Title : Similarities and dissimilarities between the blocking and anti-blocking polyhedra
Abstract : The study of similarities and dissimilarities between the blocking and anti-blocking polyhedra began with a series of celebrated papers by Fulkerson (1970, 1971, 1972), and it has grown up a mature theory by significant contributions of Lehman, Lovász, Padberg, and others in 1970s and 1980s. Even today, this theory still shows a big progression such as the perfect graph theorem of Seymour et al. (2006). In this paper, we survey the current status of this research field with a focus on the conjecture of Conforti & Cornuéjols and the conjecuture of Grinstead.
Shinya Fujita (Yokohama City University, Japan), January 16 (Mon), 2017. 15:30 -- 16:15
Title : Color degree and monochromatic degree conditions for short properly colored cycles
Abstract : For an edge-colored graph, its minimum color degree is defined as the minimum
number of colors appearing on the edges incident to a vertex and its maximum
monochromatic degree is defined as the maximum number of edges incident to a
vertex with a same color. A cycle is called properly colored if every two of its adjacent
edges have distinct colors.
In this work, we give a complete solution to a problem on the minimum color degree
condition for the existence of properly colored cycles. We also introduce some new
results on the minimum color degree and maximum monochromatic degree conditions
for an edge-colored complete graph to contain properly colored triangles, for an edgecolored
complete bipartite graph to contain properly colored cycles of length 4, and
those passing through a given vertex or edge, respectively.
This is joint work with Ruonan Li (University of Twente) and Shenggui Zhang
(Northwestern Polytechnical University).
2016
Ji Sun Huh (허지선 Yonsei University 연세대학교), September 19 (Mon), 2016. 15:00 -- 16:00
Title : Strong semi-complete digraphs
Abstract : A digraph is strongly connected if for all pair x, y, distinct vertices, has a path from x to y. A simple digraph is semi-complete if for every pair x and y of distinct vertices at least one of the arcs (x,y), (y,x) is present. In this talk, we give a combinatorial interpretation of a relation between the number of labeled strong semi-complete digraphs and the number of labeled colored graphs.
Rinki Kim (김린기 University of Waterloo, Canada), September 7 (Wed), 2016. 15:00 -- 16:00
Title : Unavoidable subtournaments in tournaments with large chromatic number
Abstract : For a tournament T, the chromatic number of T is the minimum number of transitive sets with union V(T).
We say a set ℋ of tournaments is heroic if there exists c such that every tournament excluding all members of ℋ has chromatic number at most c.
Berger et al. explicitly characterized all heroic sets of size one. In this talk, we study heroic sets of size two.
Hanchul Park (박한철 KIAS 고등과학원), August 18 (Thu), 2016. 17:00 -- 17:50
Title : Simplicial wedges and classification of toric varieties
Abstract : In this talk, we review the concept of the simplicial wedge construction and characteristic maps, and explain the algorithm to find all toric varieties of given Picard number. This is an ongoing work jointly with Suyoung Choi.
Matthias Franz (University of Western Ontario, Canada), August 18 (Thu), 2016. 16:00 -- 16:50
Title : Big polygon spaces
Abstract : Polygon spaces are configuration spaces of polygons with prescribed edge lengths. We present a related family of compact orientable manifolds, called big polygon spaces. They come with a canonical torus action, whose fixed point set is a polygon space. Big polygon spaces are particularly interesting because they provide the only known examples of maximal syzygies in equivariant cohomology. We will therefore briefly review the theory of syzygies in equivariant cohomology and its relation to the equivariant Poincaré pairing and the "GKM method".
Title : Computational approach of real toric variety
Abstract : In the talk, we present how to use the maple package for computing the rational Betti number of real toric varieties associated to Weyl chambers.
