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.

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