ITP

[May, 2010 - March, 2011]

Preamble. As the second JSPS-ITP activity of mine, I revisited the Fourier Institute (UFR de Mathématiques, Université de Grenoble I) in May 2010 after two years. Thereafter I have stayed there for most of a whole year till the end of April 2011. Now, I would like to digest my activity log of the past year in the hope that it could be of any assistance to someone else and also to myself in the future. I'm afraid that I couldn't say enough about how valuable and unforgettable it has been to me because of my inability in English. However, I am sure I won't have traded this experience for anything in future. Now, I should take this opportunity to extend my heartfelt thanks to everyone concerned both in France and in Japan, especially to Professor Alexei Pantchichkine and Madame Marina Pantchichkine for their hospitality and their generosity during my stay in Grenoble.

[May, 2010]

After a long flight passing through Tokyo, Amsterdam and Lyon, I arrived at Grenoble on May 1st. I was really happy to see Professor Alexei Pantchichkine and the other staff members of the Fourier Institute, who have been well and continued to work aggressively in various fields since we've last met two years ago. The Fourier Institute immediately provided me a favorable research environment typified by the usages of a personal office, the library and the faculty restaurant as they had done on the previous occasion. Then I could start participating in the regular seminars here soon after my arrival. On the weekend of Pentecôte [Pentecost], I could also take a good opportunity to participate in the 2nd joint workshop of Clermont-Ferrand and Grenoble which was organized by Alexei. At the event, I gave a 60-minute talk “Certaines familles p-adiques des formes modulaires de Siegel de degré pair [Some p-adic families of Siegel modular forms of even genus]”, and it's been very exciting to discuss various issues on automorphic forms in arithmetic and their L-functions with Professors Siegfried Böcherer (Universität Mannheim), Freydoon Shahidi (Purdue University), Steve Gelbart (Weizmann Institute), Dr. Kirill Vankov (Université Franche-Comté) and many participants from Clermont-Ferrand. Around the same time, I had to go through the procedure for "Titre de long séjour [Long Resident Permit]" before my Schengen visa expires. Thanks to an elegant assistance of the Centre National de la Recherche Scientifique (CNRS), the procedure went quite smoothly and in the end, I could receive it within one month as the shortest amount of time. As you may see from the above, many people saved me to get off to the best start of my stay in Grenoble.

Group photos of the 2nd joint workshop of Clermont-Ferrand-Grenoble (at the Fourier Institute)
A photo at the Mémorial troupes montagne, mont Jalla	A birds-eye view of Grenoble on the Fort de la Bastille

[June, 2010]

During the period from June 14th to June 20th, I visited University of California at Los Angeles (UCLA) to participate in the instructional RTG/FRG workshop on Arithmetic Geometry “Modular/Geometric Iwasawa Theory and p-adic L-functions” which was organized by Professor Haruzo Hida. As the term indicates, the workshop was carried out with sufficient attention given to both of specialists and nonspecialists, and in fact, many talks were devoted to conscientious instructions accessible to beginners as much as advanced topics. Especially, in relation to my own results, I myself was very interested in the serial talks of Professors Chris Skinner (Princeton University), Eric Urban (Columbia University) and Vincent Pilloni (Columbia University) concerning on p-adic families of Siegel modular forms of finite slope. Just for the record, around the same time as the above-mentioned workshop, Alexei, Siegfried and Kirill participated in the 3rd conference on zeta functions in Moscow. Unfortunately I was unable to attend it at this time, but I would like to attend the next conference very much if circumstances permit.

