DiscoverMy Favorite TheoremEpisode 90 - Corrine Yap
Episode 90 - Corrine Yap

Episode 90 - Corrine Yap

Update: 2024-01-23
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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. And this is your other host.



Kevin Knudson: Hi, I'm Kevin Knudson, professor of mathematics at the University of Florida. How's it going?



EL: All right. Yeah, I was I was trying to think about what to say. And I was like, well, the most exciting thing in my life right now is that our city is starting a pilot program of food waste, like a specific food waste bin.



KK: Okay.



EL: But then I realized I also did an 80 mile bike ride last Saturday, and that's the first time I've biked that far. And that might be slightly more exciting than compost.



KK: Are you working up the centuries? Are you are you heading for?



EL: We’ll see. I felt pretty fine after 80. I also don't feel like I wanted to do 20 more miles. So we'll see. Someday, maybe



KK: The last century I did was, wow, it was 2003. It was 20 years ago. This is one called the six gap century in Georgia. And it goes over six mountain passes in the mountains of North Georgia, one of which has, like, a 15% grade, which is quite steep. It took me about eight hours. And then I hung up my bike and didn't ride it for like three months.



EL: Well, I mean, it would probably take me at least eight hours to do a flat century.



KK: Yeah, but back in my youth I could do a flat century in about five, but not anymore. Not anymore. So let's keep this banter going because I — so Ben Orlin, a former guest on our podcast, I saw Math with Bad Drawings today had various golden ratios. One of which was the golden ratio of hot fudge to ice cream in a hot fudge sundae, which he argues is one to one, but that's way too much fudge.



EL: That is so much fudge!



KK: But the podcast, like, substance to banter golden ratio, he claims is like two to one. So like a third of this should just be like us, you know, just shooting it.



EL: Saying nothing.



KK: Yeah.



EL: Well, I must admit, that's why I listen to fewer podcasts that maybe I would want to because I have a low banter tolerance. Which brings us to our guest today. Yeah, so we are very happy to welcome Corrine Yap today. Would you like to tell us a little bit about yourself?



Corrine Yap: Yes. So I am currently a visiting assistant professor at the Georgia Institute of Technology, Georgia Tech, in the math department. I'm also a postdoc affiliated with the Algorithms and Randomness Center. But I just got my PhD in the spring from Rutgers University.



KK: Congratulations!



CY: Thank you! I do a lot of, like, probabilistic combinatorics, and stuff around that. So that's sort of my main research work. I also do some performing and some playwriting as well. I actually just got back from a performance yesterday Worcester Polytechnic Institute in Massachusetts.



EL: Oh, wow.



CY: So very busy this time.



EL: Yeah. That’s actually one of the reasons that I've been wanting to invite you for a while. And I was like, well, I should wait until I've seen one of her shows. And then it just has not aligned to work out. Because I know you've done them at the Joint Meetings and things, and the times that I have been there and you have been there, it’s just not been a good time. So it's like, well, I'm not going to put this off forever. So even though I have not yet seen one of your shows, I'm very glad that that we could invite you and have you here and yeah, well, can you talk a little bit about the kinds of theater that you do, or kinds of — I don't know if it's mostly theater or more, like other? I don't know, speaking performances?



CY: Yeah. So it really started when I was a lot younger. And also in college, I primarily studied both mathematics and theatre, with no sort of vision as to what that would turn into in terms of a job or career or anything. I just really enjoyed doing both of them. And as an undergraduate I thought I was mainly interested in acting, but I started studying playwriting while at Sarah Lawrence College in Westchester, New York. And I started writing this play, which is the play that I continue to perform. It's called Uniform Convergence. And it's a one-woman play that's about math. It tells the story of Sofia Kovalevskaya, who is a historical Russian mathematician. She was born in 1850. And it tells a little bit about her life and how she faced a lot of obstacles to be successful as one of the first few women in academia. But it also has a portion that is sort of inspired by my experiences being Asian American, and also being a woman pursuing mathematics. And the setting is that of a real analysis classroom, a lecture where the character Professor….



