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

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