2,822 research outputs found
Lagrangian Topology and Enumerative Geometry
We use the "pearl" machinery in our previous work to study certain
enumerative invariants associated to monotone Lagrangian submanifolds.Comment: 86 page
Enumerative geometry of dormant opers
The purpose of the present paper is to develop the enumerative geometry of
dormant -opers for a semisimple algebraic group . In the present paper,
we construct a compact moduli stack admitting a perfect obstruction theory by
introducing the notion of a dormant faithful twisted -oper (or a
"-do'per" for short. Moreover, a semisimple d TQFT (= -dimensional
topological quantum field theory) counting the number of -do'pers is
obtained by means of the resulting virtual fundamental class. This d TQFT
gives an analogue of the Witten-Kontsevich theorem describing the intersection
numbers of psi classes on the moduli stack of -do'pers.Comment: 64 pages, the title is changed, some mistakes are correcte
BPS Spectra, Barcodes and Walls
BPS spectra give important insights into the non-perturbative regimes of
supersymmetric theories. Often from the study of BPS states one can infer
properties of the geometrical or algebraic structures underlying such theories.
In this paper we approach this problem from the perspective of persistent
homology. Persistent homology is at the base of topological data analysis,
which aims at extracting topological features out of a set of points. We use
these techniques to investigate the topological properties which characterize
the spectra of several supersymmetric models in field and string theory. We
discuss how such features change upon crossing walls of marginal stability in a
few examples. Then we look at the topological properties of the distributions
of BPS invariants in string compactifications on compact threefolds, used to
engineer black hole microstates. Finally we discuss the interplay between
persistent homology and modularity by considering certain number theoretical
functions used to count dyons in string compactifications and by studying
equivariant elliptic genera in the context of the Mathieu moonshine
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