In this talk, I will discuss my work in birational geometry with Professor Lena Ji (no relations) at the 2022 UMich Mathematics REU. The other goal is to share some perspectives about what it was like to do mathematical research for the first time.
 
A conic bundle is a morphism of smooth varieties \pi: X -> S such that every fiber is a conic and the generic fiber is smooth. In this talk, we will examine the real rationality of a particular family of conic bundles (previously studied by Frei, (Lena) Ji, Sankar, Viray, and Vogt) over RP^2 that are smooth away from a smooth quartic discriminant curve. A classic theorem of Zeuthen classifies the real locus of smooth quartic curves into 6 isotopy types. We use this topological result, together with the Magma and Sage computer algebra systems, to construct rational and irrational examples of conic bundles. Motivated by these examples, we also characterize the rationality using the vacuity and topology of the real locus and the intermediate Jacobian torsor obstruction of Hassett-Tschinkel and Benoist-Wittenberg for 4 out the 6 real isotopy types.