Tainara Borges is a Ph.D. student at Brown University, advised by Dr. Jill Pipher. Tainara is expected to graduate in May 2025.

In this talk, Tainara discusses new bounds for general bilinear averaging maximal operators and connections between the study of bilinear spherical averages and a geometric measure theory question with a Falconer distance problem flavor. This talk is based on her joint work with Foster, and Ou, as well as her joint work with Iosevich, and Ou.

Keywords: bilinear multipliers, spherical averages, Falconer distance problem, Sobolev smoothing estimates, maximal functions.

MSC2020: 42***, 28***.