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Apoorva Panidapu

Apoorva Panidapu

Age: 16
Hometown: San Jose, CA

Mathematics: “Short-Interval Sector Problems for CM Elliptic Curves”

About Apoorva

I’m Apoorva Panidapu, a 16-year-old rising junior from San Jose, California. I began homeschooling in sixth grade, and because of homeschooling, I’ve had the chance to forge my own unconventional path full of exciting experiences of all flavors, including learning from a conglomerate of institutions, including San Jose State University, Columbia University and Johns Hopkins University. 

In my free time, I enjoy playing the violin, practicing kung fu, and reading classical literature. I also founded my own art gallery, Apoorva Panidapu’s Art Gallery, as an online platform to share my artwork and raise funds for charity.

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"Being a Fellow is such an enormous honor and opportunity. I can’t believe I get to join this community of innovative and brilliant young mathematicians, scientists, authors, and more. I’m so excited to meet all the other 2021 Fellows and to see the cutting-edge research they continue to do in the future."

Project Description

Much like atoms make up our universe, primes are the building blocks of the mathematical universe. We don’t only want to know how many primes there are (infinitely many!), we also want to know how they’re distributed. This question has led to some of the greatest problems in not just number theory, but all of mathematics, such as the Riemann Hypothesis. Now, my project takes this question even further, or to be exact, even smaller. In particular, I study prime distribution in short intervals, looking at their fine-tuned behavior in these extremely zoomed-in settings. Going from general distribution to short intervals restricts the tools we could use previously and requires much more careful handling of the details and highly refined theorems, which is what my project navigates through to prove my result in this delicate setting.

Deeper Dive

My project, “Short-Interval Sector Problems for CM Elliptic Curves,” studies prime distribution in short intervals. Specifically, I am looking at the fine-tuned behavior of primes in extremely zoomed-in settings, like the distribution of primes represented by binary quadratic forms. The study of prime distribution has led to some of the greatest problems in all of mathematics, like the Riemann Hypothesis. Despite the hundreds of years of literature surrounding my research problem, there is really no such paper that clearly outlines the relationship between the prime distribution I study, algebraic number theory, and combinatorics, and I wanted to bridge this gap. Hence, I took an interdisciplinary approach to this problem, exploring seemingly disparate areas and the actual close ties between them, such as the relationship between binary quadratic representations of primes and elliptic curves over the rationals, the bond between modular forms and Hecke Grossencharacters, and the combinatorial properties of newforms. In addition to this, I prove a more refined result of previous related work.

As a ninth-grader, I was accepted into a prestigious number theory research program, geared towards high-level undergraduates, where I navigated graduate-level work from a research perspective. My mentor, Dr. Jesse Thorner, and I worked together to find a project that would apply the high-level math I had learned to analyzing and uniquely reformulating a historical problem. Thus, I decided to work on a project studying short-interval CM Sato-Tate distribution. This work was like my baby–it took me 9 months to complete. One of my main difficulties with my project was figuring out how I wanted to present it. I chose to speak through the lens of elliptic curves, but I included a note at the end about how this result can be extended with just a little more work. To me, it was surprising that my main difficulty lay in the introduction of my paper, instead of the more technical, easy-to-trip-up parts of it. I can’t express my gratitude enough to Dr. Thorner, without whom I wouldn’t have had the chance to explore this unique intersection in math to the extent I did in my project. His guidance throughout the process of writing and publishing a mathematical research paper was invaluable, and his advice will no doubt stay with me for my future research.

My project offers a different viewpoint on the distribution of primes in short intervals that makes the advanced ideas used in my proof, which are often rather technical and analytical in nature, more accessible to those in more combinatorial or algebraically flavored fields. It provides a path to a deeper understanding of such analytic number theory results through a new, more approachable lens for people outside this field. My work may also be used to adapt other theorems to similarly different settings, by intertwining such algebra and combinatorics into the standard analysis that goes into proving these results.


What’s the best thing you’ve bought so far this year?

Posca pens! They’re these really cool acrylic paint markers that I’m obsessed with.

What is your favorite Olympic sport?

Racewalking, hands down.

There’s a round-trip free shuttle to Mars. The catch: it’ll take one year of your life to go, visit, and come back. Are you in?

Nope, I’ve seen Gravity.

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In The News

San Francisco – The Davidson Fellows Scholarship Program has announced the 2021 scholarship winners. Among the honorees are Apoorva Panidapu, 16, of San Jose; Bala Vinaithirthan, 18, of Danville; Franklin Wang, 17, of Palo Alto; Adarsh Ambati, 16, of San Jose; and Sean Li, 17, of Danville. Only 20 students across the country to be recognized as scholarship winners each year.

Download the full press release here