2014 academic year

Special Seminar: Workshop on Geometry of the equations of Fuchsian type

Date: December 5 (Fri) - 6 (Sat)

Place: B707, Fac. Sci., Hiroshima University

Speakers: Kazuki HIROE (Josai Univ.), Shingo KAMIMOTO (Kyoto Univ.), Yasunori OKADA (Chiba Univ.)

HP (in Japanese)

No. 3

Date: September 10 (Wed) 15:00 - 16:00

Place: B702, Fac. Sci., Hiroshima University

Speaker: Masaki HIBINO (Meijo University)

Title: On the summability of divergent power series solutions for complex analytic differential equations

Abstract:

    When we have obtained divergent power series solutions for differential equations with complex variables, some new problems arise. One of them is the problem of "(k-) summability" of such divergent solutions.
    In this talk, we first introduce main results in the theory of ordinary differential equations for this problem. Next we introduce the result which was obtained by Lutz-Miyake-Schäfke, for heat equations, and explain the difference between ordinary differential equations and partial differential equations. Finally, we explicate some results for partial differential equations of nilpotent type which have been studied by the speaker so far.

No. 2

Date: July 18 (Fri) 15:00 - 16:00

Place: B707, Fac. Sci., Hiroshima University

Speaker: Sampei HIROSE (Shibaura Institute of Technology)

Title: Exact WKB analysis for systems of partial differential equations and versal unfoldings

Abstract:

    The exact WKB analysis is mainly developed for ordinary differential equations. In this talk, we consider the exact WKB analysis for systems of partial differential equations. In particular, we discuss the following topics:
1) The relationship between the new Stokes curve of the BNR equation and the Stokes surface of the Pearcey system
2) The WKB-theoretic transformation for a system of partial differential equations near a cusp of the set of turning points
3) The relationship between this transformation and versal unfoldings

No. 1

Date: July 2 (Wed) 15:00 - 16:00

Place: B702, Fac. Sci., Hiroshima University

Speaker: Hiroshi YAMAZAWA (Shibaura Institute of Technology)

Title: Holomorphic and singular solutions of q-Briot-Bouquet type equaions

Abstract:

    In 1990, Gérard and Tahara gave the definition of the Briot-Bouquet type equations for nonlinear first order partial differential equations, and constructed all solutions on a function class with a singularity at t=0. In this talk we consider existences of holomorphic solutions and singular solutions on the function class of q-difference-differential equations.

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