Department of Mathematics, UCLA

Westwood Medical Plaza

[July-August, 2010]

At the beginning of July, the season for summer vacances has come over France. Every day, more and more people started their holidays or their journeys, and then the campus was becoming thinly-peopled little by little. On a weekend, I went on an excursion to Lac du Crozet [Lake Crozet] together with Alexei and Siegfried. To be honest, it was very tough for me who haven't much exercise recently, to get there but I could eventually enjoy a very paradise having a delightful outlook. Thereafter, while a muscle pain in my foot lingered for some time, I concentrated on writing my preprint concerning on some constructions of p-adic families of Siegel modular forms of even genus by means of the lifting techniques in the sense of Saito-Kurokawa and Duke-Imamoglu-Ikeda which is based on some numerical evidences observed by myself in 2008. At time like that, I received the sad news of the passing away of Professor Hiroshi Saito (Kyoto University) who has greatly influenced me since I was in graduate school. Indeed, now I still remember that I saw him at the annual workshop on automorphic forms in Hakuba (Nagano, Japan) five years ago, and at that time, he encouraged what I used to be very much. A few weeks after the sad news, I created a preliminary version of my preprint entitled “On certain constructions of p-adic families of Siegel modular forms of even genus” which could be dedicated to him. In mid-August my family came to France, and then I spent a few weeks in Paris for my own vacance.

Siegfried Böcherer and Alexei Pantchichkine in front of the Chamechaude

At the Lac du Crozet

[September, 2010]

The Fourier Institute has been thinly-peopled for a bit while after September has come. As days went by, staff members gradually came back from their vacances and we were getting prepared for the new semester. In accordance with this, my office was moved from the 3rd floor to the 1st floor. After a few moments, my colleague at Hokkaido University, Dr. Yoko Umeta came visit here on September 6th. In the days ahead, she's going to stay here for a whole year as well. On the last weekend, the annual meeting of the Fourier Institute was organized at the Centre de l'Escandille, Autrans in order to welcome newcomers. Unfortunately the weather's been terrible during the event, however I hope it was a great time for Yoko and for my colleagues to know each other.

Yoko Umeta and Alexei on a bridge across the Isère

Centre de l'Excandille, Autrans

[October, 2010]

The new semester started and then our scientific activities became progressive. Every week, regular seminars were given in various fields of Mathematics. On October 15th, I attended my friend, Alexander Rahm's Ph.D defense at the Fourier Institute. Eventfully he got his Ph.D, and afterwards he moved to the Weizmann Institute of Science in Israel. On October 26th, I was invited to Institut Mathématiques de Luminy by Professor Marc-Hubert Nicole, and I gave a 60-minute talk “Sur certaines constructions de familles p-adiques de formes modulaires de Siegel en degré pair [On some constructions of p-adic families of Siegel modular forms of even genus]” at the regular seminar. After that time until October 28th, I have stayed in Marseille to discuss some topics on Siegel modular forms of genus 2 and the Siegel three-fold with Marc-Hubert as a beginning of our future collaboration in Mathematics. During the period, we also went on excursions to the calanques in Luminy and also to some sightseeing spots in Marseille. En passant, a long strike in Marseille continued for most of the whole month. Fortunately Marc-Hubert arranged my itinerary between an interval of the strike date, and hence there's no problem at all for my trains between Grenoble and Marseille. The strike disrupted not merely the public transportation, but also the garbage collection by the public. Of course, I've already understood the summer and early fall have a lot of strikes everywhere in France, but I've never seen the garbage being piled up mountain-high in the streets of Marseille like that. Anyway, I enjoyed a short but fulfilling stay there at the last minute before the cold winter comes, and Marseille became one of the most attractive cities in France I've ever visited.

Alexander Rahm in his Ph.D defense	Marc-Hubert Nicole at the Calanque de Morgiou, Luminy
A wharf of Marseille	A demonstration in Marseille

[November, 2010]

At the beginning of November, Alexei and I decided to organize a mini workshop on automorphic forms, special values of L-functions, p-adic congruences and Shimura varieties here in the coming February, and then we started preparing a draft of the list of speakers at the event. On November 18th, I first attended “Séminaire d'arithmétique à Lyon” organized by Professor Laurent Berger (Ecole Normale Supérieur de Lyon), and then I saw Professor Vincent Pilloni, who moved from Columbia University to ENS de Lyon in this September, again for the first time in 5 months after the previous workshop at UCLA. Returning to my everyday life in Grenoble, the coming of winter brought a decline of temperature and the short daytime here. For your information, as is evident from the fact that the latitude of Grenoble is about the same as that of Sapporo, the winter of Grenoble is a bit colder than average, but is at least as sustainable as that of Sapporo. On the contrary, I guess that the snowy mountains around the city are magnificent and impressive for everyone to see. On the very last night of November, the city of Grenoble was first in for a heavy snowfall this winter.

