Tribute to Jim Simons by Vasily Pestun

I was only 20 when I first encountered Jim Simons’ work. It was in February 2001, in the freezing cold of Chernogolovka, a small Soviet scientific town. I was in the middle of my senior year at the Moscow Institute of Physics and Technology, and I had taken a long, two-hour bus ride to Chernogolovka to attempt to be admitted to the quantum field theory section of the famous Landau Minimum Series of Theoretical Physics exams, established by Lev Landau himself in 1933. The tradition of these notoriously difficult exams, which test the mathematical skills of graduate students in physics at the cutting-edge of theoretical physics research, was carried on first by Landau, then by his students and their students ever since.

The examiner, Igor Polybin, wrote “$S = \frac{k}{4\pi} \int$ tr $(AdA + \frac{2}{3} A^3)$ in $3d$” on a small sheet of paper and asked me if I recognized the Lagrangian. While my coursework had covered quantum electrodynamics and quantum Yang Mills theory in 3+1-dimensional space-time, I couldn’t identify this one. “No“, I said. “Well, it’s called Chern-Simons theory,” he explained, “and this Lagrangian makes sense in 2+1-dimensional space-time—at least classically. Could you check if this Lagrangian also makes sense in quantum theory, and in particular, what happens to the coupling constant $k$ if you compute one-loop quantum effects?” I understood the question and began my calculations. I quickly encountered subtle “infinity minus infinity” quantum field theory Feynman diagram-style cancellations that seemed to produce a reliable finite result in this theory no matter how I approached them. While the Lagrangian described a continuous, soft, and wavy theory, the computations in Chern-Simons theory had a discrete, deterministic, rigorous, and well-defined feel.

I solved the problem in Chern-Simons theory and passed my student exam, unaware at the time of the depth of this theory and its connections to everything from pure mathematics (algebraic and differential topology, knot theory) to theoretical physics (one could view string theory as a generalization of Chern-Simons theory), and quantum computing. I didn’t realize then how much my life would be influenced by Jim.

I also didn’t know that two years later, in 2003, I would move to Princeton to pursue a PhD in theoretical physics with Edward Witten, the inventor of Chern-Simons topological quantum field theory. Witten based his work on the Chern-Simons three-form and named it after Chern and Simons. After two years in Princeton, I wrote The Hitchin Functionals and the Topological B-Model at One Loop, which is set in 5+1-dimensional space-time but is heavily influenced by ideas on the quantization of 2+1-dimensional space-time Chern-Simons theory.

In August 2005, I attended the Simons Summer Workshop in Stony Brook, Long Island, NY. This month-long gathering brought together a crowd of junior and senior string theorists working on various geometrical problems arising from string theory. I presented my paper in a seminar, and a few days later, I met Jim at the large social event that he hosted every summer for the Simons Summer Workshop participants at his property in the woods near Stony Brook. I was well aware of the depth and importance of Jim’s prolific contributions to mathematics, but I knew very little about his other work. In 2008, I learned that a new institute, the Simons Center for Geometry and Physics, had been founded in Stony Brook. In 2011, I even received an offer for a three-year position there but decided to stay at the Institute for Advanced Study in Princeton. I now realized that Jim contributed significantly to many areas beyond pure mathematics. At the time, I had heard about Renaissance Technologies but didn’t know much about it, except that its profits contributed to the Simons Foundation, which, with its multi-million-dollar funding, generously supports science and mathematics.

In 2014, I accepted a permanent professorship at IHES and moved to Bures-sur-Yvette, in France, where I continued my work in mathematical physics and string theory. My research focused on understanding the emergence of precise and rigid, discrete-like structures supported by the infinite-dimensional continuous realm of quantum field theories, much like the way Chern-Simons theory connects continuous path integration and discrete topological knot invariants.

While my work was primarily funded by the European Research Council, IHES also received significant donations from the Simons Foundation, supporting visitor programs, conferences, and large grant collaborations. This funding was essential to the rapid pace of scientific discovery at IHES, and I was able to enjoy a perfect research environment thanks to the support of public funds, taxpayers, and private donors such as Jim and Marilyn.

In 2022, I finally joined Renaissance Technologies and moved to Stony Brook with the goal of helping to channel market inefficiencies into funding for math and science. In doing so, I aimed to form a new topological link with Jim Simons’ path and align with his legacy and farsighted vision.

Jim will not only be remembered for his extraordinary beautiful and highly impactful scientific work. Even more impressive was his ability to foster thriving work environments for others—whether it be at the Stony Brook Department of Mathematics, the Simons Center for Geometry and Physics, the Simons Collaborations at IHES, or at Renaissance Technologies. Jim had a unique gift for transforming his additive personal talent into a multiplicative one, i.e. a force that multiplies the strengths of everyone and everything around him. I feel incredibly grateful and fortunate that my own path was touched by his magic as well.

Vasily Pestun
New York, August 2024