Diophantine problems in solvable groups, Bulletin of Mathematical Sciences, Vol. 10, No. 01, 2050005 (2020), 21 pages, with Alexei Miasnikov and Denis Ovchinnikov.
Diophantine problems in rings and algebras: undecidability and reductions to rings of algebraic integers, preprint, with Alexei Miasnikov and Denis Ovchinnikov.
In these papers we study the problem of solving equations in different types of rings, algebras, and solvable groups. A connection is established between this problem and the problem of solving polynomial equations in rings of algebraic integers O. The latter, a generalization of Hilbert's 10th Problem (undecidability of integer polynomial equations), is a major open problem in number theory. Informally speaking, we prove that, for large classes of rings, algebras, and solvable groups A, solving equations in O can be reduced to solving equations in A. In some cases, we are able to prove that solving equations in A is an undecidable problem.
Here is a talk I gave on this topic.
Results of the Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC), with Renee Hlozek et al. The Astrophysical Journal Supplement Series, Volume 267, Number 2, 2023, doi
This paper describes the 10 best solutions to the Kaggle competition Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC). In this challenge, participants had to infer the type of a star given time-series data of its light emissions.
Our solution was ranked 9th out of 1089