norway Generic rank 2 distributions on 5-manifolds, i.e. "(2,3,5)-distributions", are interesting geometric structures arising in the study of non-holonomic systems, underdetermined ODE of Monge type, conformal 5-manifolds with special holonomy, etc. The origins of their study date to Élie Cartan's "5-variables" paper of 1910, where …
Speaker Laurent Stolovitch Universite Cote d’Azur In this short lecture, I will introduce the notion of normal form and resonances. I will also explain the phenomenon of "small divisors" and give some fundamental results of holomorphic conjugacy to a normal form.
Speaker Laurent Stolovitch Universite Cote d’Azur In this short lecture, I will introduce the notion of normal form and resonances. I will also explain the phenomenon of "small divisors" and give some fundamental results of holomorphic conjugacy to a normal form.
Speaker Yunhyung Cho Sungkyunkwan University This is a survey talk of current progress of mirror symmetry of Fano varieties. For a given smooth Fano variety X, it has been conjectured that there exists a Laurent polynomial called a (weak) Landau-Ginzburg mirror (or weak LG mirror shortly) which encodes a quantum cohomology ring structure …
Speaker Donghoon Jang Pusan National University We briefly review group actions on manifolds and equivariant cohomology, which is cohomology of a manifold with a group action. We review classification results for circle actions on various types of manifolds in low dimensions. An almost complex manifold is a manifold with a complex structure on …
Speaker Insong Choe Kunkuk University We first review the known results on the Quot schemes on a smooth algebraic curve. Next we explain how they can be generalized to the Lagrangian Quot scheme, which parametrizes Lagrangian subsheaves on a symplectic vector bundle. Also we discuss the parallel results for orthogonal bundles. This will …
Speaker Donggun Lee IBS-CCG Hessenberg varieties are subvarieties of flag varieties with interesting properties in both algebro-geometric and combinatorial perspectives. The Shareshian-Wachs conjecture connects their cohomology with the chromatic quasi-symmetric functions of the associated graphs, which are refinements of the chromatic polynomials. In this talk, we introduce generalized Hessenberg varieties and study their …