Last update: February 4, 2014

Toric Topology 2014 in Osaka

Dates : January 21 (Tue) -- 24 (Fri), 2014

Venue : Room 833 (Jan. 21, 23, 24), Room 224 (Jan. 22), Osaka City University

On the campus map

Room 833 is on the 3rd floor in the building No. 18

Room 224 is on the 2nd floor in the building No. 17

Guest House is No. 25 and Department of Mathematics is No. 29 on the campus map.

This meeting is an activity of the bilateral program between Japan and Russia: “Topology and geometry of torus actions and combinatorics of orbit quotients”

Organizers

Mikiya Masuda (Osaka City Univ.), Shintaro Kuroki (OCAMI), Hiroaki Ishida (RIMS)

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

Previous meeting:

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

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

Future related meeting:

Topology of torus actions and applications to geometry and combinatorics (Aug. 7-11, 2014, Daejeon in Korea) a satellite conference of ICM 2014

Useful link on toric topology The Manchester Toric Topology Page

Accommodations: Osaka City University Guest House, Kansai Kenshu Center

Access: Brief travel instructions from Kansai International Airport

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

Conference photo: (photo1) (photo2)

Participants (G means stay at the guest house, K means stay at the KKC, ○ shows speakers)

K ○* ABE Hiraku (Tokyo Metropolitan Univ. Japan) 1/20-22, 23-26

G ○* AYZENBERG Anton (Osaka City Univ. Japan)

K ○ BAHRI Tony (Rider Univ. USA) 1/19-24

G ○* BOOTE Yumi (Manchester Univ. UK) 1/20-27

G ○* BUCHSTABER Victor (Steklov Institute, Russia.) 1/19-25

K CAI Li (Kyushu Univ. Japan) 1/20-24

K ○* CHEN Bo (Huazhong Univ. of Science and Technology, China) 1/20-25

G ○ CHO Yunhyung (KIAS, Korea) 1/20-26

K CHOI Suyoung (Ajou Univ., Korea) 1/20-23

G ○* DARBY Alastair (Manchester Univ. UK) 1/19-27

G ○* EROKHOVETS Nickolay (Moscow State Univ. Russia) 1/20-25

FUKUKAWA Yukiko (Osaka City Univ. Japan)

HARA Yasuhiro (Osaka Univ. Japan)

G HARADA Megumi (McMaster Univ. Canada & Osaka City Univ. Japan)

○ HASUI Sho (Kyoto Univ. Japan)

○ HATANAKA Miho (Osaka City Univ. Japan)

HAYASHI Atsuhiro (Osaka City Univ. Japan)

○ HIGASHITANI Akihiro (Osaka Univ. Japan)

○ HORIGUCHI Tatsuya (Osaka City Univ. Japan)

K ○ HUDSON Thomas (KAIST, Korea) 1/20-25

○ IKEDA Takeshi (Okayama Univ. of Science, Japan) 1/21-23

IRIYE Kouemon (Osaka Pref. Univ. Japan)

○* ISHIDA Hiroaki (RIMS, Japan)

KATO Hironao (OCAMI, Japan)

KIMURA Yoshiyuki (OCAMI, Japan)

○* KISHIMOTO Daisuke (Kyoto Univ. Japan) 1/21-23

KITAZAWA Naoki (Tokyo Institute of Tchnology, Japan) 1/21-22

○ KUROKI Shintaro (OCAMI, Japan)

KUWATA Hideya (Osaka City Univ. Japan)

G LEE Eunjeong (KAIST, Korea) 1/20-24

LI Changzheng (IPMU, Japan)

G ○ LIMONCHENKO Ivan (Moscow State Univ. Russia) 1/19-31

K ○* LU Zhi (Fudan Univ., China) 1/20-25

G MA Jun (Fudan Univ. China) 1/20-25

MASUDA Mikiya (Osaka City Univ. Japan)

G ○ MATSUMURA Tomoo (KAIST, Korea) 1/20-24

○ MURAI Satoshi (Yamaguchi Univ. Japan) 1/22-24

NAGASE Teruko (Doshisha Univ. Japan)

NARUSE Hiroshi (Okayama Univ. Japan) 1/21

K NISHIMURA Yasuzo (Fukui Univ. Japan) 1/21-24

OKADO Masato (Osaka City Univ. Japan)

OKAZAKI Ryota (Fukuoka Univ. of Education, Japan)

