[geometry-ml:00696] "Concrete theory of Abelian functions and its applications"

[Yoshihiro ONISHI]

geometry-ml のみなさま

大西良博(＠岩手大学)と申します. 
下記の様なセミナーを行ひます. 
急ではありますが, ご参加いただければ幸ひです. 
日曜ですのでお昼に弁当 (1500円位) をご用意する予定です. 
ご参加の場合は事前にご連絡いただければと存じます. 
(この mail に返信しないで onishi ＠ iwate-u.ac.jp までその旨お伝へ下さい. )

セミナー名 : Concrete theory of Abelian functions and its applications
 日  時    : 2008 年 7 月 20 日 (日曜)
 会  場    : 岩手大学人文社会科学部 2 号館 H221 教室
             盛岡駅からタクシーで 10 分位です. 
プログラム : 下記の通り:

10:00-10:40
Yoshihiro Onishi (Iwate University)
   "Frobenius-Stickelberger-type-formulae for purely pentagonal 
    curves of degree six and its generalization"
  
  Abstract: Combining suitable (higher) derivatives of the sigma-function
    for a higher genus curve in the title, I will explain Frobenius-
    Stickelberger-type formula for purely such curves in the title.  
    I will talk about how the formulae is generalized for any $d$-gonal 
    curves with unique point at infinity. This is joint work with 
    Shigeki Matsutani. 


11:00-12:00
Shigeki Matsutani (Sagamihara):
   "Jacobi inversion and addition structure on strata of the Jacobian of
    an affine plane curve $y^r = f(x)$"

  Abstract: I will give a talk on the recent results with Emma Previato
    (to appear in J Math Soc Jpn) on the Jacobi inversion formulae
    on strata of the Jacobian of an affine plane curve $X$ given
    by $y^r = f(x)$. I will also mention a naive addition structure
    on $S^k X$. Using the addition structure and the relation between
    proper Abelian differentials of third kind and the sigma functions,
    we have the results. I will give a rough sketch of their proof.


13:30-14:30
Atsushi Nakayashiki (Kyushu University):
   "Expressions of theta functions in terms of the prime form 
    and their applications"

  Abstract: For any compact Riemann surface, a choice of canonical homology 
    basis of it, a point on it we give an expression of the corresponding 
    Riemann theta function in terms of the prime form. We use it to study 
    the series expansion of the theta function.


15:00-16:00
 John Christopher Eilbeck (Heriot-Watt University, Edinburgh):
   "Some recent explicit results for Abelian functions for low genus curves"  

  Abstract: I will attempt a brief survey of generalisations of the Weierstrass
    function theory for elliptic curves to curves of higher genus, in 
    particular recent results for trigonal curves of genus 3 and 4 and a 
    cyclic tetragonal curve of genus six.  Corresponding two-term and 
    three-term addition theorems for generalised sigma- and \wp- functions 
    will also be discussed.


16:30-17:30
Victor Z.Enolski (Institute of Magnetism, Kiev):
   "Finite-gap integration of the SU(2) Bogomolny equation"
  
  Abstract: The ADHMN construction of magnetic monopoles is given in 
    terms of normalizable solutions of an associated Weyl equation. 
    The Weyl equation is solved by direct algebro-geometric means. 
    That's done by solving first the adjoint Weyl equation using Nahm's 
    Ansatz and Baker-Akhiezer function of associated linear spectral problem. 
    The principal observation of this consideration is that solution of 
    Nahm equation is not directly used to solve the Weyl equation. 
    Complete version of the lecture is published in arXiv: 0806.1807v1 [math-ph]
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