We relate the Algebra of the Infrared of Gaiotto-Moore-Witten with the theory of perverse schobers which are (conjectural, in general) categorical analogs of perverse sheaves. A perverse schober on a complex plane C can be seen as an algebraic structure that can encode various categories of D-branes of a 2-dimensional supersymmetric field theory, as well as the interaction (tunnelling) between such categories. We show that many constructions of the Algebra of the Infrared can be developed once we have a schober on C. These constructions can be seen as giving various features of the analog, for schobers, of the geometric Fourier transform well known for D-modules and perverse sheaves.
We consider the systems of diffusion-orthogonal polynomials, defined in the work [1] of D. Bakry, S. Orevkov and M. Zani and (particularly) explain why these systems with boundary of maximal possible degree should always come from the group, generated by reflections. Our proof works for the dimensions 2 (on which this phenomena was discovered) and 3, and fails in the dimensions 4 and higher, leaving the possibility of existence of diffusion-orthogonal systems related to the Einstein metrics.The methods of our proof are algebraic / complex analytic in nature and based mainly on the consideration of the double covering of C d , branched in the boundary divisor.Author wants to thank Stepan Orevkov, Misha Verbitsky and Dmitry Korb for useful discussions.
We propose the new construction of complex surfaces with h 1,0 = h 2,0 = 0 from smoothings of normal crossing surfaces with noncollapsible dual complexes and carry it out for the simplest case of the duncehat complex, obtaining the surface with h 1,1 = 9 (presumably Barlow surface).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.