Select a year:
2018 Davidson Fellows
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001

Age: 17

Irvine, CA

Category: Mathematics

Project Title: The Rational Cherednik Algebra of Type A_1 with Divided Powers

My project studied a class of mathematical objects called rational Cherednik algebras, which appear in the intersection of algebraic geometry, representation theory, and mathematical physics. These objects were extensively studied in zero characteristic (essentially one of two perspectives in algebra), but in recent years, a theory of Cherednik algebras started to develop in positive characteristic. In this latter case, a big part of these algebras disappears, which causes them to lose a lot of their interesting structure. In my research, I worked on a way to recover this lost structure using divided powers and investigated what the new recovered object looks like. I proved a number of useful structural results about these extensions, and I constructed a generalization which unifies the zero characteristic perspective with the divided power version. Overall, the theory of Cherednik algebras in positive characteristic is still in its early stages, and since Cherednik algebras are so ubiquitous, my work could lead to many unforeseen results.

**Q&A**

**Where do you see yourself in 10 years? **

Working on a PhD in theoretical math, after that I’ll be figuring out what to do with a PhD in theoretical math.

**If you could have dinner with the five most interesting people in the world, living or dead, who would they be?**

Alexander Grothendieck, Evariste Galois, Ada Lovelace, Isaac Newton, Paul Erdos

“A little nonsense now and then is relished by the wisest men.” - Roald Dahl

**Media**

**In the News**

**IRVINE TEEN AWARDED $25,000 SCHOLARSHIP FOR UNMATCHED ACHIEVEMENT IN MATHEMATICS RESEARCH**

Irvine, Calif. – The Davidson Fellows Scholarship Program has announced the 2020 scholarship winners. Among the honorees is 17-year-old Lev Kruglyak of Irvine. Kruglyak won a $25,000 scholarship for his project, The Rational Cherednik Algebra of Type A_1 with Divided Powers. He is one of only 20 students across the country to be recognized as a scholarship winner.

“I feel immensely grateful to be named a Davidson Fellow and am humbled to be included in a community of such brilliant peers,” said Kruglyak.

For his project, Kruglyak studied a class of mathematical objects called rational Cherednik algebras, which appear in the intersection of algebraic geometry, representation theory, and mathematical physics. The novel approaches developed by Kruglyak will serve as a foundation for researchers to build upon in future research.

“I love math because it is the purest form of creative expression, an art form removed from the physical limitations of the real world,” said Kruglyak. “Theoretical math is as useful as literature or music — it represents humanity’s desire to take the chaotic world and transform it into something of beauty.”

Kruglyak will be attending Harvard University in the fall of 2021 to study pure math, following a gap-year internship in software engineering.