Abstract: Gravitational instantons are defined as no n-compact non-flat complete hyperkahler 4-manifolds with L^2 curvature deca y. They have been recently classified and all arise as bubbling limit s of K3 surfaces. The Modularity Conjecture posits that any gravitati onal instantons arises as the moduli space of gauge-theoretic equatio ns. In this talk, I’ll focus on a special kind of gravitational insta nton: ALG-D_4 gravitational instantons. These can be conjecturally re alized as moduli spaces of Hitchin’s equations, a system of gauge-theoretic equations on a Riemann surface that are recognized as a central object in mathematics. In joint work https://arxiv.org/abs/2603.170 20. Click or tap if you trust this link.">2603.17020 and ongoin g work with Rafe Mazzeo, Jan Swoboda, and Hartmut Weiss, we prove the modul arity conjecture in this case.
X-ALT-DESC;FMTTYPE=text/html:Abstract: Gravitational instantons are defined as no n-compact non-flat complete hyperkahler 4-manifolds with L^2 curvature deca y. They have been recently classified and all arise as bubbling limit s of K3 surfaces. The Modularity Conjecture posits that any gravitati onal instantons arises as the moduli space of gauge-theoretic equatio ns. In this talk, I’ll focus on a special kind of gravitational insta nton: ALG-D_4 gravitational instantons. These can be conjecturally re alized as moduli spaces of Hitchin’s equations, a system of gauge-theoretic equations on a Riemann surface that are recognized as a central object in mathematics. In joint work h ttps://arxiv.org/abs/2603.17020. Click or tap if you trust this link."& gt;2603.17020 and ongoing work with Rafe Mazzeo, Jan Swoboda, and Hart mut Weiss, we prove the modularity conjecture in this case.
CONTACT:Laura Fredricson (University of Oregon) DTSTAMP:20260826T094726 DTSTART;TZID=America/New_York:20260421T110000 DTEND;TZID=America/New_York:20260421T120000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR