Last update: June 25, 2015

Toric Topology 2015 in Osaka

Dates : June 16 (Tue) -- 19 (Fri), 2015

Venue : Room E408 (June 16-18), Room F405 (June 19), Osaka City University

Rooms E408, F405 (and our math. department) are in the building E, F of No. 12 on the campus map

Guest House is No. 25 on the campus map.

This meeting is an activity of JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers

対称性,トポロジーとモジュライの数理， 〜数学研究所の国際研究ネットワーク展開〜

“Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI”

Organizers

Mikiya Masuda (Osaka City Univ.), Shintaro Kuroki (The Univ. of Tokyo), Hiroaki Ishida (RIMS)

Please contact Mikiya Masuda (e-mail: masuda[at]sci.osaka-cu.ac.jp) if you have any question.

Previous meetings:

Toric Topology 2014 in Osaka (Jan. 21-24, 2014)

Toric Topology 2012 in Osaka (Nov. 16-19, 2012)

Toric Topology 2011 in Osaka (Nov. 28-30, 2011)

Future related meetings (many in this year):

Combinatorial and Toric Homotopy (Aug. 1 - 31, 2015, National University of Singapore, Singapore)

Combinatorial Constructions in Topology (Aug. 17-21, 2015, University of Regina, Regina, Canada)

Toric Topology, Number Theory and Applications (Sep. 6-12, 2015, Pacific National University, Khabarovsk, Russia)

International Open Chinese-Russian Conference -- Torus Actions: Topology, Geometry and Number Theory (Oct. 26-29, 2015, Chinese Academy of Sciences, Beijing, China)

Useful link on toric topology The Manchester Toric Topology Page

Accommodations: Osaka City University Guest House, Kansai Kenshu Center

About Japan: Guide to Japan for foreign visitors (due to Megumi Harada)

Conference photo: photo1 photo2 photo3

Participants (G: the guest house, K: the KKC, *: cancelled)

G42 ABE Hiraku (OCAMI, Japan & Toronto Univ, Canada) 6/12-20

G44 AYZENBERG Anton (Osaka City Univ. Japan)

G24,25 BUCHSTABER Victor (Steklov Institute, Russia) 6/7-23

K CHEN Bo (Huazhong Univ. of Science and Technology, China) 6/15-21

G34 CHIANG River (National Cheng Kung University, Taiwan) 6/13-22

* CHOI Suyoung (Ajou Univ., Korea) 6/15-19

G17 DARBY Alastair (Fudan Univ. China) 6/15-22

HARA Yasuhiro (Osaka Univ. Japan)

HASUI Sho (Kyoto Univ. Japan)

HATANAKA Miho (Osaka City Univ. Japan)

HIGASHITANI Akihiro (Kyoto Sangyo Univ. Japan)

HORIGUCHI Tatsuya (Osaka City Univ. Japan)

IRIYE Kouyemon (Osaka Pref. Univ. Japan)

ISHIDA Hiroaki (RIMS, Japan)

KAMIYAMA Yasuhiko (The Univ. of Ryukyu, Japan)

KISHIMOTO Daisuke (Kyoto Univ. Japan)

G33 KUROKI Shintaro (The Univ. of Tokyo, Japan) 6/15-20

KUWATA Hideya (Osaka City Univ. Japan)

* LEE Eunjeong (KAIST, Korea) 6/14-20

MASUDA Mikiya (Osaka City Univ. Japan)

MATSUMURA Tomoo (Okayama Univ. of Science, Japan)

MURAI Satoshi (Osaka Univ. Japan)

OKITSU Yushi (The Univ. of Tokyo, Japan)

OHNITA Yoshihiro (Osaka City Univ. Japan)

G21 PANOV Taras (Moscow State Univ., Russia) 6/1-30

G46 PARK Hanchul (KIAS, Korea) 6/15-20

G43 PARK Seonjeong (NIMS, Korea) 6/8-19

SATO Takashi (Kyoto Univ. Japan)

* SONG Jongbaek (KAIST, Korea) 6/14-20

* SUH Dong Youp (KAIST, Korea) 6/14-20

SUYAMA Yusuke (Osaka City Univ. Japan)

TANISAKI Toshiyuki (Osaka City Univ. Japan)

TSUCHIYA Akiyoshi (Osaka Univ. Japan)

K WANG Wei (Shanghai Ocean Univ. China) 6/15-20

ZENG Haozhi (Osaka City Univ. Japan)

Titles and some abstracts

ABE Hiraku

Title: Representations of symmetric groups on the cohomology of Hessenberg varieties

AYZENBERG Anton

Title: Macaulay's dual systems, volume polynomials, and cohomology of torus manifolds

BUCHSTABER Victor

Title: Toric topology of fullerenes slides1

Abstract: A mathematical fullerene is a convex three dimensional simple polytope with all $2$-faces being pentagons and hexagons. In this case the number $p_5$ of pentagons is $12$. The number $p_6$ of hexagons can be arbitrary except for $1$. The number of combinatorial types of fullerenes as a function of $p_6$ grows rapidly. At that moment the problem of classification of fullerenes is well-known and is vital due to applications in chemistry, physics, biology and nanotechnology. It involves classical and modern methods and results in graph theory, polytope theory and geometry of surfaces. We give the review of progress in this direction. Any fullerene has a moment-angle manifold. Our starting point was to find particular features of such manifolds using approaches of toric topology. We present our results in this area. This is a joint work with Nikolay Erokhovets.

