Sebius speaks very fondly of Herb Keller and it is clear that Herb has been of great importance for his career. "Sadly, Herb passed away on January 26 this year." [Ed.: see also the announcement in this issue.] The last time Sebius saw Herb was in July 2007 during the small workshop at the Centre de Recherches Mathématiques in Montreal on the occasion of Sebius's 60th birthday. "Herb was incredibly inspirational. He used to give courses at Caltech: we would go for lunch first and Herb would come up with an idea for his course; then he would spend two hours teaching, where he would discuss the idea, work out some of the details, but leave it as an open-ended problem. It was in these courses that I learnt about things like a Hopf bifurcation."

At the time, Herb Keller was working on continuation methods and wrote the seminal paper Numerical solution of bifurcation and nonlinear eigenvalue problems [in Applications of bifurcation theory (Proc. Advanced Sem., Univ. Wisconsin, Madison, Wis., 1976), pp. 359-384. Publ. Math. Res. Center, No. 38, Academic Press, New York, 1977]. Sebius had started working on a software program to solve nonlinear two-point boundary value problems with the use of collocation methods and Herb asked him to help with the examples and produce a nice illustration.

"I must have mixed up Herb's example with the examples I used in my own paper" [Ed.: Finite difference collocation methods for nonlinear two-point boundary value problems SIAM J. Numer. Anal. 16(2): 173-185, 1979]. "Years later R.R. Huilgol from Australia contacted Herb and asked about the figures and associated equations; it turned out that they did not match!" The underlying dynamical systems in both papers had a particular form using polynomials. "Luckily I was able to reconstruct the polynomial coefficients based on the figures in Herb's famous paper!"

After a two-year postdoc with Herb Keller, Sebius went to Vanderbilt University to work with George Reddien. "George had visited Caltech before and was very much interested in bifurcation theory. He really reinforced my interest in dynamical systems and I began wondering what would be a good way to compute and follow periodic solutions." Already after 18 months, Sebius left Nashville and took up an Assistant Professorship in the Faculty of Engineering and Computer Science at Concordia University in Montreal. "I started at Concordia in the winter of 1979 and essentially developed AUTO in less than a year." Most young Assistant Professors find it difficult to adjust to their new job and in their first year they are more occupied with preparations for teaching than doing research. "Things at Concordia were excellent! My office was located in the attic of an annexe building; one had to negotiate a lot of stairs and get past the secretary who operated like a watch dog. Only the best students were able to find me!"

The truth is that Sebius only taught one course that semester, on the topic of Numerical Methods, and he very much enjoyed preparing for it. However, he also realized that his research should not suffer and he set himself firm deadlines. "In the summer of 1980 I visited UBC and gave my first presentation on AUTO. I then refined my results and completed the work at Concordia in the fall."

The experience of being totally immersed in a foreign culture is clearly what Sebius values enormously. He has traveled to many countries, not just once, but regularly for research visits that grew into long-term collaborations and often have been extremely fruitful and successful. Most of Sebius's sabbatical leaves, the first one in 1985, were spent at Caltech with Herb Keller. "Herb Keller was a fantastic host. He would give moral and technical support, while I could work on whatever I fancied." The visits to Caltech were usually extended and lasted sometimes more than a year. "Once I was at Caltech for almost three years!" Sebius admits cheekily.

Financial support for such endeavors would be a combination of stipends for his sabbatical leave and support from Herb Keller during the extended period of unpaid leave. Often the net income would actually be less than what Sebius would earn at Concordia, but adventures and experiences clearly outweighed this minor inconvenience. "My visits to Caltech could be compared to the kind of Research Fellowships that exist nowadays in some countries for Assistant/Associate Professors. They were fantastic opportunities to focus completely on research."

Other long-term research collaborations followed. In 1994, Sebius began visiting Alejandro Rodríguez Luis (and later also Jorge Galán Vioque) at the Universidad de Sevilla. They met at a small workshop on numerical methods for bifurcation theory and dynamical systems, organized annually by Yuri Kuznetsov at the CWI in Amsterdam. In 1997, Sebius met Carlos Pando Lambruschini from the Benemérita Universidad Autónoma de Puebla, who attended a course Sebius gave at the Centre de Recherches Mathématiques in Montreal.

Both Spanish and Mexican researchers had interesting and challenging research projects that could be tackled using AUTO. For Sebius, the added benefit of these collaborations would be the cultural experience and the foreign language. "You do not go there as a tourist. You live there, you go to work like everybody else, and then you get invited to weddings, parties, religious celebrations, etc. Particularly in Mexico I found it very easy to make friends with the local people. In Puebla we start late and from 8:30 to 10:30am I can be found on the Zócalo to practice my Spanish and chat with the local people. I regularly meet up with entire families! Then I go to the university and Carlos and I work 11-6 with only a short break for a light lunch."

A lifestyle of the past?

Sebius clearly is a master of combining business with pleasure, but one wonders whether he was also extremely lucky in that he just happened to be making his career in a time where it was easy to maintain his lifestyle. Certainly, he was extremely lucky that his wife had a job that she could easily (and was willing to) leave. "The kids have been to schools in Alhambra (CA), Salt Lake City (UT), Minneapolis (MN), Cuernavaca Mexico... It probably was rather disruptive, but it was also very good for them." One also gets the impression that the teaching load has gone up, but Sebius has, in fact, been teaching two courses per semester almost every year that he was not on leave.

"I do feel that teaching seemed to take less time in those days. I now spend a lot more time to prepare my classes –– and not necessarily with a better result! –– because new technologies allow you to make better lecture notes; students also expect more from you in this sense. Moreover, student evaluations did not matter as much as they do now." Sebius definitely thinks that the increased bureaucracy at universities has made it much more difficult to organise frequent and long-term research visits. "There is so much more pressure now at higher level to measure the research quality. Of course, I would have to undergo regular internal reviews to assess my research and teaching, but these were always very good. Just the software developments for AUTO or a single high-quality paper would be considered a good achievement. Things have changed in that respect: the measure is much more focused on quantity, impact factors, and citations. These are dangerous tools in the hands of bureaucrats, because they have no idea what it means to do research."

The author of this article with husband (Bernd Krauskopf, University of Bristol), leaving Sebius's home in Montreal on their way to the airport, March 2008.