January 12, 2022
TITLE: Some progress in unification of enumerative and differential geometry and quantization(s)
In the first part of the talk I will review the recent progress in our attempts to approach the hyperkahler geometry of the 3d Coulomb branches through the localization computations in 4d gauge theories (based on the joint work with S.Jeong and N.Lee). In the second part I will talk on the global magnificence, i.e. an attempt to build an 8+1 dimensional gauge theory unifying K-theoretic Donaldson-Thomas theories of threefolds, a cohomological eleven dimensional supergravity and maybe more (based on the joint work with N.Piazzalunga). In the third part I will make some observations on the action of compact support cohomology on cohomology and its implications for 5d susy gauge theories realized by M-theory on toric Calabi-Yau threefolds (based on the joint work with N.Piazzalunga and M.Zabzine), and connections to my old formulas (proven in some cases by L.Gottsche, H.Nakajima and K.Yoshioka, and by E.Gasparim) for partition functions of 4d theory on toric surfaces (based on the joint work with M.del Zotto, N.Piazzalunga, and M.Zabzine).