G ○ PANOV Taras (Moscow State Univ., Russia) 1/14-25

G ○ PARK Hanchul (Ajou Univ. Korea) 1/20-25

G PARK Kyoungsuk (Ajou Univ. Korea) 1/20-1/24

G PARK Sang Gun (Ajou Univ. Korea) 1/20-25

G ○* PARK Seonjeong (NIMS, Korea) 1/20-25

G ○ RAY Nigel (Manchester Univ. UK) 1/20-27

G ○ SARKAR Soumen (Univ. of Regina, Canada) 1/19-25

○* SATO Takashi (Kyoto Univ. Japan)

G ○* SONG Jongbaek (KAIST, Korea) 1/20-24

K ○ STANLEY Donald (Univ. of Regina, Canada) 1/20-25

K SUH Dong Youp (KAIST, Korea) 1/20-24

○ SUYAMA Yusuke (Osaka City Univ. Japan)

SUZUKI Taro (Chuo Univ. Japan)

TANISAKI Toshiyuki (Osaka City Univ. Japan)

K ○* WANG Wei (Shanghai Ocean Univ. China) 1/20-25

G ○ WIEMELER Michael (Karlsruher Institut fur Technologie, Germany) 1/19-25

K YOSHIDA Takahiko (Meiji Univ. Japan) 1/22-24

K YOTSUTANI Naoto (Univ. of Science and Technology of China, China) 1/21-25

K YU Li (Nanjing Univ., China) 1/20-25

ZENG Haozhi (Osaka City Univ. Japan)

Titles, abstracts and some slides

ABE Hiraku

Title: Young diagrams and intersection numbers on toric manifolds associated with Weyl chambers

Abstract: Abe.pdf

Slides: Abe(slide).pdf

AYZENBERG Anton

Title: Alexander duals to boundaries of polytopes

Abstract: Ayzenberg.pdf

Slides: Ayzenberg(slide).pdf

BOOTE Yumi

Title: The integral cohomology of the symmetric square of quaternionic projective space

Abstract:

Slides: Boote(slide).pdf

BUCHSTABER Victor

Title: Toric structure of $(2n, k)$-manifolds

Abstract: Buchstaber.pdf

Slides: Buchstaber(slide).pdf

CHEN Bo

Titile: Self-dual codes realized by small covers and polytopes

Abstract: We introduce how to obtain binary self-dual codes from small covers in toric topology. It turns out that these codes can be explicitly described in term of the combinatorics of some simple polytopes.

Slides: Chen(slide).pdf

CHO Yunhyung

Title: Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

Abstract: Cho.pdf

DARBY Alastair

Title: Torus Manifolds in Equivariant Complex Bordism

Abstract: We restrict geometric equivariant complex bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative graded ring. This is done using equivariant K-theory characteristic numbers. We then discuss the density of quasitoric manifolds in this description.

Slides: Darby(slide).pdf

EROKHOVETS Nickolay

Title: Buchstaber Invariant, 2-surfaces and matroids

Abstract: Erokhovets.pdf

Slides: Erokhovets(slide).pdf

HASUI Sho

Title: On the cohomological rigidity of quasitoric manifolds

Abstract: Hasui.pdf

HATANAKA Miho

Title: Gluing construction of topological toric manifolds

Abstract: A topological toric manifold is a smooth manifold of even dimension with effective smooth action of a complex torus, having an open dense orbit, and locally equivariantly diffeomorphic to a smooth representation space of the complex torus. The notion of topological toric manifolds was introduced by Ishida-Fukukawa-Masuda as a topological analogue of toric manifolds. They construct topological toric manifolds by generalizing the quotient construction in toric geometry. In this talk, I am going to construct topological toric manifolds by generalizing the gluing construction in toric geometry.

HIGASHITANI Akihiro

Title: Smooth Fano polytopes and their primitive collections

Abstract: It is well known that there is a one-to-one correspondence between smooth Fano polytopes and toric Fano manifolds. In this talk, after introducing some notions of smooth Fano polytopes, I will propose the problem concerning the extremal rays of toric Fano manifolds. I will also prove this problem for some particular toric Fano manifolds.