Lyon Part-Dieu

Université Lyon I

A parking lot at the Fourier Institute covered in snow

[December, 2010]

As mentioned above, everywhere in Grenoble has been white on the first morning of December. Seemingly at least 20 cm of snow fell there overnight, but almost all of the buses, the trams and the trains were in a normal circulation except on the mountain side. On December 8th, Professor Valery Gritsenko (Université de Lille I) invited me to participate in the 30th meeting of the joint French-German intercity seminar on automorphic forms at Lille. On that day, the blizzard and the snowfall played havoc with the transportation systems in the northern region of France including Paris and Lille. It caused a 2 hour delay in the arrival of my TGV train, and I managed to arrive at the university in time. At the meeting, I gave a 60-minute talk “On some constructions of p-adic families of Siegel modular forms”. I was very happy to take part in such a traditional meeting on automorphic forms, and also to hear interesting talks given by the other speakers. After coming back from Lille, I could improve some contents of my preprint by applying the so-called weak control theorem in the sense of Hida for some overconvergent Siegel modular forms that I have already constructed before. In addition, this enabled us to conduce a generalization of the Duke-Imamoglu-Ikeda lifting that is adaptable to ordinary elliptic modular forms of arbitrary p-power level. I also proceeded with preparations of the coming workshop here in February together with Alexei. We fixed the list of speakers, and then we made a preliminary schedule of the event. In the meantime Christmas was coming up, and at the same time, the streets were brilliantly illuminated in every color of the rainbow. It seemed, unlike the Japanese Christmas, many people were going home to spend holidays with their families until the New Year Day. On Christmas Day, I roasted a famous chicken form "Bourg en bresse", and I ate the bûche de Noël. As for the rest, there's nothing special and therefore I spent my free time alone reading some articles and books as usual. Looking back on the past year 2010, it has been a fulfilling year in every way because many people in France, in particular, Alexei Pantchichkine helped me on every occasion. I wish everyone in our cooperation good luck for the coming year, and hopefully I could be of any assistance to them all.

A big Christmas tree in the city center of Lille

Hospice comtesse (which was set up in 1237 by the contess Jeanne of Constantinople to care for the sick, the poor and pilgrims. )

[January, 2011]

The New Year has come. We stepped up efforts toward the forthcoming workshop. The list of participants has been updated to reach a satisfactory level to realize an attractive program in response to their requests. In accordance with it, I myself created the poster based on an excellent draft plan made by our secretary, Ms. Géraldine Rahal. (http://www-fourier.ujf-grenoble.fr/~panchish/affiche201102rev5.pdf) We're looking forward to seeing many people at the event soon later. At the end of January, Professors Yoshitaka Maeda and Naofumi Honda came together from Hokkaido University to see Yoko and myself privately. Though they only had four short days in Grenoble without any relation to the workshop, we were very happy to see them again and to introduce them to our colleagues in France. In particular, for all three of Professor Maeda, Alexei and me, it was a pleasant reunion after five years since we've last met at Hakuba, and it could be a cherished memory we'll never forget.