Donghun Lee (이동헌 삼성전자, Princeton University, USA), March 29 (Thu), 2016. 16:30 -- 17:30
supported by Ajou center for mathematics in industry
Title : 수학적으로 알파고를 바라보기
Abstract : 알파고 사건으로 한국에서 다양한 관점의 논란과 토의가 이루어졌지만, 유달리 그 수학적인 함의를 다루지는 못한 것 같다. 수학의 관점에서 알파고라는 바둑 프로그램 안에 어떠한 사실과 가정이 들어가 있는지, 인공지능 연구자로서 간추려낸 알파고의 수학을 살펴보도록 하자. 인공지능에도 수학은 들어가 있다.
Suyoung Choi (최수영 Ajou University 아주대학교), March 8 (Thu), 2016. 17:00 -- 18:00
내부 세미나 (Type B representation on the first cohomology)
Abstract : We study the first cohomology group of the real toric variety corresponding to Weyl chmaber of Type B.
Michitaka Furuya (Tokyo University of Science, Japan), February 29 (Mon), 2016. 16:00 -- 16:50
Title : Some approaches for comparing rainbow domination numbers
Abstract : Let k ≥ 1 be an integer, and set [k]:={1, … ,k}.
Let G be a graph. A function f : V(G) → 2^{[k]} is a k-rainbow dominating function (or k-RDF) of G if ∪_{y ∈ NG(x)}f(y)=[k] for all x ∈ V(G) with f(x)= ∅ . The minimum weight w(f):= ∑_{x ∈ V(G)}|f(x)| of a k-RDF f of G is called the k-rainbow domination number and denoted by Γ_{rk}(G). It has been known that every graph G satisfies Γ_{rk}(G) ≤ |V(G)|, and for k ≥ 4, the bound is sharp because Γ_{rk}(P_{n})=n. In particular, when we focus on upper bounds for the rainbow domination, there is no difference between Γ_{rk} and Γ_{rk'} with k ≠ k'. In this talk, we give some approaches for finding potentially difference.
Kenta Ozeki (National Institute of Informatics, Japan), February 29 (Mon), 2016. 15:00 -- 15:50
Title : Polychromatic colorings of plane graphs and graphs on surfaces
Abstract : For a graph G on a surface (or on the plane), a polychromatic k-coloring of G is a vertex k-coloring such that there appear all k colors in every face of G. In this talk, I will show several results from the case k = 3 or 4, including a necessary and sufficient conditions for the case of quadrangulations.
This is joint work with Atsuhiro Nakamoto (Yokohama National University) and Kenta Noguchi (Tokyo Denki University).
Soojin Cho (조수진 Ajou University 아주대학교), February 12 (Fri), 2016. 15:30 -- 17:30
내부 세미나 (Character of representation)
Abstract : We study the character of representations.
Eunjeong Lee (이은정 KAIST), February 3 (Wed), 2016. 16:00 -- 17:00
Title : A combinatorial description of untwistedness of a Grossberg--Karshon twisted cube
Abstract : Let G be a complex semisimple simply connected Lie group. Let λ be a dominant weight for G and Ι=(i_{1}, i_{2}, …, i_{n}) a word decomposition for an element w =s_{i1} s_{i2} … s_{in} of the Weyl group of G, where the s_{i} are the simple reflections. In the 1990s, Grossberg and Karshon introduced a virtual lattice polytope associated to λ and Ι, which they called a twisted cube, whose lattice points encode the multiplicities of a certain G-representation associated to λ and w. We introduce the notion of hesitant λ-walks and then prove that the associated Grossberg--Karshon twisted cube is untwisted precisely when Ι is hesitant-λ-walk-avoiding. This is joint work with M. Harada.
Li Cai (Chinese Academy of Science, China), January 25 (Mon), 2016. 17:00 -- 18:00
Title : On the integral cohomology of a small cover
Abstract : A small cover is a closed manifold admitting a special 2-torus action, such that the quotient space is a simple convex polytope. The mod 2 cohomology of a small cover has a presentation as the quotient of the associated Stanley-Reisner ring, which is Cohen-Macaulay (over the field of mod 2 integers), by a linear system of parameters. In this talk, we shall analyse the 2-torsion elements in the integral cohomology group of a small cover, using Bockstein homomorphisms.
