Pierrick Bousseau

activity

20172026

most citedTropical refined curve counting from higher genera and lambda classes

42 citations · 212 across the 25 of their papers we have counts for

collaborators

27 papers

math.AG2026

Log Calabi-Yau compactifications of $S L (2, C)$ character varieties

Hülya Argüz, Pierrick Bousseau

We prove that the $S L (2, C)$ character varieties of compact oriented surfaces and the generic relative $S L (2, C)$ character varieties of punctured surfaces admit di…

math.AG2026

Geometric helices on del Pezzo surfaces from tilting

Pierrick Bousseau

We prove that all geometric helices in the derived category of coherent sheaves on a del Pezzo surface are related by a sequence of elementary operations: rotation, shifting, ortho…

math.AG2025

BPS polynomials and Welschinger invariants

Hülya Argüz, Pierrick Bousseau

We generalize Block-Göttsche polynomials, originally defined for toric del Pezzo surfaces, to arbitrary surfaces. To do this, we show that these polynomials arise as special cases…

hep-th2024

Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs

Valery Alexeev, Hülya Argüz, Pierrick Bousseau

We study webs of 5-branes with 7-branes in Type IIB string theory from a geometric perspective. Mathematically, a web of 5-branes with 7-branes is a tropical curve in $\mathbb{R}^2…

math.AG2024

The KSBA moduli space of stable log Calabi-Yau surfaces

Valery Alexeev, Hülya Argüz, Pierrick Bousseau

We prove that every irreducible component of the coarse Kollár-Shepherd-Barron and Alexeev (KSBA) moduli space of stable log Calabi--Yau surfaces admits a finite cover by a project…

math.AG2023★ 3 cited

Quivers and curves in higher dimension

Hülya Argüz, Pierrick Bousseau

We prove a correspondence between Donaldson-Thomas invariants of quivers with potential having trivial attractor invariants and genus zero punctured Gromov-Witten invariants of hol…

math.AG2023

All-genus WDVV recursion, quivers, and BPS invariants

Pierrick Bousseau, Longting Wu

Let $X$ be a smooth projective surface and $D$ a smooth rational ample divisor in $X$ . We prove an all-genus generalization of the genus $0$ WDVV equation for primary Gromov--Witte…

math.AG2023

Quivers, Flow Trees, and Log Curves

Hülya Argüz, Pierrick Bousseau

Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula ar…

math.SG2022★ 2 cited

Holomorphic Floer theory and Donaldson-Thomas invariants

Pierrick Bousseau

We present several expected properties of the holomorphic Floer theory of a holomorphic symplectic manifold. In particular, we propose a conjecture relating holomorphic Floer theor…

hep-th2022★ 8 cited

BPS Dendroscopy on Local $P^{2}$

Pierrick Bousseau, Pierre Descombes, Bruno Le Floch +1

The spectrum of BPS states in type IIA string theory compactified on a Calabi-Yau threefold famously jumps across codimension-one walls in complexified Kähler moduli space, leading…

math.AG2022★ 4 cited

Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors

Hülya Argüz, Pierrick Bousseau

Cluster varieties come in pairs: for any $X$ cluster variety there is an associated Fock-Goncharov dual $A$ cluster variety. On the other hand, in the context o…

math.AG2021

Gromov-Witten Theory of Complete Intersections via Nodal Invariants

Hülya Argüz, Pierrick Bousseau, Rahul Pandharipande +1

We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove…

math.RT2021

The flow tree formula for Donaldson-Thomas invariants of quivers with potentials

Hülya Argüz, Pierrick Bousseau

We prove the flow tree formula conjectured by Alexandrov and Pioline which computes Donaldson-Thomas invariants of quivers with potentials in terms of a smaller set of attractor in…

math.AG2020★ 6 cited

Stable maps to Looijenga pairs: orbifold examples

Pierrick Bousseau, Andrea Brini, Michel van Garrel

In arXiv:2011.08830 we established a series of correspondences relating five enumerative theories of log Calabi-Yau surfaces, i.e. pairs $(Y, D)$ with $Y$ a smooth projective comple…

math.AG2020★ 19 cited

Stable maps to Looijenga pairs

Pierrick Bousseau, Andrea Brini, Michel van Garrel

A log Calabi-Yau surface with maximal boundary, or Looijenga pair, is a pair $(Y, D)$ with $Y$ a smooth rational projective complex surface and $D = D_{1} + \dots + D_{l} \in ∣ - K_{Y} ∣$ an ant…

math.GT2020★ 12 cited

Strong positivity for the skein algebras of the $4$ -punctured sphere and of the $1$ -punctured torus

