Mauricio Romo
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The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
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Mauricio Romo has a total of 13 co-authors. Here are the top co-authors by number of shared publications:
- Pietro Longhi
Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
6 shared publications - Jirui Guo
Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
4 shared publications - Emanuel Scheidegger
Mathematisches Institut Albert-Ludwigs-Universität Freiburg Eckerstrasse 1 D-79104 Freiburg Germany
2 shared publications - Johanna Knapp
University of Melbourne
2 shared publications - Sibasish Banerjee
Faculty of Physics, University of Warsaw, Warsaw, Poland
2 shared publications - Sibasish Banerjee
Institut des Hautes Etudes Scientifiques (IHES), Bures-sur-Yvette, France
2 shared publications
Latest Publications
- Open Access
- 3 February 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (2) , 33
Modelling A-branes with foliations
A bstract: A certain class of A -branes in mirrors of toric Calabi-Yau threefolds can be described through the framework of foliations. This allows to develop an explicit description of their moduli spaces based on a cell decomposition, with strata of various dimensions glued together in a way that is dictated by partial degenerations of the underlying special Lagrangian. Examples of A -branes associated with ‘wild’ BPS states are considered in detail. The torus fixed points in their moduli spaces provide a decomposition of m -herds spectral networks into a number |Ω| of basic connected objects, where Ω is the corresponding rank-zero Donaldson-Thomas (DT) invariant. A relation between the surgery parameters of the special Lagrangian and the baryonic semi-invariants of the representation theory of m -Kronecker quivers is also discussed, providing a local map between moduli spaces of branes related by homological mirror symmetry.
- 3 February 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (2) , 33
Open AccessModelling A-branes with foliations
A bstract: A certain class of A -branes in mirrors of toric Calabi-Yau threefolds can be described through the framework of foliations. This allows to develop an explicit description of their moduli spaces based on a cell decomposition, with strata of various dimensions glued together in a way that is dictated by partial degenerations of the underlying special Lagrangian. Examples of A -branes associated with ‘wild’ BPS states are considered in detail. The torus fixed points in their moduli spaces provide a decomposition of m -herds spectral networks into a number |Ω| of basic connected objects, where Ω is the corresponding rank-zero Donaldson-Thomas (DT) invariant. A relation between the surgery parameters of the special Lagrangian and the baryonic semi-invariants of the representation theory of m -Kronecker quivers is also discussed, providing a local map between moduli spaces of branes related by homological mirror symmetry.
- Top Cited PapersOpen Access
- 23 June 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (7) , 1-85
Exponential BPS Graphs and D-Brane Counting on Toric Calabi–Yau Threefolds: Part II
We study BPS states of 5d $$\mathcal {N}=1$$ SU(2) Yang-Mills theory on $$S^1\times \mathbb {R}^4$$ . Geometric engineering relates these to enumerative invariants for the local Hirzebruch surface $$\mathbb {F}_0$$ . We illustrate computations of Vafa-Witten invariants via exponential networks, verifying fiber-base symmetry of the spectrum at certain points in moduli space, and matching with mirror descriptions based on quivers and exceptional collections. Albeit infinite, parts of the spectrum organize in families described by simple algebraic equations. Varying the radius of the M-theory circle interpolates smoothly with the spectrum of 4d $$\mathcal {N}=2$$ Seiberg–Witten theory, recovering spectral networks in the limit.- 23 June 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (7) , 1-85
Top Cited PapersOpen AccessExponential BPS Graphs and D-Brane Counting on Toric Calabi–Yau Threefolds: Part II
We study BPS states of 5d $$\mathcal {N}=1$$ SU(2) Yang-Mills theory on $$S^1\times \mathbb {R}^4$$ . Geometric engineering relates these to enumerative invariants for the local Hirzebruch surface $$\mathbb {F}_0$$ . We illustrate computations of Vafa-Witten invariants via exponential networks, verifying fiber-base symmetry of the spectrum at certain points in moduli space, and matching with mirror descriptions based on quivers and exceptional collections. Albeit infinite, parts of the spectrum organize in families described by simple algebraic equations. Varying the radius of the M-theory circle interpolates smoothly with the spectrum of 4d $$\mathcal {N}=2$$ Seiberg–Witten theory, recovering spectral networks in the limit. - Open Access
