Invited Talks
Yunhyung Cho (IBS-CGP)
Title: Chern numbers for pseudo-free circle actions
Abstract: In this talk, we discuss an odd-dimensional analogue of ABBV-localization theorem for circle actions. While the ABBV-localization technique can be applied for a circle action with non-empty fixed point set, our theorem can be applied for a fixed-point-free circle action. We also give an explicit formula of the Chern number associated to given pseudo-free circle action in terms of local data.
Hiroaki Ishida (Kagoshima University)
Title: Torus invariant transverse K\"{a}hler forms and moment maps
Abstract: A transverse K\"{a}hler form on a complex manifold is a positive $(1,1)$-form whose kernel coincides with the subspace tangent to the leaves of a foliation. I will talk about torus invariant transverse K\"{a}hler forms and moment maps.
Donghoon Jang (KIAS)
Title: Fixed points of symplectic circle actions
Abstract: The study of fixed points of group actions is an important topic in geometry and topology. In this talk, we focus on fixed points of actions in the case where manifolds admit symplectic structures and circle actions on the manifolds preserve the symplectic structures. We discuss main theorems on fixed points of symplectic circle actions, and their relation to the question of when symplectic actions are Hamiltonian. Next, we study properties of symplectic circle actions when the fixed points are isolated, and discuss the classification of symplectic circle actions, when the number of fixed points is small.
Shizuo Kaji (Yamaguchi University)
Title: Products in equivariant homology
Abstract: We discuss an external product associated with the homology of a compact manifold with a Lie group action. It is then used to define a product on $H_G^*(LM)$ the homology of the free loop space over the Borel construction. This product unifies two known constructions in string topology; Chas-Sullivan's string product for the free loop space $LM$ over a manifold and Chataur-Menichi's string product for the free loop space $LBG$ over the classifying space of a compact Lie group. We will also introduce its secondary product, which generalises Tate's cup product in the homology of $BG$. This is joint work with Haggai Tene.
Changzheng Li (IBS-CGP)
Title: A brief introduction to Schubert calculus
Abstract: In this talk, I will talk a brief review of Schubert calculus as well as its various extensions, with an emphasis on some current issues and conjectures to my knowledge.
Boram Park (Ajou University)
Title: Real toric manifolds over pseudograph associahedra
Abstract: A graph associahedron is a simple convex polytope whose facets correspond to proper connected induced subgraphs. Recently, S. Choi and H. Park computed the rational Betti numbers of real toric manifolds over graph associahedron by introducing a graph invariant called $a$-numbers. In this talk, we focus on a pseudograph associahedron which was introduced by Carr, Devadoss, and Forcey as a generalization of a graph associahedron, and then discuss how to compute the rational Betti numbers of real toric manifolds over pseudograph associahedra. This talk is based on a joint work with Suyoung Choi (Ajou University) and Seonjeong Park (NIMS).
Contributed Talks
Hideya Kuwata (Osaka City University)
Title: An embedding map of the connected sum of two complex projective spaces
Abstract: In the workshop, I will talk about an embedding map of the connected sum of two $n$-dimensional complex projective space and the defining equations of that. It is very similar to an embedding map of the blow up of a complex projective space at a point.
Eunjeong Lee (KAIST)
Title: Constructions of flagified Bott--Samelson varieties and Bott towers, and their topology
Abstract: A Bott tower is a sequence of $\mathbb{CP}^1$-fiber bundles such that each stage of which is a toric manifold. In the paper of Grossberg and Karshon, they give a one parameter family of complex structures on a Bott--Samelson variety whose limit is a Bott tower. Even though the notion of Bott towers can be extended to generalized Bott towers and $\mathbb{CP}$-towers, there is no analogue of Bott--Samelson varieties for such extended notions. In this talk, we define a flagified Bott--Samelson variety as an extended notion of a Bott--Samelson variety. Also we will show that there is a one parameter family of complex structures on a flagified Bott--Samelson variety whose limit is a flagified Bott tower, which is a sequence of flag manifold fiber bundles. A flagified Bott tower is not a toric manifold, but a GKM manifold. This talk is based on an on-going project with Dong Youp Suh and Shintar\^o Kuroki.
Jeongseok Oh (KAIST)
Title: How to use torus action in the proof of Mirror Theorem
Abstract:In a certain step of the proof of Givental's Mirror Theorem (GMT) and Wall crossing formula (WCF) by I. Ciocan--Fontanine and B. Kim, we need torus action on the target. Both GMT and WCF deal with generating fuctions of Gromov--Witten type invariants. Torus action on the target help us to have recursion formula about that generating functions. I will give a very brief explanation about this story with easy situation but without any rigorous definitions.
Jongbaek Song (KAIST)
Title: A retraction of simple polytopes and the homology of toric orbifolds
Abstract: For a simple polytope $Q$, we introduce a certain way of retracting $Q$ to a point, which we call this an admissible retraction. There are finitely many ways of such retraction. This leads us to characterize $Q$ by an $(r_n, \cdots, r_2)$-simple polytope, where $r_j$ 's are positive integers determined by considering all possible admissible retractions of $Q$. This concept is required to develop a sufficient condition for torsion freeness in the homology of toric orbifolds. This talk is based on a joint work with Anthony Bahri and Soumen Sarkar.
Haozhi Zeng (Osaka City University)
Title: On the torsions of cohomology groups of toric orbifolds.
Abstract: The cohomology groups of toric orbifolds with rational coefficients are well known. In this talk we will discuss about the torsion part of the cohomology groups of toric orbifolds with integral coefficients. We also give a simple proof to the formula of T. Holm and A. Pires on the fundamental groups of toric origami manifolds. This talk is based on the joint work in progress with H. Kuwata and M. Masuda.