Pierrick Bousseau

The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the $S L_{2}$ character variety of a topological surface. We realize the skein algebra of t…

math.AG2020★ 2 cited

Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants

Hülya Argüz, Pierrick Bousseau

We give a tropical description of the counting of real log curves in toric degenerations of toric varieties. We treat the case of genus zero curves and all non-superabundant higher…

math.AG2020

Scattering diagrams, sheaves, and curves

Pierrick Bousseau

We review the recent proof of the N.Takahashi's conjecture on genus $0$ Gromov-Witten invariants of $(P^{2}, E)$ , where $E$ is a smooth cubic curve in the complex projective…

math.AG2020★ 19 cited

Holomorphic anomaly equation for $(P^{2}, E)$ and the Nekrasov-Shatashvili limit of local $P^{2}$

Pierrick Bousseau, Honglu Fan, Shuai Guo +1

We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X, D)$ a pair with $X$ a smooth projective variety and $D$ a nef sm…

math.AG2019★ 10 cited

A proof of N.Takahashi's conjecture for $(P^{2}, E)$ and a refined sheaves/Gromov-Witten correspondence

Pierrick Bousseau

We prove N.Takahashi's conjecture determining the contribution of each contact point in genus- $0$ maximal contact Gromov-Witten theory of $P^{2}$ relative to a smooth cubic…

math.AG2019★ 15 cited

Scattering diagrams, stability conditions, and coherent sheaves on $P^{2}$

Pierrick Bousseau

We show that a purely algebraic structure, a two-dimensional scattering diagram, describes a large part of the wall-crossing behavior of moduli spaces of Bridgeland semistable obje…

math.AG2019★ 13 cited

On the log-local principle for the toric boundary

Pierrick Bousseau, Andrea Brini, Michel van Garrel

Let $X$ be a smooth projective complex variety and let $D = D_{1} + \dots + D_{l}$ be a reduced normal crossing divisor on $X$ with each component $D_{j}$ smooth, irreducible, and nef. The lo…

math.AG2019★ 8 cited

Refined floor diagrams from higher genera and lambda classes

Pierrick Bousseau

We show that, after the change of variables $q = e^{i u}$ , refined floor diagrams for $P^{2}$ and Hirzebruch surfaces compute generating series of higher genus relative Gromov-…

math.AG2018★ 1 cited

On an example of quiver DT/relative GW correspondence

Pierrick Bousseau

We explain and generalize a recent result of Reineke-Weist by showing how to reduce it to the Gromov-Witten/Kronecker correspondence by a degeneration and blow-up. We also refine t…

Log Calabi-Yau compactifications of SL(2,C) character varieties

Geometric helices on del Pezzo surfaces from tilting

BPS polynomials and Welschinger invariants

Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs

The KSBA moduli space of stable log Calabi-Yau surfaces

Quivers and curves in higher dimension

All-genus WDVV recursion, quivers, and BPS invariants

Quivers, Flow Trees, and Log Curves

Holomorphic Floer theory and Donaldson-Thomas invariants

BPS Dendroscopy on Local P2

Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors

Gromov-Witten Theory of Complete Intersections via Nodal Invariants

The flow tree formula for Donaldson-Thomas invariants of quivers with potentials

Stable maps to Looijenga pairs: orbifold examples

Stable maps to Looijenga pairs

Strong positivity for the skein algebras of the 4-punctured sphere and of the 1-punctured torus

Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants

Scattering diagrams, sheaves, and curves

Holomorphic anomaly equation for (P2,E) and the Nekrasov-Shatashvili limit of local P2

A proof of N.Takahashi's conjecture for (P2,E) and a refined sheaves/Gromov-Witten correspondence

Scattering diagrams, stability conditions, and coherent sheaves on P2

On the log-local principle for the toric boundary

Refined floor diagrams from higher genera and lambda classes

On an example of quiver DT/relative GW correspondence

Log Calabi-Yau compactifications of $S L (2, C)$ character varieties

BPS Dendroscopy on Local $P^{2}$

Strong positivity for the skein algebras of the $4$ -punctured sphere and of the $1$ -punctured torus

Holomorphic anomaly equation for $(P^{2}, E)$ and the Nekrasov-Shatashvili limit of local $P^{2}$

A proof of N.Takahashi's conjecture for $(P^{2}, E)$ and a refined sheaves/Gromov-Witten correspondence

Scattering diagrams, stability conditions, and coherent sheaves on $P^{2}$