Arthur Parzygnat, a post-doc at IHES, reflects on his experience during lockdown

Arthur Parzygnat was born and raised in New York City by his parents Tadeusz and Ewa, who independently went to the United States from Poland and met in New York. Before becoming a postdoc at the Institut des Hautes Études Scientifiques, he was a Research Assistant Professor in the mathematics department at the University of Connecticut, and before that he was a graduate student at the CUNY Graduate Center in New York, where he obtained a PhD in physics. He works on topics ranging from category theory and quantum information theory to differential geometry, algebraic topology, and their applications in physics. The topic that interests him most recently is the application of category theory towards entropy and a Bayesian theory for quantum mechanics. Besides work, he also enjoys cooking, bouldering, snowboarding, painting, hiking, running, gardening, and a few other things.

The past two months during France’s COVID-19 lockdown have provided a unique experience of growth for me. I came to France in September 2019 for a postdoc, and I have felt very much at home since. The IHES and my friends at the Ormaille have made the COVID-19 situation as comfortable as possible, and I would have to say that we are incredibly fortunate to be in the situation we are in given the circumstances around the world. I’m grateful for everyone here, especially Mr. Hermand who has been with us at the Ormaille and has been very helpful during this time.

While jogging outside in early April, I had a thought that came to mind: this may be one of the rarest moments in our lives, where the world has essentially come to a halt. Although some of us have gone through great hardship, this can also be viewed as a unique time for self exploration and reflection. How should I spend my time? How can I grow as an individual from this? What can I learn? How can I contribute to a greater cause? How do I enjoy spending my time the most? Who or what do I miss the most? What do I value? We might not often find the time to think about these things with the normal speed and pressure in our usual lives. When things return to normalcy, we might look back at this time and wonder if we made the most of our time. We might even be nostalgic.

My typical day begins roughly between 6h00 and 7h30 with some tea, breakfast, and either French practice or, more commonly, writing down some thoughts from the night before or chatting with my friends in New York who have not yet gone to sleep. I also usually open my window to feel the fresh air and to hear all the birds chirping as I relax and work. From 7h30 on, I work pretty intensely, generally focusing on one project/topic on a given day to be as productive as possible. Interspersed throughout this time, I usually exercise for about 45 minutes to one hour, either by running, at-home exercises, yoga, or going bouldering outside. Depending on the day, I might meet with collaborators or participate in a seminar. I have been trying to cook something new every week, but I make enough so that I have leftovers for several days to avoid spending too much time cooking. Because I have been so interested in my projects, I generally do spend most of my days working, which I greatly enjoy. However, it took a while to turn this into my typical day.

The first week of COVID-19 lockdown caused some anxiety for me. I was worried about family and friends, especially those in New York and London. I was also concerned about having contracted the virus as well. I created an online forum for those of us at the Ormaille to support each other during this difficult time. I began my quarantine about four days before France ordered lockdown and obtained enough food for about one month to ensure I could not get anyone sick in case I was. Another moment of difficulty for me took place around Easter, when I would have otherwise been with family in Poland. But besides these two negative periods, my experience has been overwhelmingly positive.

The supply of food I obtained led to many interesting experiments. I had to plan all my meals based on the food I had. I learned to combine ingredients in interesting ways based on what food remained. I got to make pizza for my first time here and accidentally learned how cooking down tomatoes for a long time makes for a rich sauce. I also found out how simple it is to make hummus directly from chickpeas and sesame seeds. I even learned how to efficiently cut a pepper (if you’re curious, I recommend looking up how Gordon Ramsay does it). I also experienced some failures, such as when I attempted to make gnocchi, because all the starch from the potatoes made it nearly impossible to form nice shapes. Nevertheless, I hope these experiences help me expand my cooking/baking skills.

Sometime towards the end of the first week of lockdown, I suddenly began working fanatically. I was able to contribute more intensely to projects with my collaborators Byungdo Park, Augusto Stoffel, and Benjamin Russo, and I revisited old problems I was passionate about, namely the functorial properties of quantum entropies, while simultaneously pursuing some projects on quantum Bayesian inference. Together with Benjamin Russo, we recently completed a paper combining many areas of mathematics and physics including linear algebra, quantum information theory, category theory, operator algebras, probability theory, and positive matrix completions. We are currently in the final stages of editing before submission to a journal. I also found two online seminars on applied category theory, which I have been attending regularly, and a class taught by one of my professors, Mahmoud Zeinalian, from when I was in graduate school. I would say that it has been an incredibly productive time for me. A part of the reason for my productivity is the wonderful environment we have at the Ormaille and that I have found an ideal schedule for myself. For example, I learned that I enjoy taking an exercise break either before lunch or before dinner, and that I am more productive when I take this break as soon as the urge comes or I become tired. Taking such breaks gives me the energy to work longer and more efficiently overall.

Although we are allowed outside only within a kilometer from our residence, and for a maximum of one hour, I discovered a wonderful, and mostly isolated, section of a small forest nearby. Walking through these woods with all the lavender plants, birds, and other creatures, I have this surreal moment of peace. I had this experience so far several times during my stay in France (which is amazing considering that I don’t often have such moments). Once was out in Saint-Rémy-lès-Chevreuse in October during a long hike through the countryside and another was in the woods of the IHES. I was also fortunate to find several beautiful large rocks in the forest nearby, and have been going there on occasion to boulder. This has so far been my best substitute since I have gone to self-isolation and since the rock climbing gyms have closed.

Towards the past few weeks, a few of us at the Ormaille started participating in vegetable basket deliveries organized by Kate [Vokes]. I think this is a great way to minimize our interactions with those we would otherwise encounter in supermarkets and to help support these businesses. It also offers us an opportunity to have some social interactions in addition to the tea time organized by Diana [Davis]. It is certainly getting to the point that I miss everybody at IHES and interacting with everybody there. However, whenever I have this feeling, I remember that this period of time will pass, and there will be a time at which we will reconnect again. For now, this is the time to focus on different aspects of life and learn something about ourselves.