Mark Ronnenberg (MR): The solar system internet is a buzzword to describe space communication. Right now we already have things in space: satellites, rovers, and so forth. As part of the Artemis program, NASA is planning to send more things and people into space. 

For all of this to work out well, we need solid, robust communications that will function in space. Because our space networks are relatively small, people on earth on ground stations are managing everything. The rate that we're sending things into space is increasing, and it's not feasible to scale our current management systems to such a degree. We need autonomous systems that can run on their own without micromanaging everything. 

College: When you say autonomous systems, what do you mean? 

MR: Maybe I need two satellites to be able to communicate with each other; I don't want to have to send a message from Earth saying, “OK, satellite, send this message now,’ because there'd be a time delay because of the vast distance. It'd be better if the satellite could automatically see what other satellites are within range and communicate on its own without human input. That's what we mean by autonomous. But we don't have a firm mathematical framework with which to model that sort of network. 

That’s where we come in as interns. Our job is to figure out what kind of math might be applicable here. What tools for mathematics could we use? And how can we make nice mathematical models that we might actually be able to study?  

College: What did you do on a typical day of your internship?  

MR: I'd sign onto a platform to virtually meet with my group of six other interns. We'd often have time to informally chat with each other before more formal meetings with our group leader. He might give a talk about a technical topic, or he might have tasked us with learning about something and then presenting to the team. We’d also have lectures from external speakers, team building exercises, and NASA official meetings. 

In one meeting, we simulated being astronauts in the space station communicating with ground control. We worked through a hypothetical problem to learn a little bit about how astronauts speak and how to work as a team. 

College: What accomplishment are you most proud of from your time with NASA?    

MR: If I was going to single one out, I would say it's the fact that we got two papers accepted to the IEEE: Institute of Electrical and Electronics Engineers. The whole group worked together to write those papers and get them submitted, so it was very rewarding to have them accepted for IEEE’s 2023 aerospace conference.  

College: What research do you do here at IU? 

MR: I work in a field called topology, or, low-dimensional topology. I'm studying things called manifolds, knots, and links. A knot in math is exactly what it sounds like. You could take a rope and tie a knot in it. The only difference is that in math we fuse the ends together so that it’s like a circle. 

The question at the heart of my work is: if I gave you two different knots, how would you tell if they're really different? You could move them around until one looks like the other. And if you can do that, then they're the same. But if you can't, how would you ever prove that you can't do that? Turns out that's difficult.  

My research is focused on studying and comparing these knots by cutting them into pieces mathematically. If I can associate a number to a certain knot, then I can say if the two numbers are different, they're different knots. 

People use all kinds of crazy math to attack this problem. It sounds like I’m just playing with bits of string, which I am, but it also has important applications. 

College: What was the connection between your work at IU and your work at NASA?  

MR: Topology matters to some of the stuff we were doing at NASA. We wanted to model space communication networks, and one type of model that we had in mind uses something called a hypergraph. In a normal graph, you connect two vertices (points) with a straight line. In a hypergraph, you can connect as many vertices as you want at a time.  

Instead of a phone call from A to B, imagine a radio broadcast. You’re sending a signal out to whoever's listening. And this is modeled well by a hypergraph. We were trying to come up with ways to implement hypergraphs in our modeling of space communication. 

College: What did you enjoy most about your time with NASA? 

MR: NASA was an awesome opportunity, and I enjoyed it a lot. It helped me to branch out. Up until this point, I've mostly been working in my little pure math bubble within academia and not really focusing on real world applications because the math is cool on its own. This was a good opportunity for me to work with people from other disciplines and see how math could be used in an interesting, real-world setting. It was enlightening for me.  

College: What piece of advice would you give to other students who are considering applying? 

MR: Anyone who's interested should check it out. There's a website where they post all their internships; go there and search through the different listings. See if there's anything that aligns with what you're into. It doesn't have to be perfectly aligned; before the internship I didn’t know anything about space communications, or networking. If anything seems within the sphere of what you're interested in, you'll be able to contribute. You have nothing to lose! Really put yourself out there.