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東工大大岡山キャンパス
数学科
西8号館 W1101

※このセミナーは理学院 数学系と 情報理工学院 数理・計算科学系により運営されています。

### 平成30年度 1Q-2Q：

4月11日（水） 16:00〜17:00

Gleb Nenashev 氏（Stockholm University）

Zonotopal Algebra

I will speak about Zonotopal algebras, which were defined for arbitrary zonotopes. There are three types of these algebras: external, central, and internal. These algebras have a number of interesting properties. Their Hilbert series are specializations of the corresponding Tutte polynomial. In the case of unimodular zonotopes: the total dimensions are the number of lattice points, the volume, and the number of interior lattice points resp. In the graphical case: the first two algebras enumerate forests and trees. The external algebra of a complete graph is the algebra generated by the Bott-Chern forms of the corresponding complete flag variety. For a connected graph, the central ideal is related to the parking ideal, which is generated by stable configurations of the chip-firing game. I will focus more on the external case, which is more natural. In fact, an external zonotopal algebra remembers the combinatorial structure of its zonotope.

5月14日（月） 15:30〜17:00

Youngjin Bae氏（京都大学）

A Chekanov-Eliashberg algebra for Legendrian graphs

We define a differential graded algebra for Legendrian graphs in the standard contact Euclidean three space. This invariant is defined combinatorially by using ideas from the bordered version of Legendrian contact homology. A set of countably many generators and a generalized notion of equivalence are introduced for invariance. I will also talk about the geometry and topology of bordered Legendrians in bordered contact manifolds. This is joint work with Byung Hee An.

いつもと曜日，場所が違いますのでご注意ください．
5月16日（水） 15:30〜17:00

Byunghee An 氏（POSTECH）

Subdivisional spaces and configuration spaces of graphs

We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a \emph{subdivisional space}---a kind of diagram object in a category of cell complexes. After developing a version of Morse theory for subdivisional spaces, we decompose $X$ and show that the homology of the configuration spaces of $X$ is computed by the derived tensor product of the Morse complexes of the pieces of the decomposition, an analogue of the monoidal excision property of factorization homology. Applying this theory to the configuration spaces of a graph, we recover a cellular chain model due to Świątkowski. Our method of deriving this model enhances it with various convenient functorialities, exact sequences, and module structures, which we exploit in numerous computations, old and new.

6月13日（水） 13:30〜14:30

いつもと時間，場所が違いますのでご注意ください．