1) After my arrival on the 1st of March I gave a talk on the 7th of March 2018 at the Colloquium of Hyogo University of Teacher Education:

Title: Resultants of polynomials

Abstract: I introduced the classical notion of resultant (and discriminant) of polynomials over arbitrary rings and concentrate on the case when the leading coefficients may vanish. (This may happen for instance in family of polynomials.)
Our intention is try to understand the case when the discriminant does not vanish (at least locally).
A series of examples were discussed.

2) Discussed with Prof Koike about our research program on the Geometric Directional Bundle Properties (GDB for short).

I happily report that we succeeded to give a necessary condition for a bi-Lipschitz homeomorphisms to preserve the GDB structure. The GBD-(SSP) structure preserving theorem we have anticipated is already reflected in our above result. Our work here will be incorporated in a paper in the honour of Tzee-Char Kuo's 81st birthday.

3) Next we will try to develop the transversality theory in therms of the GDB data, not simply using the directional cones.

4) In the period 21-22 March I participated in the Kobe Singularities conference where I gave a talk with the title: Arc-analytic trivializations.

In conclusion I consider that this was a very fruitful visit and I want to take this opportunity to point out the usefulness of the HORN program for facilitating our research and at the same time to warmly thank the sponsors and my host for a wonderful time in Hyogo University of Teacher Education.