The following year MSRI had a big topology program that included Bill and me. Rob made sure that Abby could come as well. Sadly, Bill had to return to Buffalo in the middle of the year, so I took over as Abby's ad hoc adviser. At the end of the year, Abby decided to finish her PhD thesis in Santa Barbara, where we were to have a special year in topology, rather than follow Bill to Buffalo. I'm sure that the weather -- Santa Barbara vs Buffalo -- had nothing to do with it.
The topology year at UCSB was exciting and fun, with lots of emerging young topologists, several of whom are at this conference. Almost every day we would gather for a big lunch and talk about math. One day, when I went by Abby's office to get her for lunch, I found that she was on the phone with Rob. She seemed remarkably comfortable with the conversation, and I mentioned to her afterwards how great that was, since Rob still scared me a bit -- after all he was my adviser. As I nattered on about this, Abby interrupted: "wait...that wasn't Rob Kirby, that was my Uncle Rob."
Abby's uncle Rob was a friendly and interesting man who was then arranging to visit Abby for some months in Santa Barbara. He added a lot to the ambience, arranging for Abby to give a cello concert, etc. One evening at a party at our house, he told me how proud he was of how well Abby was doing, especially since, according to family lore, she had been an accident. Wow, I thought, that's pretty cool, since I had learned some years before that I too was an accident. So the next day at lunch, surrounded by a horde of topologists, I mentioned to Abby how interesting it was that we had that origin story in common. You can guess the upshot: up until that moment Abby had never heard that bit of family lore.
She did forgive me for blabbing at lunch (but maybe won't for bringing it up again here!) and, almost entirely on her own, finished her thesis. So, at least unofficially, she became my first successful PhD student. Eventually we began a decades long math collaboration. Modesty forbids me from giving our joint mathematical work the praise it deserves; mostly she was the architect, thinking up imaginative approaches to old problems, and I was the plumber, working to make sure the technical arguments held water.
One piece of her own work really does need singling out: after hearing Hyam Rubinstein give a talk on how he believed the 3-sphere could be recognized, Abby invented her own architecture for such a proof, a plan that combined emerging ideas in 3-manifold topology such as thin position, and almost normal surfaces. Furthermore, she was able to nail all the technical details. She wrote up her proof in a way that convinced everyone, and the 3-sphere recognition problem was finally put to rest. It is interesting to contemplate that if it weren't for an accident 60 years ago, we might still be unsure whether we could recognize the 3-sphere!
Abby's work now continues, currently in 4-manifolds, and now in collaboration with my own thesis adviser Rob Kirby. Rob thus continues his remarkable record of collaboration and mentorship as he enters his ninth decade. Yikes! I'll never live up to that sort of role model, but I'm delighted to be here to celebrate with all of you, including Abby and Rob's ongoing contributions to mathematics, with a special appreciation of the difference that both of them have made to my life and career.