Title: An algebraic approach for recovering an unknown timing solution from a list of TOAs
Fast radio burst (FRB) progenitors are expected to be neutron stars. Solving the astrophysical conundrum of their origin is one of the central challenges in astrophysics. If a periodic solution for their arrival time is discovered, we will immediately learn of their age, magnetic field, and binary properties. Finding such a periodicity is a hard algorithmic question, especially if FRB progenitors are predominantly in binary systems. Interestingly, the same problem arises in gamma-ray pulsar astronomy, where solving a timing model for thousands of Fermi-LAT unassociated sources could identify them as pulsars, reveal their exact position and nature. The timing problem is currently unsolvable in the case of a binary system, and even for single pulsars it is solvable only under restrictive conditions using substantial computational resources. In this talk, I will show a novel algebraic framework for solving the timing problem using lattice reduction techniques. As a proof of concept, I present the solution of a previously intractable problem with a runtime of a few seconds. Then, I will discuss the limitations of the proposed approach and the path towards applying these methods to real data. Time permitting, I will discuss a possible path towards implementing similar methods to recover pulsars using CHIME.