This week I’ve been giving lectures at an algebraic geometry workshop in Mombasa. I know what some of you are thinking: ‘But Tom, you’re nothing like an algebraic geometer!’ And that’s true. But often the best way to learn something is by putting yourself in a position where you have to know it, like standing in front of fifty people expecting a clear explanation. In this case, I’ve learned some basics of Grobner bases (mostly from an excellent book by Cox, Little, and Shea) and have been augmenting the lectures and exercise sessions with Sage. I’ve written up some notes on the talks, and I’ll probably convert them into a web-based format with Sage cells and stuff sometime next week…

The workshop has participants attending from Kenya, Tanzania, Uganda, Rwanda, and Zambia. The participants have been super motivated; we’re just finishing up the third and final week of the workshop, and the participants have been staying up late working on final projects. Attendance has stayed high throughout the workshop, to a degree you wouldn’t expect in (say) North America. The chance for exposure to math going on at the international level is a big draw, since it’s still so rare for international mathematicians to come through East Africa. I imagine it’s like if you only got to eat ice cream once every year or three: you’re not going to let anything go to waste.

This workshop is a sort-of-yearly event; it bounces around between the East African countries each year (Tanzania last year, Uganda next year), and has been running in some form since about 2004. Sometimes it’s paired with a conference, though, and in those years the workshop usually only runs for a week; in the other years, it has run for two weeks. These sorts of workshops usually have a number of difficulties: the participants often come from very diverse backgrounds (many applied and financial math types at a pure maths workshop), the short timespan often means that the lecturers get through some basic linear algebra then have to leave, and it’s difficult to gauge longer-term impacts beyond the span of the current gathering.

This workshop has been quite successful, I think, owing to the following factors.

- The biggest factor is that the organization was done by an extremely motivated group from the University of Nairobi. This group has been focused on learning algebraic geometry for a couple-few years now; two of the strongest members of the group are out now for their PhD’s, and when everyone settles back into Nairobi the hope is to have a critical mass of people with research-level grounding in the subject. This kind of group-oriented, many-year game plan is very impressive, to say the least. This group is the reason for the choice of topic, of course. (From their group, James Katende deserves some special props for being an incredible organizer and fixer for everyone at the workshop.)

- The workshop, for the first time, is three weeks long. There have been seven lecturers (two per week, with three in the final week) during the workshop. And after covering basic linear algebra and commutative algebra in the first week, there’s been space for later lectures to build into more interesting topics. For this final week, we have Balázs Szendrői teaching toric geometry, and Ruriko Yoshida (a fellow Davis graduate!) teaching algebraic statistics, and me doing Grobner bases. (To round out the list, we also had Gavin Brown, who’s been around the whole time and glued together the whole program, Joe Grant, who has been fantastic at working with the participants on their projects, Georg Hein, who gave some very nice lectures in the second week, and Greg Berczi, who climbed Kilimanjaro before the workshop and is doing an Ironman in Hungary just after the end.)
- The structure of the workshop has been helpful as well: we have half of the day for lectures and half of the day for exercise sessions, where the participants get their hands dirty working out basic problems. This has really helped the participants stay on top of the material, and facilitated a LOT of interaction with the lecturers.
- We’ve also asked for some ‘final projects’ – 2-3 page write-ups of either a problem suggested by us, or a topic from the workshop chosen by the participant. The projects give us a good way to judge the overall engagement of the participants, and see that they can communicate some of the ideas they’ve picked up during the workshop. We gave some small prizes (mainly more math books) to the students who gave the best projects, as well as a ‘certificate of merit.’ The students definitely worked very hard on the projects; there were many reports of people staying up late at night.

The participants are, of course, varied in their backgrounds, as usual, but there are a number of quite impressive participants I hadn’t been aware of before. The most impressive work I’ve seen this week (from my particular vantage point) has been by David Kihato. He has a master’s degree from the University of Nairobi, and is currently working at a private secondary school in Nairobi. Over the course of the week, he’s more-or-less independently learned Sage and Grobner bases, and came to me with a mostly-working Sage program for computing Grobner bases before I’d even given the formal definition of a Grobner basis! He had been reading Dummit and Foote’s abstract algebra book at night, a bunch of Sage tutorials, and was able to put it all together into a nice algorithm. He’s actively interested in going for a PhD somewhere, so if anyone wants to support a strong student from Kenya, it would be great to get in touch. I’ve also been talking a bit with Jackson Katei, who also has a Master’s from the UoN, and is very interested in learning more about computational algebra. He also seems like a strong student, and it would be great to get him a good PhD.

We’ve also identified a very interesting group from Zambia; we don’t really have any prior experience with Zambia and were surprised to find that the main university’s math department is almost entirely populated with people with international master’s and PhD’s. This makes it a very interesting place to pursue further contact with, and a good place to encourage people to attend for post-graduate degrees.

On the whole, it’s been a fascinating couple of weeks! Again, I think the biggest factor for success is the motivated local group; this is something we saw clearly with the Ethiopian maths camp, too. In the case of the workshop, probably the best ‘extra’ I can think of would be some additional time for the local organizers who were so motivated to put the conference together and bring out the lecturers. Some of these local organizers already had a decent foundation in commutative algebra, due to a year-long reading course they were already engaged in. Leaving some extra time for the international lecturers to spend some time with the local organizers specifically to further their research interests would be a nice bonus. Actually, I’m kind of doing this anyway on an independent basis: I’ve scheduled a Sage workshop for the following Thursday at the University of Nairobi, and given some week-long assignments for people to work on.

Note: This post was edited for accuracy and clarity just after the end of the conference.

Sounds great! Does anyone at the University of Nairobi teach algebraic geometry, or do research on it?

The algebraic geometry group there is building itself up more-or-less from scratch. The first to finish their PhD was Dr Damian Maingi (who I just saw give a talk on building vector bundles from monads), and there are two others out of country for PhD’s in algebraic geometry right now. The hope is to get enough people through to build a critical mass for a research group.