09Aug. 2018

Prof. Kishimoto was staying at l’Université de Bourgogne for a joint work with Prof. Dubouloz in a period: 29 August–25 November, 2017 

Professor Takashi Kishimoto 


From 29 August to 25 November 2017, namely almost three months, Prof. Kishimoto belonging to Department of Mathematics was staying at l’Université de Bourgogne (Dijon, FRANCE) in order to develop the consecutive joint works with Prof. Adrien Dubouloz. More precisely, this three months stay in France has been realized by virtue of a combination of the financial support of CNRS (= Centre National de la Recherche Scientifique) Research Fellow and Saitama University Lab-to-Lab.


As mentioned just above, this stay at France was mainly devoted to a remarkable devel- opment of our consecutive joint research in the area of Algebraic Geometry. In fact, since our first joint work inaugurated at 2011, every year we are trying to meet directly to stimulate researche projects. Different from the other studies of science, we have not to do any experimentation, namely, in Mathematics, we never need any expensive instrument for experimentation. Instead, one of the most important matters is a direct discussion with the other mathematicians having a common research interest. As for us, certainly we have a common mathematical interest (by use of terminology, affine and projective algebraic geometry with algebraic group actions), however our techniques to tackle a bunch of problems are not always same. Nevertheless, to my opinion, a fusion of various techniques from different point of view will produce often quite interesting mathematical inventions.


To be short, key word of our research lies in an observation of intrinsic properties of affine algebraic varieties from a viewpoint of projective, birational geometry and algebraic group actions. Usually, affine geometry and projective or birational geometry can not be treated simultaneously because of difference of characters of them. But, a fusion of our growing techniques yield us sometimes a chance to connect these two different kinds of geometry with a help of algebraic group actions.


This time three months international collaboration has fortunately allowed us to find sev-eral significant mathematical results in algebraic geometry. These results have been summed up as two research articles, one of which has been already accepted by a famous mathematical journal in high level (Mathematiche Annalen), and the other one has been submitted. I’m afraid that I could not get such achievements if I was to work alone. We are sincerely grateful to CNRS from France and at the same time to Lab-to-Lab from Saitama University.

  • One shot of 1 hour research talk in the workshop at Bourgogne University, Dijon, France.
  • A discussion with Prof. Dubouloz (left hand side) to develop our joint work in front of a black board