# Mathematician

Jason Liu is a senior at the Davidson Academy at the University of Nevada, Reno. The 17-year-old’s work in mathematics earned him a finalist position at this year’s Regeneron Science Talent Search, a national high school competition rewarding original scientific research. He and the other finalists will fly to Washington D.C. on March 5 for the next round of judging.

**So, what was your project?**

So, my project was in math. It basically takes these things called integer-valued polynomials, which are just polynomials that send integer inputs to integer outputs. It takes these integer-valued polynomials and works on characterizing a generalization of those. So, it’s based off of a paper by two other guys that generalizes these integer-valued polynomials to a *q*-deformed version, which means that, instead of plugging in integers, you plug in these *q*-integers that are polynomials in *q*. And in a sense, what I’m doing is I’m characterizing all *q*-integer valued polynomials that send positive *q*-integers to polynomials in *q*, and negative *q*-integers to polynomials in *q*-inverse.

**OK. I think I’m following. I was never much of a math guy myself. But what’s the practical application for this?**

So, as far as direct applications, I’m not quite sure. The only other paper I’ve found on *q*-integer valued polynomials is that paper by the other two guys. But, in their paper, they do mention that the set of all *q*-integer valued polynomials—that is, in some sense, equivalent to a quantum group, a specific quantum group. And these quantum groups are very important for quantum mechanics. So, it’s possible that, with the help of my characterization for specific types of q-integer valued polynomials, researchers in quantum mechanics might be able to benefit from that and better understand quantum mechanics.

**So, your work is essentially broadening the material that quantum mechanics is built on?**

Yes.

**Gotcha. What’s happening next at the contest?**

So, at the moment, because I made the top 40, I get around $25,000 from Regeneron, and I believe 11th place through 40th place, that’s all they get—other than meeting all the wonderful people at the camp. But for the top 10 places, there’s larger money prizes. I think for first place it’s a quarter million. And I think this the last round of judging.

**Wow. So, you’ve already won $25,000 for this?**

Yes, conditional on me actually going to the camp.

**That’s awesome. Are you the only one representing Northern Nevada in this competition?**

I think I’m the only one representing Nevada in general, yeah.

**Well, congratulations, Jason. Do you have a main goal that you’re working towards right now for your future?**

As far as college goes, I was accepted early into MIT, so I think I’ll be going there if nothing goes wrong. As far as line of work, I’m not 100 percent sure what I want to do after I graduate. I think I’ll probably still work on this project a bit more, but I don’t know if I’ll be doing that long term after I graduate. So, basically, no set plans.