HORIGUCHI Tatsuya

Title: The equivariant cohomology rings of Springer varieties

Abstract: Springer varieties are subvarieties of a flag variety which are parametrized by nilpotent matrices. It is well-known that the cohomology ring of a Springer variety is the quotient of a polynomial ring by the ideal called Tanisaki's ideal. On the other hand, Springer varieties admit a natural torus action. In this talk, we give an explicit description of the equivariant cohomology ring of Springer varieties as the quotient of a polynomial ring by a generalization of the Tanisaki's ideal. (Joint work with H. Abe)

HUDSON Thomas

Title: Schubert classes in the algebraic cobordism of type C flag bundles

Abstract: Let V be a vector bundle over a smooth scheme X. In order to establish a Schubert calculus for the full flag bundle FL V it is necessary to identify a basis for CH^*(FL V) as a module over CH^*(X). For this purpose one considers the fundamental classes of Schubert varieties, which can be described by means of double Schubert polynomials. Analogous constructions are also available for flags of bundles which are isotropic with respect to a given symplectic form on V. I will illustrate one possible way of defining Schubert classes in the context of a general oriented cohomology theory and more specifically in algebraic cobordism.

IKEDA Takeshi

Title: How to compute Schubert classes

Abstract: I will discuss how we can compute *torus* equivariant Schubert classes from two different points of view. First point is a role of the equivariant parameter, which enables us to calculate the Schubert classes by the *left* divided difference operators, while in the classical literature, the right one has been mainly used. The left one is much important because the right one is not available in the parabolic cases. The second point is an equivalence between the degeneracy loci formula of vector bundles and the description of a torus equivariant Schubert class. This gives a pleasant modern interpretation of some classical results that stem from a problem posed by R. Thom. Also, this point of view, on the other hand, enable us to calculate the equivariant Schubert classes by direct geometric arguments.

ISHIDA Hiroaki

Title: Smooth structures on moment-angle complexes for simplicial posets

Abstract: Ishida.pdf

Slides: Ishida(slide).pdf

KISHIMOTO Daisuke

Title: Decomposing real moment-angle complexes

Abstract: Kishimoto.pdf

Slides: Kishimoto(slide).pdf

KUROKI Shintaro

Title: On classification of locally standard torus manifolds up to equivariant diffeomorphism

Abstract: Kuroki.pdf

LIMONCHENKO Ivan

Title: Minimally non-Golod simplicial complexes and moment-angle manifolds

Abstract: Limonchenko.pdf

LU Zhi

Title: Examples of quasitoric manifolds as special unitary manifolds

Abstract： In this talk, we shall show that for each $n\geq 5$ with only $n\not= 6$, there exists a $2n$-dimensional specially omnioriented quasitoric manifold $M^{2n}$ which represents a nonzero element in the unitary bordism ring $\Omega_*^U$. This provides the counterexamples of Buchstaber--Panov--Ray conjecture. (Joint work with Wei Wang).

Slides: Lu(slide).pdf

MATSUMURA Tomoo

Title: Schubert Calculus for Grassmannians of C-type

Abstract: Schubert polynomials are polynomials that represent Schubert classes in flag varieties, in a sense that there is a ring surjection from a "polynomial ring" to the cohomology of the flag varieties and each Schubert polynomial maps to the corresponding Schubert classes. Those polynomials are characterized by divided difference operators. However the problem of writing these polynomials in a closed formula still remains open in general, e.g. Giambelli problem. In a joint work with Takeshi Ikeda, we found a closed formula for the (double) Schubert polynomials corresponding to the equivariant Schubert classes of the Grassmannians in type C (the space of isotropic subspaces in a complex symplectic vector space). Our formula generalizes non-equivariant case solved by Buch-Kresch-Tamvakis, the Lagrangian case solved by Ikeda, and proves the conjecture given in Wilson's thesis. Our work is based on the paper by Ikeda-Mihalcea-Naruse in which they constructed the double Schubert polynomials for Type B,C,D equivariant case, which generalize Billey-Haiman's non-equivariant version.

MURAI Satoshi

Title: Ring isomorphisms of cohomologies of Bott manifolds

Abstract: In this talk, we discuss graded ring isomorphisms between the cohomology rings of Bott manifolds. We present new simple necessary conditions for these isomorphisms and introduce two applications of the conditions. First, we show that any ring isomorphism between the cohomology rings of Bott manifolds preserves their Pontrjagin classes. Second, we show that the strong cohomological rigidity holds for Bott manifolds arising from matrices all whose entries are even. This is a joint work with Suyoung Choi and Mikiya Masuda.

