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.

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.