복소기하학연구단
Speaker Taiki Takatsu Tokyo University of Science We will discuss Mukai’s conjecture that the virtual cohomological dimension of the automorphism group of a K3 surface is equal to the maximum rank of its Mordell-Weil groups. The action of the automorphism group on the second cohomology induces a natural action on a hyperbolic space. …
Speaker Katharina Neusser Masaryk University A cone structure on a manifold $M$ is given by a closed submanifold $\mathcal C\subset \mathbb P TM$ of the projectived tangent bundle of $M$, which is submersive over $M$. Such geometric structures arise naturally in differential and algebraic geometry and they come often equipped with a conic …
Speakers Invited Lecturers (three one-hour lectures) Dawei Chen (Boston College) Gavril Farkas (Humboldt University of Berlin) Francesco Russo (University of Catania) Invited Speakers (one-hour talk) Minyoung Jeon (IBS-CCG) Donggun Lee (KIAS) Li Li (IBS-CCG) Abstracts PDF file Schedule Mar 10 (Tue) Mar 11 (Wed) Mar 12 (Thu) Mar 13 (Fri) 10:00~11:00 Russo, Lec 1 Russo, …
Speaker Dae-Won Lee Ewha Womans University The study of cylinders in normal projective varieties is of significant interest due to their intrinsic link to unipotent group actions on affine algebraic varieties. Over a field $\mathbb{k}$ of characteristic zero, it is known that cylindricity in lower-dimensional varieties (appearing as generic fibers) implies the existence …
Speaker Dae-Won Lee Ewha Womans University This talk provides a brief survey of recent results and applications concerning the anticanonical minimal model program. Furthermore, we present examples of varieties that admit an anticanonical minimal model despite not being Mori dream spaces. This talk is based on joint work with Sung Rak Choi, Sungwook …
Speakers Shigeyuki Kondo (Nagoya University) JongHae Keum (KIAS) Fei Si (Xi’an Jiaotong University) Kyoung-Seog Lee (POSTECH) Sang-Bum Yoo (Gongju National University of Education) Junchao Shentu (USTC) Haesong Seo (IBS-CCG/KAIST) Minzhe Zhu (KIAS) Yen-An Chen (KIAS) Abstracts PDF file Schedule May 27(Wed) 15:00-16:00, Shigeyuki Kondo 16:30-17:30, JongHae Keum May 28(Thu) 11:00-12:00, Fei Si 13:30-14:30, Kyoung-Seog Lee …
Speaker Hyunmoon Kim Ewha Womans University We present a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. Its stable manifolds generalize the Lagrangian, symplectic, isotropic, and coisotropic Grassmannians to include the Grassmannians of linear subspaces that are neither isotropic, coisotropic, nor symplectic. The …
Speaker Yan Li Beijing Institute of Technology Let $G$ be a connected, reductive, linear algebraic group that acts on a normal variety $X$, and $B$ be a Borel subgroup group of $G$. The complexity of the $G$-action on $X$ was defined by E. B. Vinberg in 1985 as the codimension of $B$-orbit at …
Speaker Yan Li Beijing Institute of Technology Let $G$ be a connected, reductive, linear algebraic group that acts on a normal variety $X$, and $B$ be a Borel subgroup group of $G$. The complexity of the $G$-action on $X$ was defined by E. B. Vinberg in 1985 as the codimension of $B$-orbit at …
Speaker Daebeom Choi University of Pennsylvania In this talk, we discuss the existence and nonexistence of certain birational contractions of \(\overline{\mathrm{M}}_{g,n}\). Somewhat surprisingly, this depends on the characteristic of the base field: many such contractions exist only in positive characteristic. We present a precise form of this phenomenon and discuss two examples that …
Speaker Yunhyung Cho Sungkyunkwan University It is well known that there is a bijective correspondence between the set of positive integer solutions to the Markov equation and the set of Fano triangles mutation equivalent to the Fano triangle of $\mathbb{P}^2$. In this talk, we establish a higher dimensional generalization of this correspondence for …
Speaker Sung Gi Park Princeton University I will discuss the indeterminacy locus of the period map from the moduli space of hypersurfaces to the period domain and its compactifications. In the case of quartic K3 surfaces, the result verifies the expectation of Laza and O'Grady that the period map from the GIT compactification …