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The goal of the this workshop is for communicating with mathematicians in Korea and near countries who are interested in toric topology and computational topology. This meeting will be informal and relaxed for intensive discussions.
2014 December 26th (Seminar Room)
14:0014:30 
Registration 
14:3015:30 
Masuda, Mikiya (Osaka City University) Cohomology of regular Hessenberg 
15:3016:00 
Cho, Jin Hwan (NIMS) 
16:0016:30 
Cho, Yunhyung (Instituto Superior Técnico, Lisbon) On the hard Lefschetz property of symplectic 


17:0018:00 
Suh, Dong Youp (KAIST) About transformation group 


18:0020:00 
Banquet (Ocean Palace Hotel Jeju) 
2014 December 27th (Seminar Room)
9:009:30 
Discussion 
9:3010:00 
Tomoo, Matsumura (KAIST) Determinant and Pfaffian formulas for Schubert varieties 
10:0010:30 
Jerome, Tambour (KSA of KAIST) Second basic Betti numbers of certain toric foliations 


11:0011:30 
Kuroki, Shintaro (Tokyo University) Cohomological rigidity and nonrigidity of CPtowers 
11:3012:00 
Hwang, Taekkyu (KIAS) Integrable systems 


14:0014:30 
Park, Seonjeong (NIMS) Origami structures on quasitoric 
14:3015:00 
Park, Hanchul (KIAS) Generalized permutohedra and torsions of cohomology of small covers 


16:0016:30 
Park, Dae Hee (Chonnam National University) 
14:3015:00 
Discussion 
2014 December 28th (Meeting Room)
9:009:30 
Discussion 
9:3010:30 
Choi, Suyoung (Ajou university) 
10:3011:00 
Closing 
Hessenberg varieties Hess(X,h) are subvarieties of a flag variety Flag(\C^n) parametried by two data X and h where X is an endomorphism of \C^n and h is a function
[n] → [n] such that i ≤ h(i) ≤ h(i+1) for i=1,2, … , n1 and h(n)=n.
Springer varieties and Peterson varieties are important examples of Hessenberg varieties and their cohomology rings are well studied. However, the cohomology rings of the others are not well understood. In this talk I will discuss the cohomology rings of Hess(X,h) when X is regular nilpotent or regular semisimple.
This is a joint work with H. Abe, M. Harada and T. Horiguchi.
TBA
In this talk, we introduce a new method to construct a closed symplectic manifold of nonhard Lefschetz type. Using our construction, we also give an answer for KhesinMcDuff's question for the existence of continuous family of symplectic structures with varying symplectic Hodge numbers.
TBA
For a Schubert variety of a certain type, we can construct the resolution of singularities as a projective tower. By pushing forward its fundamental class, we can derive the determinant formula in type A and the Pfaffian (sum) formula in type C. In this talk, I will try to explain this method, following Kazarian's preprint "On Lagrange and symmetric degeneracy loci". This is a joint work with T. Ikeda, T. Hudson, and H. Naruse.
Following the works of Lopez de Medrano, Verjovsky and Meersseman,
Bosio described in 2001 a construction of non kahler compact complex manifolds.
Those manifolds, known as LVMB manifolds, are parametrized by simplicial
complete fans and, when the fan is rational, one can also define a foliation on a
LVMB manifold N whose leaves are closed and diffeomorphic to compact tori.
Moreover, the leaves space can naturally be identified with a compact toric variety.
The Betti numbers of the cohomology of this torus variety are closely related to
the combinatorics of the fan describing N.
In the non rational case, one can still define a foliation on a LVMB manifold N but
the leaves are not closed anymore. The leaves space being non Hausdorff, it is
more convenient to study instead the basic cohomology of the foliation. In the case
where the fan is shellable, computations have been made by Battaglia and Zaffran.
In this talk, we will present the problem of the computation in the general case.
This is a work in progress with Dan Zaffran.
Let M, N be (quasi)toric manifolds. In 2006, MasudaSuh asked the following problem: is M homeomorphic (or diffeomorphic) to N if their cohomology rings are isomorphic? This is now called a cohomological rigidity problem for (quasi)toric manifolds. There are many affirmitive answers to this problem; however, the original question is still open even for the restricted class of manifolds such as the generalized Bott manifolds.
In this talk, I introduce a more general calss of manifolds than the generalized Bott manifolds, called a CPtower which is defined by an iterated complex projective bundles obtained by projectivizations of complex vector bundles. And I show that 6dimensional CPtowers satisfy the cohomological rigidity but 8dimensional CPtowers do not satisfy the cohomological rigidity. Note that a CPtower M is a (quasi)toric manifold if and only if M is a generalized Bott manifold. This is a joint work with Prof. Dong Youp Suh.
I will introduce the notion of integrable systems and discuss how the situation is different from the case when there is a torus action.
An origami template is a collection of Delzant polytopes with some additional gluing data encoded by a template graph. In this talk, we discuss the existence of an origami template for a simple polytope which is the orbit space of a quasitoric manifold. This is a joint work with A. Ayzenberg, M. Masuda, and H. Zeng.
The small cover and the real toric manifold has been an important subject in toric topology, but its topological properties are not known very well. In this talk, we introduce a family of polytopes called generalized permutohedra and use it to construct an infinite family of real toric manifolds having torsion in their cohomology. This is jointly done by Suyoung Choi.
TBA
TBA