EL: Hence, uniform convergence.



CY: Yeah, and she is lecturing to her students. So at one point, they do reach the point of the class where they do uniform convergence as a topic. So, you know, in the past, I did a lot more — like, in college, I did, you know, the auditioning for plays and being involved in rehearsals, and all this sort of stuff. But since going to graduate school, and now having an actual job, this one play is sort of the main way that I keep my ties to doing theater and the theater world.



KK: Very cool.



EL: Yeah. Well, that's cool. I didn't realize that Kovalevskaya was the subject of this. I actually just read Alice Munro's short story, Too Much Happiness, which is based on her life. And actually was not my favorite short story in the collection that it’s in, but it, you know, she is such a compelling figure and another woman who was interested in math, you know, at a time when it was a lot harder for a woman to have an academic career in any field, and was interested in literature. Wrote, I think both memoirs and fiction?



CY: She also wrote a play.



EL: Oh, wow.



CY: Yeah. But it wasn't about math. But yeah, she was very much also in both of these worlds in, you know, sort of a more artistic, creative mindset as well as a mathematical one.



EL: Yeah. Fascinating person. So yeah, that's really interesting. And hopefully someday I'll get to see it.



CY: Yeah, I'm still performing. I didn't think I necessarily would be. But it's been since 2017. I've been performing it at different college campuses, and sometimes at conferences at different parts of the country. And I still get invited places. So as long as that keeps happening, I'll keep going.



EL: Yeah, when I was still in academia and doing a postdoc, I did, you know, I'd started doing writing. And sometimes I would get invited to do both like a research seminar talk and a public engagement kind of talk. And so that that might be in your future as well.



CY: Yeah, maybe.



KK: Yeah. Broader impacts.



EL: Wearing both hats on one trip.



CY: Yeah, I actually, I forgot I am doing that. I think this is the first time I'm doing it. At Duke in October, when one day I'll be giving a seminar talk, and then the next day, I'll be performing the play.



EL: Yeah, cool. Well, we invited you on here to talk about your plays, but also to talk about your favorite theorem. So what have you chosen?



CY: Yeah, so I've chosen Mantel’s theorem as my favorite theorem. So this is a theorem that is in the area called extremal combinatorics. And I'll explain what that means. But the statement of the theorem is pretty straightforward. It says that if you have a graph, which I’m a combinatorialist, so for me graphs mean, collections of vertices with edges connecting pairs of vertices. If you have a graph on N vertices, then the maximum number of edges you can have without forming any triangles — so just three edges and three vertices connected to each other — the maximum number of edges you can have with no triangles is N squared over four with appropriate floor.



KK: Yeah, sure.



CY: And this seems like, okay, this is this is just a statement, maximum number of edges. What's so cool about that? You actually, we actually also know where the N squared over four comes from. It’s, the extremal example is the complete bipartite graph on parts of size N over two. So what that means is, you split your vertices up into two sets, each of size half the total universe. And all of your edges go between the two parts. So from one part to the other, not inside the vertices of the parts. So complete means you have all the possible edges crossing between the parts, and then bipartite because you have the two parts of the vertices, and that has N squared over four edges. And it has no triangles in it.



KK: Not even any cycles.



CY: Yes. Yeah, no odd cycles. Yeah.



KK: Okay, all right.



CY: Yeah. So, one reason I really liked this is because when I first learned it, I didn't really think much of it, I learned it in an undergraduate class in combinatorics. And there are, like, three, maybe four proofs that we learned that were all pretty short and straightforward. One of the most basic proofs is just via induction on the number of vertices, and there's nothing, there's no really heavy machinery that's needed at all. And I didn't think much of it. And I didn't have any context as to like, why do we care about this sort of thing. But every year, I learn more and more things that make me appreciate this theory, more and more, because it really was the foundation for this whole field that we call extremal combinatorics, which is really centered
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Episode 90 - Corrine Yap

Episode 90 - Corrine Yap

Kevin Knudson & Evelyn Lamb