Suyoung Choi (최수영 Ajou University 아주대학교), January 21 (Wed), 2016. 15:30 -- 17:30
내부 세미나 (S_{n+1}-action on the toric variety associated to Weyl group of type A_{n})
Abstract : We discuss the S_{n+1}-action on the complex and real toric varieties associated to Weyl group of type A_{n}
supported by Ajou center for mathematics in industry
Title : A topological algorithm for shape deformation in computer graphics
Abstract : In computer graphics, mathematics has been a fundamental toolbox. The Navier-Stokes equations is indispensable for generating clouds and fires, reproducing kernel Hilbert space is used for mixing different facial expressions, and simplicial complex and piecewise linear map (PL-map, in short) provide a natural framework for shape manipulation.
In this talk, I will discuss an algorithm to blend/deform shapes based on PL-map and Lie theory. A shape is represented by a simplicial complex and its deformation by a PL-map. Then, creating an animation boils down to finding a nice path in the space of 3-dimensional PL-maps.
Seonhwa Kim (김선화 IBS-CGP, 기하학 수리물리 연구단, Institute for Basic Sience), December 31 (Thu), 2015. 11:00 -- 12:30
Title : Volume of hypercubes clipped by hyperplanes and combinatorial identities
Abstract : There was an elegant expression for the volume of hypercube [0,1]^{n} clipped by a hyper-plane. We generalize the formula to the case of more than one hyperplane. Furthermore we derive several combinatorial identities from the volume expressions of clipped hyper-cubes.
Seonjeong Park (박선정 NIMS 국가수리과학연구소), November 3 (Tue), 2015. 17:00 -- 18:00
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. 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 we discuss how to compute the rational Betti numbers of real toric manifolds over pseudograph associahedra.
Dong Ho Moon (문동호 Sejong University 세종대학교), October 19 (Mon), 2015. 17:00 -- 18:00
Title : A Schur-Weyl Duality Approach to Walking on Representation Graphs
Abstract : A representation graph is a (directed) Cayley graph which encodes the representation theory of a group. I will present how we study combinatorics of representation graphs of finite groups using Schur-Weyl dualities.
Kang-Ju Lee (이강주 Seoul National University 서울대학교), October 6 (Tue), 2015. 17:45 -- 18:45
Title : Path-intersection matrix and applications to network
Atsuhiro Nakamoto (Yokohama National University, Japan), September 15 (Tue), 2015. 17:00 -- 18:00
Title : Domination number of graphs on surfaces
Abstract : Let G be a graph and let S be a subset of the vertex set of G.
We say that S is a dominating set of G if for each vertex v of G, v or a neighbor of v is contained in S.
The domination number of G, denoted by γ(G), is the minimum cardinality of all dominating sets of G.
Finding the domination number of a given graph is a classical and important problem in graph theory, and many people are interested in it.
In our talk, we introduce several results on dominating sets of planar graphs and graphs embeddable on fixed surfaces.
In particular, we describe some elegant proofs for them using a graph coloring, and discuss whether they can be used for solving other related problems.
Stephanie van Willigenburg (Univerisity of British Columbia, Canada), June 30 (Tue), 2015. 11:00 -- 12:00
Title : Maximal supports and Schur-positivity among connected skew shapes
Abstract : The Schur-positivity order on skew shapes B and A is denoted by B<A if the difference of their respective Schur functions is a positive linear combination of Schur functions. It is an open problem to determine those connected skew shapes that are maximal with respect to this ordering.
In this talk we see that to determine the maximal connected skew shapes in the Schur-positivity order it is enough to consider a special class of ribbon shapes. We also explicitly determine the support for these ribbon shapes.
This is joint work with Peter McNamara and assumes no prior knowledge.