PANOV Taras

Title: Bott towers and equivariant cobordism

Abstract: We describe how Bott towers (in particular, bounded flag manifolds) are applied in several problems of equivariant cobordism theory. These include constructing toric generators for the complex cobordism ring, and representing coefficients in the expansion of the universal toric genus by smooth manifolds.

PARK Hanchul

Title: Odd torsions in the cohomology of small covers

Abstract: In this talk, we compute the cohomology of small covers when the coefficient ring is $\mathbb{Q}$ or a cyclic group of odd order. This is a generalization of a result of Suciu-Trevisan. As an application, we construct infinitely many examples of real toric manifolds whose cohomology admits an odd torsion element. This work is jointly with Suyoung Choi.

PARK Seonjeong

Title: Quasitoric manifolds and toric origami manifolds

Abstract: S. Park.pdf

Slides: S. Park(slide).pdf

SARKAR Soumen

Title: Triangulation of real projective spaces with few vertices

Abstract: P. Arnoux and A. Marin showed that any triangulation of RP^n contains more than (n+1)(n+2)/2 vertices if n >2. We construct some natural triangulations of RP^n with n(n+5)/2+1 vertices for all n >2. We also construct some equivariant triangulations of RP^n with n(n+1) vertices for n > 2.

SATO Takashi

Title: The $T$-equivariant integral cohomology ring of $E_6/T$

Abstract: The GKM theory claims that the equivariant cohomology of some good manifold with a torus action is completely determined by the fixed point sets of subtori of codimension $1$. First I will explain some result of Guillemin, Sabatini, and Zara, which makes us able to analyze some good fiber bundles by the GKM theory. Then applying their result to the fiber bundle $\mathrm{Spin}(10)/T^5 \to E_6/T \to EIII$, I give a concrete description of the equivariant integral cohomology ring of the exceptional flag manifold $E_6/T$.

Slides: Sato(slide).pdf

SONG Jongbaek

Title : The cohomology ring of toric orbifolds with integer coefficients

Abstract : A fan is called simplicial if the set of 1-dimensional rays for each cone is linearly independent. We call a toric orbifold the toric verieties coming from a simplicial fan. For the case of non-singular fan, it is well-known by Danilov and Jurkiewicz that the cohomology ring of non-singular toric variety is isomorphic to Stanley-Reisner ring of underlying simplicial complex modulo linear relations, and Bahri et al showed that the cohomology ring of non-singular toric variety obtained by simplicial wedge construction or more generally J-construction can be easily computed from the original one. In this talk, we shall discuss the orbifold analogue for these results.

Slides: Song(slide).pdf

STANLEY Donald

Title: The Rational Homotopy of Complements

Abstract: Let N be a closed submanifold of a closed manifold M. The complement of Ni in M, M-N is involved in geometric constructions such as the blowup, configuration spaces and the connected sum over N. We describe the rational homotopy type of M-N and apply it to examples coming from toric topology.

SUYAMA Yusuke

Title: Examples of toric manifolds which are not quasitoric manifolds

Abstract: It is known that if a toric manifold is projective or has complex dimension $n \leq 3$, then it is a quasitoric manifold. We show that there are infinitily many toric manifolds which are not quasitoric manifolds for any complex dimension $n \geq 4$.

WANG Wei

Title: Equivariant cohomology Chern numbers and equivariant K theory Chern numbers

Abstract: Given a closed unitary G-manifold M, one can define equivariant cohomology Chern numbers and equivariant K theory Chern numbers of M. We try to understand the relation between these different Chern numbers. More precisely, suppose all equivariant cohomology Chern numbers vanish, does it imply that all equivariant K theory Chern numbers vanish? Or suppose all equivariant K theory Chern numbers vanish, dose it imply that all equivariant cohomology Chern numbers vanish? When G is a torus, we try to give an answer by using equivariant Riemann-Roch relation.

Slides: Wang(slide).pdf

WIEMELER Michael

Title: Rationally elliptic and non-negatively curved torus manifolds

Abstract: I will discuss the classification of torus manifolds which admit an invariant metric of non-negative curvature. If M is a torus manifold which admits such a metric, then M is diffeomorphic to a quotient of a free linear torus action on product of spheres. I will also classify rationally elliptic torus manifolds up to rational homotopy equivalence and homeomorphism.