A draft of the poster

Alexei and Yoshitaka Maeda

[February, 2011]

Eventually on February 09-10th, Professors A. Pantchichkine, S. Böcherer and I could organized a mini-workshop on automorphic forms, special values of L-functions, congruences and Shimura varieties at the Fourier Institute with inviting the main guests, Professors L. Berger, Denis Benois (Université Bordeaux 1), V. Gritsenko, Hidenori Katsurada (Muroran Institute of Technology), M.-H. Nicole, Jacques Tilouine (Université Paris 13) and V. Pilloni. We're very pleased to have the great 12 participants and then to have fruitful discussions on various issues with each of them. On the second day of the event, I also gave a 60-minute talk “Certaines constructions de familles p-adiques de formes modulaires de Siegel et leurs applications [Some constructions of p-adic families of Siegel modular forms and their applications]”. On behalf of my coorganizers, I sincerely appreciate everyone concerned for their cooperation to a successful end of the event. I'm also grateful to Alexei and Siegfried for their many valuable suggestions in organizing a workshop. Soon after the workshop, I restarted research activities of my own including some constructions of p-adic families of Siegel modular forms of odd genus by means of an algebraic pullback formula for p-adic families of forms of even genus that I've already obtained.

A group photo of the workshop in February (at the Fourier Institute)

A lunch together with Yoko, Hidenori Katsurada, Siegfried, Marc-Hubert and Alexei at the Café des Aples

[March, 2011]

In March, I've spent most of time in traveling over Germany. First, I was invited by Professor Siegfried Böcherer to visit Universtät Mannheim for five days starting from March 7th. On March 10th, I gave Siegfried and Professor Rainer Schulze-Pillot (Universität des Saarlandes) a series of 60-minute talks at Number Theory Seminar entitled “Some constructions of p-adic families of Siegel modular forms of even genus” and “On a generalized Duke-Imamoglu-Ikeda lifting of ordinary elliptic modular forms of p-power level”, respectively. I was very glad they gave me fruitful comments and suggestions on my results. After that, I was also invited to the Max-Planck Institute für Mathematik (MPIM) in Bonn for a week until March 18th. On March 16th, I gave a 60-minute talk “Certain constructions of p-adic families of Siegel modular forms and their applications” at Number Theory Lunch Seminar. It's been a great pleasure for me to talk to many celebrated mathematicians typified by Professors Friedrich Hirzebruch, Gerd Faltings and Günter Harder. For the rest of my stay, I spent a lot of time discussing a new project undergoing jointly with Marc-Hubert Nicole who was staying there as a long-term visitor. Whenever I visit MPIM, I always get inspired to improve my research achievement by a lively atmosphere in their research activities. When I went back to France, I begun to organize my research results into my preprint “Pullback of p-adic families of Siegel modular forms and its application” to be presented as a joint paper with Alexei. At time like that, Steve Gelbart visited us again in Grenoble. In addition, a young Vietnamese student Anh Tuan Do started pursuing his Ph.D at the Fourier Institute. I surely recognized we hold active research discussions on Number Theory focused on Alexei.

Institut für Mathematik, Universität Mannheim

Wasserturm um Friedrichs platz, Mannheim

Max-Planck Instiut für Mathematik, Bonn

First thing I knew, most of a year has passed after coming to Grenoble. It might be kind of a worn out expression, a quality time flew by like a flash. After all, I owe it to my colleagues and my friends that I've been able to have a full and fruitful life stay in Europe. Once again, thank you for this opportunity to express my gratitude to everyone concerned and also to the JSPS-ITP.

Excursus. Here I would be remiss if I didn't touch on the huge earthquakes and tsunami hit the northeastern district of Japan on March 11th. As mentioned above, I was staying in Germany at that moment, but when I actually saw on TV the devastation happening in affected areas, I was very shocked beyond words expressing the deepest sorrow I felt as a fellow Japanese. However, at the same time, I was also struck and impressed with how many people who concerned about Japan vicariously I saw in Europe. I should take this opportunity to express my sincere appreciation for all the kind and encouraging words for affected people that I have received in Germany and also in France. I should also like to transmit all of them to my colleagues in Japan. In addition, as a Japanese, I hope I could be of any assistance toward Japan's earliest possible restoration.