Michel Brion, Introduction to Complete Symmetric Varieties
B236-1 IBS, Korea, Republic ofSpeaker Michel Brion U. Grenoble This is an introductory lecture on compactifications of symmetric spaces in algebraic geometry.
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Workshop on Geometry of Homogeneous Varieties
B109 IBS, Korea, Republic ofSpeakers Michel Brion (U. Grenoble) Jarek Buczynski (IMPAN, Warsaw) Thibaut Delcroix (U. Montpellier) Minseong Kwon (KAIST/IBS-CCG) Qifeng Li (Shandong U.) Yoshinori Namikawa (RIMS, Kyoto) Kyeong-Dong Park (Gyeongsang National U.) Boris Pasquier (U. Poitiers) Léa Villeneuve (U. Poitiers) Abstracts PDF file Schedule April 15 (Monday) 10:00-11:00 Brion 11:20-12:20 Brion 12:30-13:20 Lunch 15:00-16:00 Kwon 16:20-17:40 Li April …
In-Kyun Kim, Wall-crossing of K-moduli Spaces of Weighted Projective Spaces
B236-1 IBS, Korea, Republic ofSpeaker 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 …
Chuyu Zhou, K-stability of Fano Varieties – Various Viewpoints
B236-1 IBS, Korea, Republic ofSpeaker Chuyu Zhou Yonsei University We will present various criterion for K-stability for Fano varieties, including viewpoints from test configurations, valuations, and filtrations.
Chuyu Zhou, Moduli for Fano Varieties with K-stability
B236-1 IBS, Korea, Republic ofSpeaker 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.
Chuyu Zhou, Wall Crossing for K-stability
B236-1 IBS, Korea, Republic ofSpeaker 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.
Benjamin Bakker, Hodge Theory and Lagrangian Fibrations
B236-1 IBS, Korea, Republic ofSpeaker 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 …
Benjamin Bakker, A Proof of Matsushita’s Conjecture
B236-1 IBS, Korea, Republic ofSpeaker 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 …
Shigeyuki Kondo, A Review on Enriques Surfaces: Moduli, Automorphism Groups and Positive Characteristics, I
B236-1 IBS, Korea, Republic ofSpeaker Shigeyuki Kondo Nagoya University The Enriques surface was discovered, in 1894 by Federigo Enriques, as a counter-example of a rationality problem. First I would like to recall the moduli space and the automorphism groups of Enriques surfaces over the complex numbers. In the later half, I shall mention a recent progress in …
Shigeyuki Kondo, A Review on Enriques Surfaces: Moduli, Automorphism Groups and Positive Characteristics, II
B236-1 IBS, Korea, Republic ofSpeaker Shigeyuki Kondo Nagoya University The Enriques surface was discovered, in 1894 by Federigo Enriques, as a counter-example of a rationality problem. First I would like to recall the moduli space and the automorphism groups of Enriques surfaces over the complex numbers. In the later half, I shall mention a recent progress in …
Hsueh-Yung Lin, Motivic Invariants of Birational Automorphisms of Threefolds
B236-1 IBS, Korea, Republic ofSpeaker Hsueh-Yung Lin National Taiwan University The motivic invariant c(f) of a birational automorphism f : X - → X measures the difference between the birational types of the exceptional divisors of f and those of the inverse f-1. In general c(f) is nonzero: this is the case when f is some Cremona …
Ching-Jui Lai, Anticanonical Volume of Singular Fano Threefolds
B236-1 IBS, Korea, Republic ofSpeaker Ching-Jui Lai National Cheung Kung University The set of canonical Fano threefolds form a bounded family by results of Kawamata, Mori-Miyaoka-Kollar-Tagaki, and in a much more general setting by Birkar. In particular, the anticaonical volume -KX3 is bounded. An optimal lower bound is 1/330 by the work of Chen-Chen. In this talk, …