USC Topology Seminar: Lattice homology and q-series invariants of 3-manifolds

Event details Date: Monday, September 21, 2026 Time: 2:00 PM to 3:00 PM Location: Kaprielian Hall (KAP) - 265 - 3620 South Vermont Avenue, Los Angeles, CA 90089 Type: Lecture / Talk / Workshop Campus: University Park Campus Department: Mathematics About this event Ross Akhmechet, USC Title: Lattice homology and q-series invariants of 3-manifolds Abstract: I will discuss an invariant of negative definite plumbed 3-manifolds that unifies and extends two theories with quite different origins. The first is lattice (co)homology, due to Némethi, whose degree zero part is encoded by a certain graph and is isomorphic to Heegaard Floer homology for a large subclass of such 3-manifolds. The second theory is the Z-hat q-series of Gukov-Pei-Putrov-Vafa, a power series which recovers Witten-Reshetikhin-Turaev quantum invariants at roots of unity. I will explain lattice homology, Z-hat, and our unification of them in joint work with Peter Johnson and Slava Krushkal. I will also discuss work with Peter Johnson and Sunghyuk Park on extending the construction to knot complements and a surgery formula relating the two. Time permitting, I will mention ongoing work with Krushkal. Official event details: https://calendar.usc.edu/event/usc-topology-seminar-lattice-homology-and-q-series-invariants-of-3-manifolds