Title: Embedding theorems of quasitoric manifolds slides2

Abstract: We will discuss embedding theorems of quasitoric manifolds into Euclidean and complex projective spaces. The results are formulated in terms of combinatorial data determining quasitoric manifolds. This led to effective bounds for dimensions of embeddings. In the case of quasitoric manifolds having additional structures (such as invariant complex or symplectic structures) we have obtained a new approach to classical results and their generalizations. The talk is based on a paper with Andrey Kustarev.

CHEN Bo

Titile: Codimesion-one embedding of some small covers into Euclidean space

CHIANG River

Title: Cyclic actions on symplectic 4-manifolds

CHOI Suyoung (cancelled)

Title: The topology of real toric spaces

DARBY Alastair

Title: Stunted Weighted Projective Spaces and Thom Orbispaces

HASUI Sho

Title: Strong cohomological rigidity of (C P^2 # C P^2)-bundle type quasitoric manifolds

HATANAKA Miho

Title: On representation decompositions of cohomology rings of toric manifolds associated to cycle graphs

HIGASHITANI Akihiro

Title: Toric Fano manifolds and some equivalence relations

HORIGUCHI Tatsuya

Title: Hessenberg varieties and chromatic quasisymmetric functions

ISHIDA Hiroaki

Title: Infinitesimal automorphisms of moment-angle manifolds with complex-analytic structures

KISHIMOTO Daisuke

Title: Fat wedge filtrations and moment-angle complexes

Abstract: The fat wedge filtration (FWF) of the polyhedral product $Z_K(CX,X)$ was introduced to elucidate the intrinsic homotopical nature of the polyhedral product. We will first review the basics of FWFs, and then will investigate the FWF of the moment-angle complex $Z_K$. As an application we will give a necessarily and sufficient condition for $Z_K$ being a co-H-space in terms of the FWF. This is a joint work with Kouyemon Iriye.

KUROKI Shintaro

Title: On extended actions of complexity one torus manifolds

KUWATA Hideya

Title: On the space of sections of an associated line bundle on a nice topological toric manifold

LEE Eunjeong (cancelled)

Title: Grossberg-Karshon twisted cubes and their untwistedness

MATSUMURA Tomoo

Title: Determinant formula for the full flag of type A and Vexillary permutations

Abstract: A cohomology Schubert class of a Grassmannian is explicitly written as the determinant of a matrix whose entries are the Chern classes of the tautological bundles (Giambelli-Thom-Porteous, Kempf-Laksov). Hudson-Ikeda-M-Naruse (2015) generalized this formula to the K-theory Schubert classes. In this talk, I will explain how one can generalizes these formulas to the Schubert classes of so-call Vexillary type in the full flag varieties (this includes the result of Anderson-Fulton (2015) for the cohomology case). This is a joint work with Thomas Hudson.

MURAI Satoshi

Title: New inequalities for face numbers of d-colorable simplicial d-polytopes

PANOV Taras

Title: On toric generators in the unitary and special unitary bordism rings

PARK Hanchul

Title: Wedge operations and a new family of projective toric manifolds

Abstract: The wedge operation or $P(J)$-construction of simple polytopes is a useful tool for classification of toric spaces, because by a result of Choi-P, one can classify toric spaces over $P(J)$ once the classification of toric spaces over $P$ is known. For example, the generalized Bott manifolds are toric manifolds over wedges of hypercubes $I^k$ and toric manifolds of Picard number 3 are over the wedges of either the cube $I^3$ or the pentagon. In this talk, we completely classify toric manifolds over wedges of polygons and show that they are all projective. The projectivity can be thought as a generalization of the fact that every toric manifold of Picard number 3 is projective. This is a joint work with Suyoung Choi.

PARK Seonjeong

Title: Real toric varieties corresponding to pseudographs

SATO Takashi

Title: p-local stable splitting of quasitoric manifolds

SONG Jongbaek (cancelled)

Title : Odd degree cohomology of projective toric varieties

SUH Dong Youp (cancelled)

Title: Chern classes and symplectic circle actions

Abstract: abstract(Suh).pdf

SUYAMA Yusuke

Title: Non-singular fans and triangulated surfaces

Abstract: We show that a simplicial 2-sphere satisfying a certain condition is the underlying simplicial complex of a non-singular complete fan in $\mathbb{R}^3$. We also show that for any $g \geq 1$, there exists a triangulation of a closed orientable surface of genus g which cannot be the underlying simplicial complex of a non-singular multi-fan.

WANG Wei

Title: Toric generators of some bordism groups

Abstract: The main purpose of this talk is to find some quasitoric manifolds to represent the generators of some bordism groups geometrically. This talk divides into two parts. In the first part, we will collect some basic facts about the structures of some bordism groups. In the second part, we will choose some classes of qusitoric manifolds ( Bott towers, etc.) and discuss whether these manifolds can be generators of these bordism groups. This work is in progress.

ZENG Haozhi

Title: On equivariant b-cohomology groups