Chuyu Zhou, Lecture 2: Non-linear Wall Crossing Theory

B236-1 IBS, Korea, Republic of

    Speaker Chuyu Zhou Yonsei University In this lecture, we will talk about two properties of K-semistable domains in non-proportional setting. One is the finiteness criterion, which states that the number of domains is finite for a family of couples. The other is about the shape of each domain, which states that they are

Sungmin Yoo, Convergence of Sequences of the Bergman Type Volume Forms

B236-1 IBS, Korea, Republic of

    Speaker Sungmin Yoo Incheon National University Following the Yau-Tian-Donaldson conjecture, the construction of sequences of Bergman-type metrics converging to a canonical metric on a polarized manifold has been studied by many mathematicians including Tian, Donaldson, Tsuji, Berman, Berndtsson, and others. In this talk, I will introduce my recent findings on the uniform convergence

Yonghwa Cho, Double Point Divisors from Projections

B236-1 IBS, Korea, Republic of

    Speaker Yonghwa Cho Gyeongsang National University Consider a smooth projective variety of codimension e. A general projection from a linear subspace of dimension (e-2) is birational, hence the non-isomorphic locus forms a proper closed subset of X. Mumford showed that this non-isomorphic locus is not merely a closed subset, but is naturally endowed

Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program I

B236-1 IBS, Korea, Republic of

    Speaker Sung Wook Jang IBS CCG Minimal model program (abbreviated as MMP) is a central problem in birational geometry. The MMP is a sequence of divisorial contractions or flips, which makes the canonical divisor closer to a nef divisor. If the MMP successfully terminates, then we have either a minimal model or a

Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program II

B236-1 IBS, Korea, Republic of

    Speaker Sung Wook Jang IBS CCG We are interested in an anticanonical divisor and hope to establish the MMP for an anticanonical divisor. We believe that the beginning point is the potential log discrepancy that controls singularities of a possible resulting model of MMP for an anticanonical divisor. In this talk, we will

Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program III

B236-1 IBS, Korea, Republic of

    Speaker Sung Wook Jang IBS CCG We can run an MMP for an lc pair. However, in general, we do not know whether the MMP terminates or not. Nevertheless, we can show that special MMP terminates. Immediately, we can prove the existence of minimal models for certain pairs. Analogously, for an anticanonical divisor,

Sung-Yeon Kim, Real orbits in flag manifolds

B236-1 IBS, Korea, Republic of

    Speaker Sung-Yeon Kim IBS CCG Let G​ be a complex semisimple Lie group, P​​ be a parabolic subgroup and G0​​ be a real form of G.​​ Then the flag manifold G/P​​ decomposes into finitely many G0-orbits. The complex structure of G/P​​ yields a natural homogeneous CR manifold structure on the real orbits such

Sung-Yeon Kim, Proper holomorphic maps between bounded symmetric domains

B236-1 IBS, Korea, Republic of

    Speaker Sung-Yeon Kim IBS CCG In this talk, we study the rigidity of proper holomorphic maps f: Ω→Ω'​​ between irreducible bounded symmetric domains Ω​​ and Ω'​​. First, we will define the moduli maps induced by f​​. This moduli maps are CR maps between real orbits in flag maniflods. If the rank difference is

Ngoc Cuong Nguyen, Equidistribution of Fekete points on projective manifolds

B236-1 IBS, Korea, Republic of

    Speaker Ngoc Cuong Nguyen KAIST We survey recent developments on the speed of convergence of Fekete points on projective manifolds where the equidistribution was proved by Berman and Boucksom (2011). In particular, the convergence speed can be obtained for a large class of polynomially cuspidal compact sets introduced by Pawłucki and Pleśniak (1988).

Lorenzo Barban, General results on C*-actions on projective varieties

B236-1 IBS, Korea, Republic of

    Speaker Lorenzo Barban IBS CCG In this lecture series we aim to describe the rich relation between C*-actions on complex normal projetive varieties and the birational maps among the associated geometric quotients. We will begin this first seminar by explaining a motivating example, called the Atiyah flop. We will then discuss general results

Lorenzo Barban, Geometric Invariant Theory for C*-actions

B236-1 IBS, Korea, Republic of

    Speaker Lorenzo Barban IBS CCG In this second talk, which is the technical core of the lecture series, we describe several tools to study C*-actions on projective varieties, such as the bandwidth, the AMvsFM Lemma, and the pruning of a variety. With this, we will be able to describe the -birational geometry of

Lorenzo Barban, Geometric realization of birational maps among Mori dream spaces

B236-1 IBS, Korea, Republic of

    Speaker Lorenzo Barban IBS CCG Given a birational map ϕ among normal projective varieties, a geometric realization of ϕ is a normal projective C*-variety such that the birational map among geometric quotients parametrizing general orbits coincides with ϕ. Geometric realizations can be thought of as a projective algebraic version of the notion of

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