Zachary Porat

A Mostly Mathematical Travelogue

Welcome to my blog! Here, I chronicle my mostly mathematical travels as a grad student studying number theory.

A complete archive of my blog posts can be found here. Copy my RSS feed link to add this blog to your favorite RSS reader:   RSS Feed

If you have somehow stumbled here accidentally and were actually looking for information about me, please visit my homepage.

All opinions expressed here are my own and do not necessarily reflect the opinions of the institutions that I represent.

Un Week-end Parfait

Posted on October 29, 2024

I recently returned from a weekend in the city of Québec, where I attended the Québec-Maine Number Theory Conference at Université Laval. Before the trip, I expected today’s blog post to be brief. A weekend conference didn’t seem likely to offer a compelling story–let alone one with a moral, as in my previous posts. Instead, I intended to use this post as an opportunity to announce my first solo preprint, which can be found here: arXiv:2410.02734.

I am happy to report that I was wrong, and so I will now (briefly) wax poetic on my perfect weekend! My travel companion throughout this journey was my undergrad advisor, Jeff, who has since become a mentor and close friend. I made my way to Albany on Friday morning, and then we proceeded onward together. Once in Québec, we quickly made our way to the old city. We meandered through the Plains of Abraham and Parc du Bastion-de-la-Reine, which gave way to some breathtaking views:

After exploring the riverfront, numerous art galleries, and surprisingly affordable real estate, we eventually found a place to eat dinner. Jeff was eager to speak in (very good) French,¹ while I was much more hesitant. Not only is my French rusty, but I also vividly remember an incident when my dad, after asking a gas station attendant for the bathroom in crude French, was met with, “I speak English, you know!” This incident happened outside the city over 15 years ago, but it certainly didn’t help my trepidation. Further complicating the matter is that I have several food allergies. I ended up speaking English to the waitress that first night.

Saturday marked the official start of the conference. I attended several excellent talks, but the opening presentation by Mathilde Gerbelli-Gauthier was a real standout. She eloquently weaved her thesis work into the grander story of her mathematical relationship with Nicolas Bergeron, to whom the conference was dedicated after his tragic passing earlier this year. It was a beautiful talk and a touching tribute that emphasized the humanity of mathematics. (Also selfishly, I’m grateful that she spent several minutes covering some material that I was going to have to hurry through in my own talk!)

On Saturday evening, after the day’s talks had concluded, we again made our way to the old city. We were joined by Rylan–one of Jeff’s academic siblings–who I first met at a Connecticut Summer School in Number Theory a few years ago. It turns out that they are a pretty rad family tree! While wandering through the old city, we came across a vendor selling maple taffy (aka perfection, according to Jeff). From the moment our interaction began, he exuded pure joy, welcoming us to his store and his city as he poured a fresh batch. (Here is an unrelated picture of the Château Frontenac that I took that night.)

This delightful interaction would’ve been the highlight of most trips, yet somehow–in this magical place–every exchange felt just as charming. The locals were happy to meet us, curious about our visit, and kind enough to let me fumble my way through their language; every conversation felt inviting and authentic. As the weekend progressed and I saw how open all of the locals were, I became more confident to lead with French rather than English.

So, on the last day at breakfast, I was determined to speak only French. Jeff and I went to Normandin, a local chain that had breakfast poutine (and a really detailed allergen menu). After ordering coffee smoothly enough, the waitress returned for our food orders. I clumsily explained my food allergies and went on to order the breakfast poutine. Everything was going well, until she asked how I wanted my eggs. Unfamiliar with the French term for “scrambled,” I was immediately lost. After one (or maybe two), “Pardon”s, the waitress graciously repeated the question in English. I responded and we carried on. Jeff pointed out later that we carried on in French, not English, something I didn’t realize in the moment. There was no judgement or disdain from the waitress, she just helped me through that little hiccup and we continued as usual.

For me, this small gesture encapsulated my time in Québec: kind, generous folks simply being human. I had spent the weekend anxious about making mistakes or not knowing a word that could derail a conversation. But in the end, when this worst-case scenario happened, it was no big deal. If you make a sincere attempt to speak to someone in their native language, chances are they won’t be mad if you make a few mistakes. So here’s my moral: If you ever find yourself in a similar situation, I recommend just putting yourself out there. People will appreciate the effort, and small stumbles often make for the most genuine connections anyway.