Sun-Young Nam (남선영 Sogang Univerisity 서강대학교), June 17 (Wed), 2015. 11:00 -- 12:00
Title : Schur P-functions and shifted Littlewood-Richardson coefficients
Abstract : In this talk, we provide bijections among three combinatorial models for shifted Littlewood- Richardson coefficients:
(a) Littlewood-Richardson-Stembridge tableaux due to Stembridge,
(b) λ-good semistandard decomposition tableaux due to Cho, and
(c) shifted Littlewood-Richardson decomposition tableaux due to Grantcharov, Jung, Kang, Kashiwara, and Kim.
Uijin Jung(정의진 Ajou University 아주대학교), May 13 (Wed), 2015. 17:00 -- 18:00
내부 세미나 (Combinatorics arising from symbolic dynamics: Digraphs, shifts of finite type, Perron eigenvectors and PASEP)
Abstract : In this introductory seminar, we will review basic concepts of symbolic dynamics, which form a subclass of discrete dynamical systems, and combinatorial objects related to symbolic dynamics. We will focus on how notions from directed graphs corresponds to those from shifts of finite type.
Kyoung Sook Park (박경숙 Ajou University 아주대학교), April 8 (Wed), 2015. 16:30 -- 18:00
내부 세미나 (Eulerian numbers, tableaux, and the Betti numbers of a toric variety)
Abstract : 이번 세미나는 지난 4월 1일 세미나의 연속으로, Eulerian numbers, tableaux, and the Betti numbers of a toric variety 논문의 Combinatorial part를 다룰 예정입니다.
Soojin Cho (조수진 Ajou University 아주대학교), April 1 (Wed), 2015. 16:30 -- 18:00
내부 세미나 (Eulerian numbers, tableaux, and the Betti numbers of a toric variety)
Abstract : Eulerian numbers, tableaux와 Betti numbers of a toric variety에 대하여 알아본다.
Kang-Ju Lee (이강주 Seoul National University 서울대학교), March 27 (Fri), 2015. 16:30 -- 18:30
Title : High-Dimensional Trees and Matroids
Abstract :
Part 1. High-dimensional trees
We introduce high-dimensional trees as a high-dimensional analogue of spanning trees. G. Kalai (1983) initiated a study of these objects, giving a formula for the high-dimensional tree numbers of standard simplexes as a high-dimensional analogue of Cayley's fomrula (for the number of spanning trees in complete graphs). We also present our formula for high-dimensional weighted tree numbers. Part 2. Introduction to matroid theory
We see the definition of a matroid and some terminologies, examples, and invariants from matroid theory. Part 3. Weighted tree numbers of matroid complexes
We give a new formula for the weighted high-dimensional tree numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes are polynomials in the weights. In the formula, Crapo's β-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree numbers for matroid complexes. As an application of our formula, we answer the question posed by R. Adin (1992) for weighted tree numbers of complete colorful complexes.
This is a joint work with Woong Kook (SNU).
Suyoung Choi (최수영 Ajou University 아주대학교), March 16 (Mon), 2015. 18:30 -- 19:30
내부 세미나 (On permutohedron)
Abstract : Permutohedron에 대해 소개하고 Permutohedron이 가지는 위상적, 조합적 성질에 대하여 알아본다.
Shinya Fujita (Yokohama City University, Japan), January 26 (Mon), 2015. 15:30 -- 16:30
Title : Safe Set Problem on Graphs
Abstract : For a connected graph G=(V(G),E(G)), a vertex subset S of V(G) is a safe set if for every component C of G[S],
|C| ≥ |D| holds for every component D of G-S such that there exists an edge between C and D; and moreover, if G[S] is connected,
then S is called a connected safe set. In this talk, we discuss the minimum sizes of safe sets and connected safe sets in connected graphs.
This is joint work with Gary MacGillivray (University of Victoria) and Tadashi Sakuma (Yamagata University).
