210 citations · 311 across the 18 of their papers we have counts for
22 papers
Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence
Vestislav Apostolov, Brent Pym, Jeffrey Streets
We introduce a notion of K-polystability for compact Kähler holomorphic Poisson manifolds. On the one hand, this notion of stability is well-adapted to constructions of moduli spac…
Bondal's conjecture in dimension five
Stéphane Druel, Jorge Vitório Pereira, Brent Pym +1
Bondal's conjecture in Poisson geometry gives lower bounds on the degeneracy loci of Poisson Fano manifolds, where the rank of the Poisson structure drops. By work of several autho…
Weighted blowups and 3d Poisson desingularizations
Simon Lapointe, Mykola Matviichuk, Brent Pym +1
We establish existence of functorial orbifold reductions of singularities for Poisson subvarieties in smooth Poisson threefolds. Namely, we show that with enough weighted blowups,…
Creating quantum projective spaces by deforming q-symmetric algebras
Mykola Matviichuk, Brent Pym, Travis Schedler
We construct a large collection of "quantum projective spaces", in the form of Koszul, Calabi-Yau algebras with the Hilbert series of a polynomial ring. We do so by starting with t…
Numerically flat foliations and holomorphic Poisson geometry
Stéphane Druel, Jorge Vitório Pereira, Brent Pym +1
We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact Kähler manifolds. Extending earlier results on non-uniruled projectiv…
Semiclassical Hodge theory for log Poisson manifolds
Aidan Lindberg, Brent Pym
We construct a mixed Hodge structure on the topological K-theory of smooth Poisson varieties, depending weakly on a choice of compactification. We establish a package of tools for…
Logarithmic morphisms, tangential basepoints, and little disks
Clément Dupont, Erik Panzer, Brent Pym
We develop the theory of "virtual morphisms" in logarithmic algebraic geometry, introduced by Howell. It allows one to give algebro-geometric meaning to various useful maps of topo…
Regularized integrals and manifolds with log corners
Clément Dupont, Erik Panzer, Brent Pym
We introduce a natural geometric framework for the study of logarithmically divergent integrals on manifolds with corners and algebraic varieties, using the techniques of logarithm…
Holonomic Poisson geometry of Hilbert schemes
Mykola Matviichuk, Brent Pym, Travis Schedler
We undertake a detailed study of the geometry of Bottacin's Poisson structures on Hilbert schemes of points in Poisson surfaces, i.e. smooth complex surfaces equipped with an effec…
Resurgence of a de Sitter Glauber-Sudarshan State: Nodal Diagrams and Borel Resummation
Suddhasattwa Brahma, Keshav Dasgupta, Mir-Mehedi Faruk +4
We show that an explicit construction of a four-dimensional de Sitter space may be performed using a diagrammatic approach via nodal diagrams emanating from the path integral repre…
A global Weinstein splitting theorem for holomorphic Poisson manifolds
Stéphane Druel, Jorge Vitório Pereira, Brent Pym +1
We prove that if a compact Kähler Poisson manifold has a symplectic leaf with finite fundamental group, then after passing to a finite étale cover, it decomposes as the product of…
A local Torelli theorem for log symplectic manifolds
Mykola Matviichuk, Brent Pym, Travis Schedler
We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. I…
Multiple zeta values in deformation quantization
Peter Banks, Erik Panzer, Brent Pym
Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a sy…
Holonomic Poisson manifolds and deformations of elliptic algebras
Brent Pym, Travis Schedler
We introduce a natural nondegeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manif…
Constructions and classifications of projective Poisson varieties
Brent Pym
This paper is intended both an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifo…
Shifted symplectic Lie algebroids
Brent Pym, Pavel Safronov
Shifted symplectic Lie and algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical…
Motivic Donaldson--Thomas invariants of some quantized threefolds
Alberto Cazzaniga, Andrew Morrison, Brent Pym +1
This paper is motivated by the question of how motivic Donaldson--Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi-…
Elliptic singularities on log symplectic manifolds and Feigin--Odesskii Poisson brackets
Brent Pym
A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface a…
Quantum deformations of projective three-space
Brent Pym
We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi--Yau algebras that serve as their homogeneous coordinate rings. We p…
The Stokes Groupoids
Marco Gualtieri, Songhao Li, Brent Pym
We construct and describe a family of groupoids over complex curves which serve as the universal domains of definition for solutions to linear ordinary differential equations with…
Poisson modules and degeneracy loci
Marco Gualtieri, Brent Pym
In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of "residue" for a Poisson module, anal…
Dynamical Blueprints for Galaxies
Lawrence M. Widrow, Brent Pym, John Dubinski
We present an axisymmetric, equilibrium model for late-type galaxies which consists of an exponential disk, a Sersic bulge, and a cuspy dark halo. The model is specified by a phase…