# KPPY 65

July 26, 2014. 11:00am-6:00pm at PNU

Schedule | ||

11:00am - 11:50 |
Osamu Shimabukuro Nagasaki University | Modular adjacency algebras of Grassmann schemes |

12pm - 1:25 | Lunch | |

1:30 - 2:20 |
Seungjae Eom PNU | On Isometric Dimension and Irreducible graphs |

2:30 - 3:20 |
Koji Tasaka POSTECH | The algebra of multiple zeta values and multiple Eisenstein series |

3:30 - 4:20 |
Juhyun Nam Seoul National Universit | Analytic approach to coherence of adjoint ideal sheaves |

4:30 - 5:20 |
Javad Nadja-Arani Sungkyunkwan University, University of Kashan | Cut method: Update on recent development and equivalence of independent approaches |

## Abstracts

Osamu Shimabukuro

Modular adjacency algebras of Grassmann schemes

Modular adjacency algebras of Grassmann schemes

The adjacency algebra of an association scheme is defined over an
arbitrary field. In general, it is always semisimple over a field of
characteristic zero but not always semisimple over a field of positive
characteristic. The structures of adjacency algebras over fields of positive
characteristic have not been sufficiently studied.
In this talk, we consider the structures of adjacency algebras of some
P-polynomial schemes of class d with intersection numbers $c_i \not\equiv 0$ modulo $p$
for $1 \leq i \leq d$ over fields of positive characteristic $p$. The classes of these
$P$-polynomial schemes include association schemes originating from
Grassmann graphs, double Grassmann graphs, and all types of dual polar
graphs. We will discuss the structures of the modular adjacency algebras of
Grassmann graphs with particular parameters. This is based on a joint
work with Masayoshi Yoshikawa (Nagano Prefecture Azusagawa Senior
High School).

Seungjae Eom

On Isometric Dimension and Irreducible graphs

On Isometric Dimension and Irreducible graphs

For a simple connected graph $G$, we define a canonical embedding which is an isometric embedding from $G$ to a product of graphs. And we define the isometric dimension and irreducible graph. In this talk, we will show some examples of the isometric dimension and we focus on decreasing of the isometric dimension of non-irreducible graphs. Finally, we calculate the isometric dimension of strongly regular graphs.

Koji Tasaka

The algebra of multiple zeta values and multiple Eisenstein series

The algebra of multiple zeta values and multiple Eisenstein series

The multiple zeta value (abbreviated MZV) is a kind of
generalization of the well-known Riemann zeta values $\zeta(n), n \in \mathcal{Z}_{>1}$, and
is an important real value related to knot theory, quantum field theory and
so on. It is known that the space of MZVs has the structure of a
commutative algebra over $\mathcal{Q}$. This algebra is deeply connected with the
theory of mixed Tate motives.
In this talk, we consider the multiple Eisenstein series (abbreviated MES).
The MES, defined by Gangl-Kaneko-Zagier in 2006, plays key role in
understanding a connection between MZVs and modular forms for $\rm{SL}_2\mathcal{Z}$.
One of the goal is to construct the multiple Eisenstein series algebra by
making use of the Goncharov coproduct which gives a Hopf algebra
structure in the MZV algebra. This is based on a joint work with Henrik
Bachmann (Hamburg University).

Juhyun Nam

Analytic approach to coherence of adjoint ideal sheaves

Analytic approach to coherence of adjoint ideal sheaves

We start by defining algebraic multiplier ideal sheaves with
respect to divisors. With a divisor, one can get a plurisubharmonic function
which can define analytic multiplier ideal sheaves. Naturally, these two
sheaves are the same thing if they came from one divisor. And the sheaves
are coherent. Using this theories, we introduce the algebraic analogue of
multiplier ideal, called adjoint ideal sheaves, and define the analytic adjoint
ideal sheaves attached to plurisubharmonic function. We suggest a analytic
approach to proof of coherence of adjoint ideal sheaves.

Javad Nadja-Arani

Cut method: Update on recent development and equivalence of independent approaches

Cut method: Update on recent development and equivalence of independent approaches

Let $\Theta^*$ be the transitive closure of the Djokovic-Winkler's
relation $\Theta$. $\Theta^*$ is an essential relation in metric graph theory which has
many applications; we will present a number of them. In this talk, a history
of isometric embedding and a general description of the cut method is
presented. More precisely, a computation of the Wiener index and more
distance base graph invariants is described. Finally, we present some open
problems and conjectures in metric theory of graphs.