Title : Simplicial spheres and moment-angle manifolds
Abstract : A moment-angle complex $\mathcal{Z}_K$ is a topological space equipped with an $(S^1)^m$-action, defined for an abstract simplicial complex $K$ on the vertex set $\{1,\dots, m\}$. It has been shown that a moment-angle complex $\mathcal{Z}_K$ is a topological manifold if the geometric realization of $K$ is homeomorphic to sphere, and it admits a smooth structure invariant under the torus action if $K$ is a star-shaped sphere. However, any necessary and sufficient condition for a simplicial complex $K$ so that $\mathcal{Z}_K$ admits a structure of smooth $(S^1)^m$-manifold.
Sinuk Kang (강신욱 NIMS), May 30 (Fri), 2014. 16:30 -- 18:30
Sinuk Kang (강신욱 NIMS), May 26 (Mon), 2014. 16:30 -- 18:30
Intensive series lectures for undergraduate course students (4 Lectures)
Title : Introduction to Mathematical signal processing : Fourier anlaysis
Abstract : The aim of this series of lectures is to show how mathematics is involved in our daily life by introducing mathematical theories of signal processing. Fourier analysis has played a fundamental and crucial role in development of the signal processing. We glance through examples of practical applications in the area, especially in audio/image processing, and see how Fourier analysis comes into play. We cover various topics which benefit from Fourier analysis, such as basis/frame theory, Shannon’s sampling theorem, wavelets etc. Both theoretical and practical aspect of the topics are to be discussed.
Basic linear algebra and analysis is prerequisite for the lectures. The lectures are intended for auditors attending all, however auditors interested in a particular topic according to the schedule below are also welcome to attend just that lecture. Link
Li Cai (Kyushu University, Japan), March 7 (Fri), 2014. 16:30 -- 17:30
Title : On the hierarchy in certain aspherical real moment-angle manifolds
Abstract : The Borel Conjecture states that any map inducing a homotopy equivalence between two closed aspherical manifolds is homotopic to a homeomorphism. It is known that aspherical real moment-angle manifolds and their quotients provide a big class of examples supporting the Borel Conjecture, when the dimension is not 4. In this talk we try to extend Haken-Waldhausen's work in dim 3 to all dimensions for these manifolds, and it turns out that there is a natural hierarchy for them.
2013
Seonjeong Park (박선정 NIMS), December 20 (Fri), 2013. 11:00 -- 12:00
Title : Introduction to topological data analysis
Abstract : Data is a finite set of discrete noisy points, sampled from an unknown space, and embedded in a high dimensional space. Topological data analysis recovers the topology of the sampled space. In this talk, we discuss two computational methods in topological data analysis: persistent homology and mapper.
Yunhyoung Cho (조윤형 KIAS), November 25 (Mon), 2013. 17:00 -- 18:00
Title : Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points
Hye Jin Jang (장혜진 POSTECH), November 11 (Mon), 2013. 17:00 -- 18:00
Title : 매듭 동형군 소개
Abstract : 매듭 동형군(Knot concordance group)의 정의를 소개하고, 매듭 동형군 연구를 통해 해결할 수 있는 4차원 위상수학 문제에 관해 논한다. 매듭 동형군 분류를 위해 사용할 수 있는 기본적인 불변량을 소개한다.
Kyoung Sook Park (박경숙 Ajou University 아주대학교), November 4 (Mon), 2013. 17:00 -- 18:30
Title : A combinatorial proof of a symmetry of (t,q)-Eulerian numbers of type B and D
Abstract : A symmetry of (t,q)-Eulerian numbers of type B is combinatorially proved using permutation tableaux of type B; we define a bijection preserving many important statistics on the set of permutation tableaux of type B.
This bijection proves a symmetry of the generating polynomial $\hat{D}_{n, k}(p,q,r)$ of number of crossings, (two types of) alignments, and hence q-Eulerian numbers of type A (defined by L. Williams).
By considering the restriction of our bijection on permutations of type D, we were lead to define a new statistic on the set of permutations of type D and (t,q)-Eulerian numbers of type D, which is proved to have a nice symmetry also. We conjecture that our new statistic is in the family of Eulerian statistics for permutations of type D.
