by Mélanie Bertelson
I recall an episode from the first YashaFest in 2007 at Stanford which illustrates both his modesty and his fine sense of humor. On the evening of the banquet, after a series of remarks by colleagues and friends praising his work and personal qualities, Yasha told us a famous Russian joke: after having watched a propaganda movie about the Soviet Union, a small Russian boy exclaimed, “Where is Soviet Union? I want to go to Soviet Union!” Yasha concluded, by way of response to the glowing praise, “Who is this Yasha Eliashberg? I want to meet him!”
The first time I met Yasha was in the spring of 1996 at Stanford. I was in my first year of graduate studies, and he had just come back from a semester at Harvard. We were attending a seminar. I had heard about him already, before coming to Stanford, and I was happy when he came to talk to me after the seminar. He chose to address me in Russian (!), a language I unfortunately do not speak.
Although I was a sort of half-student of Yasha, his influence on me has been considerable. Let me explain “half student”. When I arrived at Stanford in the summer of 1995, I had just finished writing an undergraduate dissertation with Simone Gutt in Brussels on Boris Fedosov’s newly translated proof of existence of deformation quantization on all symplectic manifolds. I was very tempted to continue in that direction. At the time, Alan Weinstein in Berkeley was also interested in these subjects, and I asked him if he could be my PhD adviser. He accepted, and Yasha accepted to be my co-adviser.
During the first few years, Yasha — perhaps feeling dissatisfied with the idea that a Stanford student was working with a Berkeley professor, or worried that I was perhaps lost — offered on several occasions to give me another thesis project. I had taken a reading course with him, together with a few other graduate students ( Davide Castelvecchi, Michael Sullivan and Mei-Lin Yau). Our task was to read Hofer and Zehnder’s Symplectic Invariants and Hamiltonian Dynamics. We would meet about once a week and each, in turn, would explain a chapter of the book. Thanks to this experience, I could appreciate the beauty of the ideas in symplectic topology and Yasha’s vision. And yet each time Yasha approached me about working with him, I felt quite tortured, but would politely say no, because I felt if I started a completely new thesis subject, my PhD would take forever. Once we ran into one another in the Stanford math department and Yasha said, with his famously irresistible mischievous glance, “I know why you want to have two advisers: to escape both!”
I should specify that Yasha did not need more students. There was an almost permanent line outside his office door of undergraduate and graduate students, postdocs or visitors waiting to talk to him. (If your meeting was during lunch time, he would offer to share his meager lunch, typically consisting of an apple and a banana.) He had and still has so many ideas, and happily shares them with anyone interested. He just hopes to see answers to the numerous questions he is interested in, out of sheer curiosity. My friend Davide Castelvecchi once complained how, in his first year of research, he would receive a new thesis subject each week from Yasha and felt quite lost as to what to work on.
Not only are Yasha’s ideas appealing but his personality is, too. Yasha enjoys discussing math a lot and seems genuinely to like people in general. Whether you are a strong mathematician or not does not seem to matter so much to him. He makes you feel very comfortable. His wife Ada told me once that when he was very young, one of his schoolteachers told his mom that he was a most tactful young person.
In this vein, I should mention how carefully Yasha prepared for Emmanuel Giroux’s months-long visit to Stanford in 1998. Each of his PhD students was given a specific task: one of us had to walk to the department with Emmanuel each morning, another would do the reverse each night. My mission was to shop once a week with Emmanuel. It was a great experience to come to know Emmanuel a little bit and to have a glimpse into a blind mathematician’s life. I also benefited greatly from several math discussions with him.
My thesis subject with Alan Weinstein eventually brought me closer to Yasha. In particular, I had an extension of Gromov’s h-principle for open invariant relations on open manifolds to the case of “open” foliations of any codimension whose proof had made me sweat a lot. Yasha was convinced that the proof should be simple. We had a discussion that became a long ping-pong game: Yasha believed he had found a simple argument. I convinced him that it was not complete. He went back to think in front of his office window, spreading chalk over his lips, and found a way to fix it. This game went on for three hours, at the end of which the question remained unsettled, and still is.
When I had completed my PhD and was about to leave Stanford, I ran into Yasha in the math department. We hugged and said we would work together “in another life”.
When I got my first tenure track job at Université Catholique de Louvain (UCL) in 2003, I was offered the chance to propose a name for the Chaire de La Vallée Poussin 2005, an annual four-day event named after the prominent Belgian mathematician Charles-Jean de La Vallée Poussin (1866 — 1962). I choose to invite Yasha, who accepted. At the time, he was still very excited about symplectic field theory and delivered a series of beautiful lectures on the subject. I believe that what Yasha enjoyed most about this experience was the poster of the event, which had his name in large letters right next to a beautiful picture of de La Vallé Poussin, a stylish man of his time, sporting a large mustache and binoculars. It really gave the impression that it was a picture of Yasha, and made the poster look like a joke. Yasha still has that poster at the back of his office door.
There have been other connections with Belgium. Frédéric Bourgeois, who became a very young member of the Académie Royales de Belgique, had proposed that one of the Académie’s prizes should be awarded to the authors of major progress on the problem of existence of contact structures. When Yasha, Emmy Murphy and Strom Borman later proved the h-principle for contact structures, it was obvious that they deserved the prize. Frédéric told me at the time that he had thought he would never see a proof of the general result during his lifetime. We organized a conference in Brussels (2015) around the official reception of the prize (whose financial component was not even sufficient to cover their travel expenses).
That “other life” (in which Yasha and I would work together) started in 2012. At the time I was separating from my husband, the father of my two children. I attended a conference in honor of Daniel Bennequin in Paris, where Yasha was one of the lecturers. At the first coffee break, Yasha came to greet me and, with that intense glance of his, asked me how I was doing. This was an impossible question at the time and tears came to my eyes instantly. Yasha immediately took me for a tea nearby. We had a long and very comforting conversation. He also convinced me to come to Stanford with my kids during the summer, which I did. He even took care of finding us an apartment on campus. This is a typical instance of Yasha’s generosity.
From that time on, I changed my research focus to symplectic topology (changing subjects was a hard decision but also a necessity as my research had become close to that of my former husband, which was problematic). And I started going regularly to Stanford, perhaps a way of “eventually doing a PhD with Yasha”. Each time was immensely inspiring. And each time Yasha and Ada kindly invited me for a dinner at their house with other colleagues or visitors. I have very fond memories of some of those dinners, where I met wonderful people and could enjoy the joyful and interesting company of Yasha and Ada.
I am extremely grateful to have met Yasha and to have been given the chance to continue to interact with him. He is one of my favorite human beings.
Born on August 8, 1970 in Brussels, Mélanie Bertelson completed a Licence en Sciences Mathématiques at the Université libre de Bruxelles in 1995, and a PhD in mathematics at Stanford University in 2000. After postdocs at the Max Planck Institute for Mathematics, Université libre de Bruxelles (ULB), she obtained tenure track at the Université Catholique de Louvain and, two years later, a permanent research position from the Fonds de la Recherche Scientifique (FNRS) at the ULB, where she is now a Professor.
