Episode 74 - Priyam Patel
Evelyn Lamb: Hello, and welcome to My Favorite Theorem, the math podcast with no quiz at the end. I'm your host Evelyn Lamb. I'm a freelance math and science writer in Salt Lake City, Utah. And this is your other host.
Kevin Knudson: I’m Kevin Knudson, professor of mathematics at the University of Florida. I almost forgot my name there for a second.
EL: It happens.
KK: I realized, like, I was hesitating, and I was like, “Who am I again?” Yeah, you know — so our listeners don't know, but it's 5:30 where I am, which, you know, doesn't sound late. But I've been at work all day, and now I'm tired.
EL: Yeah. Well, you should have made up something. You know, just tried on a different name for fun just to see.
KK: Well, yeah, so even my parents had the deal that if I was a boy, my dad got to name me. So he went with Kevin Patrick. And if I was a girl, my mother was going to get to name me. And should I tell you what I would have been?
KK: Kandi. Kay Knudson.
KK: Now, I'll let you work out why that would have been terrible for lots of reasons. Already, there are multiple axes along which that is terrible.
EL: Great. Yeah, well, my name if I had been a boy ended up with my younger brother. So it was kind of not that interesting. I mean, if you knew my family, you would be like, Okay, well, that's boring. Anyway, yeah. We are very happy today to have Priyam Patel on the show. So yeah, Priyam, could you introduce yourself a little bit?
Priyam Patel: Sure. So my name is Priyam. I am an assistant professor at the University of Utah, and I have been here for three years. Before that I was around everywhere, it feels like, for my postdoc. I was at UCSB for a few years, before that at Purdue for a few years, And I did my PhD at Rutgers, which now feels like ages ago.
EL: Yeah, you’ve been in, like, every region of the country, though, I guess not central timezone, because Indiana is right on the west edge of Eastern.
KK: That’s right.
PP: Yeah. So I was never in the Central time zone. And that's why — in the summer in Indiana, the sun sets at, like, 10:30pm. It's really bizarre.
KK: You could call that Central Daylight if you wanted to, right?
PP: Yeah. Something like that.
EL: Yeah. And as you mentioned, you've been at Utah for about three years. And you you first got here in fall 2019, and I was gone for most of the fall 2019. And then of course, we all know what happened in 2020. So part of the reason I wanted to invite you is because I feel like I should know you better because you've lived here for three years. But, like, with the weirdness of the past three years, I feel like I haven't gotten to talk with you that much. And so of course, obviously the best way to do this is, like, on a podcast that we want to just broadcast to the entire world.
PP: Yeah, perfect. So no private conversation over drinks. Just put me on the podcast.
EL: Yeah. Excellent. So So yes, I'm excited to get to chat with you. And yeah, hopefully we can do this over drinks in a real venue at some point.
KK: Wait a minute, what happened in 2020?
EL: I tried to block it out.
PP: Nothing at all.
EL: For some parts of it, really nothing.
PP: It feels like a whole blur since then. So
KK: I’m not convinced it isn’t still 2020 somehow.
PP: Yeah, yeah.
KK: Alright. Anyway, I'm being weird today, and I apologize. So let’s get to math. So Priyam, you have a favorite theorem. Which is it?
PP: Yeah. So I chose the Brouwer fixed point theorem, which I learned has been done twice already on this podcast.
EL: Yes, I'm very excited to hear more about it because in our emails, you mentioned some aspects of that I wasn't aware of. And so this is very exciting. And this is when people, when we email with people, they’re always like, “well has this been used?” And we're like, “It doesn't matter if it has, you can use it anyway.” We like to talk about theorems because it is interesting, just the different relationships people have with the same math. So for anyone who hasn't been you know, avidly listening and taking notes on every single episode we've done since 2017, can you tell us what the Brouwer fixed point theorem is?
PP: Yeah, so I'm just going to state it for the closed disk because that's the only context that I'm going to talk about it in. But basically, if you take in the plane in our two if you take the closed unit disk, then the theorem says that every continuous map from