Hyun Woong Cho (조현웅 KAIST), October 7 (Mon), 2013. 17:00 -- 18:30
Title : Periodicity of real Buchstaber invariant
Abstract : In this talk, I'll explain the conjecture in the Y.Fukukawa and M.Masuda's paper "Buchstaber Invariants of Skeleta of a Simplex". The conjecture is about the real Buchstaber invariant. The Buchstaber invariant s(K) is defined to be the maximum integer for which there is a subtorus of dimension s(K) acting freely on the moment-angle complex associated with a finite simplicial complex K. Analogously, its real version s_R(K) can be also be defined by using the real moment-angle complex. In the above paper, the authors make some computation of s_R(K) when K is a skeleton of a simplex and give a conjecture about some number which is closely related with s_R(K). I'll summarize the paper briefly. After that, we shall consider some naive reasons to think that the conjecture is true. Also I'll explain some trial to prove it.
2012
Ihyeok Seo (서이혁 KIAS), October 23 (Tue), 2012. 16:30 -- 17:30
Title : Topics in unique continuation and Schrodinger equations
Suyoung Choi (최수영 Ajou University 아주대학교), October 9 (Tue), 2012. 16:30 -- 17:30
내부세미나 (Title : Topology of real Bott manifolds)
Abstract : A real Bott manifold is a closed smooth manifold obtained as the total space of an iterated RP^1-bundles starting with a point, where each RP1-bundle is the projectivization of the Whitney sum of two real line bundles. A 2-dimensional torus and a Klein bottle provide examples of real Bott manifolds.
It is shown that the diffeomorphism types of real Bott manifolds can be completely characterized in terms of three simple matrix operations on square binary matrices symmetrically permutable to strict upper triangular form. This characterization can be visualized combinatorially in terms of graph operations on directed acyclic graphs.
Using this combinatorial interpretation, in this talk, we discuss about several properties of real Bott manifolds, and introduce recent works on this topic.
성찬영 (건국대학교), September 18 (Tue), 2012. 16:30 -- 17:30
Title : Geometry and physics of Einstein metrics
Sung Rak Choi (최성락 POSTECH), September 12 (Wed), 2012. 15:00 -- 16:50,
Lecture 1
Title : The minimal model program; birational geometry of algebraic varieties
Abstract : I will give an introduction and overview of the history of the minimal model program.
Lecture 2
Title : The minimal model program and beyond
Abstract :I will discuss the recent developments of the minimal model program (MMP).
As their applications, I will explain how the MMP can be used to study
the structure of the various cones of divisors of Fano varieties.
Jang Soo Kim (김장수 University of Minnesota), August 7 (Tue), 2012. 16:30 -- 17:30
Title : Proofs of Two Conjectures of Kenyon and Wilson on Dyck Tilings
Abstract : Recently, Kenyon and Wilson introduced a certain matrix M in order to
compute pairing probabilities of what they call the double-dimer
model. They showed that the absolute value of each entry of the
inverse matrix M-1 is equal to the number of certain Dyck tilings of a
skew shape. They conjectured two formulas on the sum of the absolute
values of the entries in a row or a column of M-1. In this talk we
prove the two conjectures. As a consequence we obtain that the sum of
the absolute values of all entries of M-1 is equal to the number of
complete matchings. We also find a bijection between Dyck tilings and
complete matchings.
Soojin Cho (조수진 Ajou University 아주대학교), June 29 (Fri), 2012. 16:30 -- 18:00
내부 세미나 (Combinatorics of Coxeter Groups)
Soojin Cho (조수진 Ajou University 아주대학교), May 29 (Tue), 2012. 16:30 -- 18:00
내부 세미나 (Combinatorics of Coxeter Groups)
최재혁 (Goldman Sachs), May 22 (Tue), 2012. 16:30 -- 17:30
Title : 금융위기 이후 퀀트의 역할
Abstract : 서브 프라임 모기지로 시작된 금융위기는 금융의 각 분야에 큰 변화를 가져오고 있습니다. 특히 파생상품 시장에 도입되는 새로운 규제와 거래 방법들은 월가에서 일하는 퀀트들의 업무에도 직접적인 영향을 미치고 있습니다. 이러한 변화들이 퀀트들에게는 기회일지 위기일지, 그리고 한국에서 퀀트를 꿈꾸는 학생들에게는 어떤 의미가 있을지에 대해서 얘기를 나눠 보겠습니다.