On Meeting Your Idols

Posted on July 27, 2024

If I had to hazard a guess, I would wager that whoever said “Never meet your idols” was not a mathematician. In my previous blog post, I wrote about meeting Barry Mazur for the first time. Despite Professor Mazur being a titan of mathematics, he was warm and kind throughout our interaction. His sincerity shone through; we were just two people chatting about math and more.

I first came to this realization—that my mathematical heroes were to be met, not ignored—when Joe Silverman visited Wesleyan a few years ago. He came to give a colloquium talk on a subject that I do not remember. What I do remember, however, is our jovial conversation as we watched some of my colleagues compete in a game of duck chess. Here was a renowned number theorist, who wrote two texts that greatly influenced my interest in the subject (Rational Points on Elliptic Curves and The Arithmetic of Elliptic Curves), talking chess theory as we drank coffee and ate cookies.

Professor Silverman’s visit was an eye-opening encounter for me. I realized that these mathematicians I revered were wonderful people as well. I am happy to report that since then, I have experienced several similarly genuine interactions with mathematical greats (including Professor Mazur)!

My most recent mathematical adventure took me to MIT, along the beautiful Charles River in Cambridge, MA, for ANTS XVI. Here is an artsy photograph I took just outside the main conference hall.

The conference attendee list was a who’s who of famous computational number theorists, including Joe Silverman, Steven Galbraith, Andrew Sutherland, John Cremona, and Bjorn Poonen (some of you might be familiar with Professor Poonen for another reason…)

Once again, I was reminded just how lovely our community is. Everyone I talked to was curious about my work and what the future has in store. So let me offer a piece of advice: “Meet your math idols.” I haven’t been disappointed yet!

P.S. If you weren’t sold on Joe Silverman’s celebrity, we witnessed an attendee ask Professor Silverman to sign a copy of Advanced Topics in the Arithmetic of Elliptic Curves. (I think this was the book being signed, but I can’t be sure; Freddy and I made this speculation based on the thickness of the book.) He, of course, obliged.

Mazur and Me

Posted on July 20, 2024

In 1977, Barry Mazur proved Ogg’s conjecture, showing that the torsion subgroup of the Mordell-Weil group of an elliptic curve over Q must be isomorphic to one of fifteen groups.¹ I can’t quite remember when I first saw this statement–it might have been in a plenary talk by Álvaro Lozano-Robledo at the 2019 Union College Mathematics Conference–but I do remember being struck by just how tidy the statement was. The classification result scratched some itch in my brain that I didn’t even know I had. It would serve as major inspiration for my undergrad thesis, and propel me towards grad school.

One aspect of grad school that was undersold to me is the travel. I knew that professional mathematicians travelled to attend conferences and give talks, but I wasn’t prepared for how often these opportunities would arise as a grad student (most of them funded too)! As I enter that last few years of my program, my travel has only increased, and I suspect that it will continue to do so. I hope this blog will serve as a place for me to share stories from these mostly mathematical travels.

My first travel story comes from this past year’s Arizona Winter School. (I originally had the idea to start this blog immediately following AWS, but, as is standard in the life of a grad student, things got busy, and I am just now getting around to actually setting it up.) AWS is a week-long program that offers four mini-courses on a set of closely related topics in number theory and algebraic geometry. The week is bookmarked by a series of talks by the Clay lecturer, who, for this year’s topic of Abelian varieties, was Barry Mazur.

Following his final talk, I lingered around for a bit, hoping for the chance to speak with him. I was not the only one with this idea, and a minor line formed. When it was my turn, I told him how important he was to my mathematical journey (something I am sure he has heard many times before). He was as gracious and kind as all the stories I had heard; we chatted for a bit about math and about academic lineage.²

I also asked him for a picture, to which he happily agreed. Here is the image:
I am so grateful to have had the opportunity to meet the man who helped set in motion this long, strange trip. Getting a PhD in math is hard, but the chance to travel all over, learning interesting math and meeting inspiring people, is truly a wonderful adventure.