**Group Members:** Tyler Campos, Andrew Gannon, Benjamin Hanzsek-Brill, Connor Marrs, Alexander Neuschotz, Trent Rabe and Ethan Winters.

**Mentors:** Rachel Bailey, Fabrice Baudoin, Masha Gordina

**Overview:** We study and simulate on computers the fractional Gaussian fields and their discretizations on surfaces like the two-dimensional sphere or two-dimensional torus. The study of the maxima of those processes will be done and conjectures formulated concerning limit laws. Particular attention will be paid to log-correlated fields (the so-called Gaussian free field).

#### “Computing Extreme Values of Continuous & Discrete Fractional Gaussian Fields on Manifolds” by Tyler Campos (Yale & UConn REU 2022) and Connor Marrs (Bowdoin & UConn REU 2022)

“Paths of the Fractional Gaussian Field on S1 and the Torus” by Andrew Gannon (University of Connecticut)