Soojin Cho (조수진 Ajou University 아주대학교), May 8 (Tue), 2012. 16:30 -- 18:00
내부 세미나 (Combinatorics of Coxeter Groups)
Suyoung Choi (최수영 Ajou University 아주대학교), April 3 (Tue), 2012. 16:30 -- 18:30
내부 세미나 (Different moment angle manifolds with the same bigraded betti numbers)
Akihiko Miyachi (Tokyo Woman's Christian University), March 27 (Tue), 2012. 16:30 -- 17:30
Title : Some results on multilinear Fourier multipliers
Suyoung Choi (최수영 Ajou University 아주대학교), March 13 (Tue), 2012. 16:30 -- 18:30
내부 세미나 (Tor algebra of polytopes)
Kyoung Sook Park (박경숙 Ajou University 아주대학교), February 23 (Thu), 2012. 16:00 -- 17:30
내부 세미나 (Poset topology; a basic)
Young Woo Choi (최영우 Ajou University 아주대학교), February 9 (Thu), 2012. 16:00 -- 17:30,
내부 세미나 (Combinatorics of Coxeter Groups Chap.4 III)
Young Woo Choi (최영우 Ajou University 아주대학교), February 2 (Thu), 2012. 16:00 -- 17:30,
내부 세미나 (Combinatorics of Coxeter Groups Chap.4 II)
Young Woo Choi (최영우 Ajou University 아주대학교), January 26 (Thu), 2012. 16:00 -- 17:30,
Title: The Weyl group action on the GKM graph of a G-manifold
Abstract: GKM theory provides a way to study the topology of manifolds with "good" torus action by means of the combinatorics of a graph. For example, the torus equivariant cohomology can be described purely combinatorially.
In this talk, I will talk about a certain kind of symmetry on the graph which arises from a Lie group action on the manifold. The main result is a combinatorial description of G-equivariant cohomology of the G-manifold.
Anna Abczynski (Bonn University), November 18 (Fri), 2011. 16:30 -- 17:30
Title : On the Polarisation of Manifolds
Abstract : In this talk I will explain how modified surgery theory can be used to study the polarised structure set. The polarised structure set of some manifold M is the set of diffeomorphism classes of manifolds whose cohomology ring is isomorphic to the one of M, preserving Pontrjagin and Stiefel-Whitney classes.
I'll give an upper bound for the order of the polarised structure set of a complex 4-dimensional Spin Bott manifold.
유환철 (KIAS), November 2 (Wed), 2011. 15:00 -- 17:00
유환철 (KIAS), October 26 (Wed), 2011. 15:00 -- 17:00
Series Lectures on hyperplane arrangements (4 lectures)
Title : Hyperplane arrangements, Weyl groups and Schubert varieties
Abstract : I will talk about some basic materials on hyperplane arrangements, Weyl groups, and Scubert varieties. I will define important invariants, including characteristic polynomial, and look at some interesting examples of hyperplane arrangements. In particular I will talk about root hyperplane arrangements of Weyl groups. Using properties of (signed) graphical arrangements, I will show how the characteristic polynomials factor. I will also briefly talk about Schubert varieties and their relation to Weyl groups if time allows. The materials are going to be used when I present the result of the joint work with Suho Oh and Alexander Postnikov that links Schubert varieties in the full flag manifolds G/B with hyperplane arrangements. The Schubert varieties are parameterized by elements of the Weyl group, and we associate a hyperplane arrangement to each of the elements. Our result is that the generating function of regions of the arrangement coincides with the Poincare polynomial of the corresponding Schubert variety if and only if the Schubert variety is rationally smooth. We also describe how they factor in terms of certain invariants of the hyperplane arrangements.
