Jeff Viaclovsky




Tuesday, April 6, 2021 - 4:00pm to 5:00pm




There are many interesting examples of complete non-compact Ricci-flat metrics in dimension 4, which are referred to as ALE, ALF, ALG, ALH gravitational instantons. In this talk, I will describe some examples of these geometries, and other types called ALG^* and ALH^*. All of the above types of gravitational instantons arise as bubbles for sequences of Ricci-flat metrics on K3 surfaces, and are therefore important for understanding the behavior of Calabi-Yau metrics near the boundary of the moduli space.  I will describe some general aspects of this type of degeneration, and some recent work on degenerations of Ricci-flat metrics on elliptic K3 surfaces in which case ALG and ALG^* bubbles can arise. This is based on joint work with Hein-Song-Zhang (to appear in JAMS) and with Chen-Zhang (to appear in CAG).