Workshop Top
小研究集会"Symbolic description and low-dimensional topology"
基盤研究B「3次元多様体のヘガード構造と幾何構造 」研究課題番号：18340018 代表者：作間誠により支援を受けています
date: 2009/10/30
place: Hiroshima University
room: Department of Mathematics B707
The event's main focus is the encouragement of exchange between participants.
1000-1130
"Symbolic behavior and symbolic manipulation 1 : with computer" Yusuke Kiriu/Studio Phones
(with T.Sakasai and A.Ushijima)
-Mathematica's pure functions as being like Lambda expressions or anonymous functions-
1300-1430
"Symbolic behavior and symbolic manipulation 2 : without computer" Yusuke Kiriu/Studio Phones
(with T.Sakasai and A.Ushijima)
-Mathematica's pure functions as being like Lambda expressions or anonymous functions-
abstract
Beginning with a short introduction to symbolic and numeric computation,
we discuss interaction between computer science and low-dimensional topology,
especially, algorithms and programming paradigms with features of
both "with computer" and "without computer"
(e.g. Turing's "computable numbers" and "computable diagrams").
In this talk, we give an extension language designed specifically to
symbolic manipulaton of pure functions by using low-level structures of Mathematica.
We can simulate the logic of any computer algorithm and symbolic deformation of algorithm.
1445-1615
"Symbolic construction of developments of surfaces" Akira Ushijima /Kanazawa University
(with Y.Kiriu)
abstract
Starting from a region with two edges, we construct a development of a surface by
truncating vertices. Such a construction is used to obtain the Dirichlet fundamental polygon
of a Fuchsian group. A symbolic manipulation of the developments in a disc plays a key
role; it clarifies when numerical computation is required in the construction. Our
construction is thus expected to grasp topological information of surfaces symbolically.
1630-1800
"A symbolization of train tracks" Hideki Miyachi /Osaka University
(with Y.Kiriu)
abstract
In this talk, I will discuss a parametrization of traintracks
"by symbols" on a closed surface of genus at least 2.
By "by symbols", I mean that our parameters consist of
several symbols, looked to be unconcerned with
any geometries of train tracks on first glance.
We hope that it yields results on geometric natures of
train tracks from the proof looked "independent of" geometries.
Information:
Yusuke Kiriu (Studio Phones) seminar.phones [at] gmail.com
Makoto Sakuma (Hiroshima University) sakuma [at] math.sci.hiroshima-u.ac.jp