Suyoung Choi (최수영 Ajou University 아주대학교), October 12 (Wed), 2011. 15:00 -- 16:30
내부 세미나 (Small remarks on Bruhat order complex of symmetric groups)
정은경 (아주대학교), October 5 (Wed), 2011. 15:00 -- 16:30
내부 세미나 (Combinatorics of Coxeter groups. Chapter 3. II)
정은경 (아주대학교), September 28 (Wed), 2011. 16:00 -- 17:30
내부 세미나 (Combinatorics of Coxeter groups. Chapter 3. I)
Suyoung Choi (최수영 Ajou University 아주대학교), September 14 (Wed), 2011. 16:00 -- 17:30
내부 세미나 ('Bruhat order complex)
유미수 (서울대학교), August 25 (Thu), 2011. 14:00 -- 15:30
내부 세미나 (Combinatorics of Coxeter groups. Chapter 2)
Shintaro Kuroki (KAIST), August 24 (Wed), 2011. 16:00 -- 17:00
Title : On cohomological rigidity problems of CP-towers
Abstract : The cohomological rigidity problem of the set of manifolds \mathcal{M} asks whether cohomology rings determine the diffeomorphism (or homeomorphism) types of \mathcal{M}. Of course for general manifolds the answer of this problem is NO. However, the answer is sometimes YES if we restricted the class of manifolds. In particular, for toric manifolds or more restricted Bott manifolds this problem is still open. In this talk, we study this problem for a little bit wider class, called CP-tower, than the Bott manifolds.
Seonjeong Park (박선정 KAIST), August 11 (Thu), 2011. 15:00 -- 16:30
내부 세미나 (cohomological rigidity of small covers)
유미수 (서울대학교), July 28 (Thu), 2011. 17:00 -- 18:00
Title : Combinatorics of Macdonald polynomials and the space of diagonal harmonics
Abstract : In 1988, Macdonald introduced a remarkable new basis for the space of symmetric functions, denoted by P_{\lambda}(X;q,t), which are called "Macdonald polynomials". They specialize to many of the well-known bases for the symmetric functions such as Schur functions, Hall-Littlewood functions, Jack symmetric functions and zonal functions. Since their introduction, Macdonald polynomials have been intensely studied and have found applications in special function theory, representation theory, algebraic geometry, group theory and quantum mechanics.
In this talk, we introduce Macdonald polynomials and combinatorial formulas concerning them including Haglund-Haiman-Loehr's. Also, we concern the space of diagonal harmonics and combinatorics of Dyck path and parking functions.
Soojin Cho (조수진 Ajou University 아주대학교), July 10 (Thu), 2011. 15:00 -- 16:30
내부 세미나 (Combinatorics of Coxeter groups. Chapter 1. III))
Suyoung Choi (최수영 Ajou University 아주대학교), Soojin Cho (조수진 Ajou University 아주대학교), June 28 (Tue), 2011. 15:00 -- 18:00
내부 세미나 (Finite reflection group과 Coxeter graph 와의 관계에 대해서. III)
내부 세미나 (Combinatorics of Coxeter groups. Chapter 1. II)
Suyoung Choi (최수영 Ajou University 아주대학교), Soojin Cho (조수진 Ajou University 아주대학교), June 22 (Wed), 2011. 15:00 -- 18:00
내부 세미나 (Finite reflection group과 Coxeter graph 와의 관계에 대해서. II)
내부 세미나 (Combinatorics of Coxeter groups. Chapter 1. I)
Suyoung Choi (최수영 Ajou University 아주대학교), June 14 (Tue), 2011. 15:00 -- 16:30
내부 세미나 (Finite reflection group과 Coxeter graph 와의 관계에 대해서. I)