복소기하학연구단
Speaker Sung Rak Choi Yonsei Univ. Choi-Park first introduced and develped the notion of potential pairs. The notion was designed to control the singularities of the outcome of the 'anticanonical' minimal model program. In this talk, after reviewing the properties of potnetial klt pairs, we examine the ACC property of the potential lc …
Speaker Christian Schnell Stony Brook Univ. The theory of variations of Hodge structure has many applications in algebraic geometry. Most of these are based on the results by Schmid, Cattani, Kaplan, Kashiwara, and Kawai from the 1970s and 1980s. I will describe a new approach that proves these results — such as the …
Speaker Ming Xiao UCSD Bounded symmetric domains are an important class of geometric objects in complex analysis and geometry, which possess a high degree of symmetry. They often serve as the model cases in the study of many rigidity phenomena. In this talk, we will discuss two mapping problems between bounded symmetric domains …
Speaker Luca Rizzi IBS-CCG Given a semistable fibration f : X → B I will show a correspondence between foliations on X and local systems on B. Building up on this correspondence we will find conditions that give maximal rationally connected fibrations in terms of data on the foliation. We will develop the …
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 Ziquan Zhuang Johns Hopkins U Several years ago, Chi Li introduced the local volume of a klt singularity in his work on K-stability. The local-global analogy between klt singularities and Fano varieties, together with recent study in K-stability lead to the conjecture that klt singularities whose local volumes are bounded away from …
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 Jakub Witaszek Princeton U What allowed for many developments in algebraic geometry and commutative algebra was a discovery of the notion of a Frobenius splitting, which, briefly speaking, detects how pathological positive characteristic Fano and Calabi-Yau varieties can be. Recently, Yobuko introduced a more general concept, a quasi-F-splitting, which captures much more …
Speaker Pak Tung Ho Sogang University In this talk, I will explain what the weighted Yamabe problem is, and mention some related results that Jinwoo Shin (KIAS) and I obtained.
Speaker Aeryeong Seo Kyungpook National University TBA
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, …