Undergraduates in research: Hacking with prime numbers | Science – Dailyuw

Undergraduates in research

One of two large tile mosaic murals completed in 1936 by Robert B. Inverarity is found on the walls of the entrance of Bagley Hall, where many undergraduates participate in research.

You’re sitting in class, hating it, not doing very well and really, you wish you didn’t have to leave your room in the first place. There are plenty of students out there who are stuck on the wrong path. Senior Rohan Hiatt knows exactly how that feels, and he has a solution.

After nearly four years at the UW and almost three years of research, Hiatt, who is pursuing a double major in math and English, believes undergraduate research is one of the best things a student can do to find their passion.

“Research is, I think, helping solve that problem of people who are looking for different areas that they want to explore, but they just can’t do that through their classes,” Hiatt said. “The cool thing about research is that it’s incredibly interdisciplinary, so you can kind of transcend the faux departmental boundaries that are set by the university.”

After choosing to major in math in his freshman year due to “genuinely enjoying” going to his classes every morning, Hiatt started shopping around for a second major. In his sophomore year, he took a class in the English department with graduate student Sam Hushagen and “started really getting into the theory” behind the literature.

Although his main research focus in the past few years has been in the math department, Hushagen’s encouragement to be curious was reason enough for Hiatt to start research in the English department. This led to him having the opportunity to go to an academic conference and talk about his ideas on “Paradise Lost” by John Milton.

This initial taste for research inspired Hiatt to continue feeding his curiosity. In winter of his sophomore year, Hiatt started research with acting assistant professor Amos Turchett in the math department through the Washington Experimental Mathematics Laboratory (WXML).

“WXML is really wonderful just because it creates more of a sense of community when you’re doing research,” Hiatt said. “The explicit focus is on communicating math to non-math audiences.”

The first project Hiatt undertook was based on finding an algorithm that can tell you whether a number is prime or not with 100 percent accuracy. His team worked to test the algorithm and measure its efficiency.

“When you go on a web browser … your connection is encrypted using an algorithm called RSA [Rivest-Shamir-Adleman],” Hiatt explained. “That’s an encryption scheme that uses really large prime numbers as its keys.”

The purpose of generating an accurate deterministic algorithm as opposed to a probabilistic one was related to internet security.

“Factorization … is probably the hardest problem to do efficiently, which is interesting because it’s the first thing we do in elementary school, but computers can’t factor numbers efficiently,” Hiatt said. “If this algorithm worked, someone could feasibly hack into encryption schemes a lot easier.”

Hiatt’s second math research project gets a bit abstract, so stick with me here. He was working with diophantine equations, which are, put simply, equations that can be solved by plugging integers in.

“We looked at a particular class of diophantine equations called plane curves, and you can literally just think of them as curves that you graph,” Hiatt said.

One of the unanswered questions in this area of math is regarding a class of plane curves called genus 2 hyperelliptic curves. Hiatt explains that the problem is determining “whether the solution set is finite or infinite.”

To those of us who have no idea what most of those words mean, Hiatt was looking at a curve that depends on the highest power of x in the equation, is defined by a set of coordinates, and has two holes in it (represented by ‘genus 2’). Throw a genus 1, genus 3, or genus 4 problem at a mathematician and they can answer immediately, but genus 2 curves are the ones they’re losing sleep over.

After attempting to use their algorithm and the information from an online database to generate results, the database updated itself and made their work “obsolete.” In other words, someone beat them to it.

“So now we’re prepping a paper that kind of describes the process we went through and is more of an exploration into this indeterminate area of math for undergraduates to be able to understand,” Hiatt said. “We’re also trying to figure out some stuff and get some data that’s not on this database so we can still potentially contribute some data.”

After a difficult freshman year of not knowing what to do, Hiatt found what he was passionate about and pursued it. He is keen to communicate the value of undergraduate research to people who don’t see its immense value.

“Doing math research specifically has really helped me understand my classes,” Hiatt said.  “It’s helped me be more precise. It’s also led me to have a natural curiosity, and enabled me to put a little bit of context to what I’m doing in my coursework, which makes [class] more bearable.”

Reach reporter Molly Slann at science@dailyuw.com. Twitter: @MollySlann

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