- 1 January 2024
- Published by International Press of Boston in Beijing Journal of Pure and Applied Mathematics
- Vol. 1 (1) , 373-404
Liouville conformal blocks and Stokes phenomena
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- 1 January 2024
- Published by International Press of Boston in Beijing Journal of Pure and Applied Mathematics
- Vol. 1 (1) , 373-404
Open AccessLiouville conformal blocks and Stokes phenomena
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- Open Access
Modelling $A$-branes with foliations
A certain class of $A$-branes in mirrors of toric Calabi-Yau threefolds can be described through the framework of foliations. This allows to develop an explicit description of their moduli spaces based on a cell decomposition, with strata of various dimensions glued together in a way that is dictated by partial degenerations of the underlying special Lagrangian. Examples of $A$-branes associated with `wild' BPS states are considered in detail. The torus fixed points in their moduli spaces provide a decomposition of $m$-herds spectral networks into a number $|Ω|$ of basic connected objects, where $Ω$ is the the corresponding rank-zero Donaldson-Thomas (DT) invariant. A relation between the surgery parameters of the special Lagrangian and the baryonic semi-invariants of the representation theory of $m$-Kronecker quivers is also discussed, providing a local map between moduli spaces of branes related by homological mirror symmetry.Open AccessModelling $A$-branes with foliations
A certain class of $A$-branes in mirrors of toric Calabi-Yau threefolds can be described through the framework of foliations. This allows to develop an explicit description of their moduli spaces based on a cell decomposition, with strata of various dimensions glued together in a way that is dictated by partial degenerations of the underlying special Lagrangian. Examples of $A$-branes associated with `wild' BPS states are considered in detail. The torus fixed points in their moduli spaces provide a decomposition of $m$-herds spectral networks into a number $|Ω|$ of basic connected objects, where $Ω$ is the the corresponding rank-zero Donaldson-Thomas (DT) invariant. A relation between the surgery parameters of the special Lagrangian and the baryonic semi-invariants of the representation theory of $m$-Kronecker quivers is also discussed, providing a local map between moduli spaces of branes related by homological mirror symmetry. - Open Access
Non-commutative resolutions as mirrors of singular Calabi--Yau varieties
It has been conjectured that the hemisphere partition function arXiv:1308.2217, arXiv:1308.2438 in a gauged linear sigma model (GLSM) computes the central charge arXiv:math/0212237 of an object in the bounded derived category of coherent sheaves for Calabi--Yau (CY) manifolds. There is also evidence in arXiv:alg-geom/ 9511001, arXiv:hep-th/0007071. On the other hand, non-commutative resolutions of singular CY varieties have been studied in the context of abelian GLSMs arXiv:0709.3855. In this paper, we study an analogous construction of abelian GLSMs for non-commutative resolutions and propose they can be used to study a class of recently discovered mirror pairs of singular CY varieties. Our main result shows that the hemisphere partition functions (a.k.a.~$A$-periods) in the new GLSM are in fact period integrals (a.k.a.~$B$-periods) of the singular CY varieties. We conjecture that the two are completely equivalent: $B$-periods are the same as $A$-periods. We give some examples to support this conjecture and formulate some expected homological mirror symmetry (HMS) relation between the GLSM theory and the CY. As shown in arXiv:2003.07148, the $B$-periods in this case are precisely given by a certain fractional version of the $B$-series of arXiv:alg-geom/9511001. Since a hemisphere partition function is defined as a contour integral in a cone in the complexified secondary fan (or FI-theta parameter space) arXiv:1308.2438, it can be reduced to a sum of residues (by theorems of Passare-Tsikh-Zhdanov and Tsikh-Zhdanov). Our conjecture shows that this residue sum may now be amenable to computations in terms of the $B$-series.
Open AccessNon-commutative resolutions as mirrors of singular Calabi--Yau varieties
It has been conjectured that the hemisphere partition function arXiv:1308.2217, arXiv:1308.2438 in a gauged linear sigma model (GLSM) computes the central charge arXiv:math/0212237 of an object in the bounded derived category of coherent sheaves for Calabi--Yau (CY) manifolds. There is also evidence in arXiv:alg-geom/ 9511001, arXiv:hep-th/0007071. On the other hand, non-commutative resolutions of singular CY varieties have been studied in the context of abelian GLSMs arXiv:0709.3855. In this paper, we study an analogous construction of abelian GLSMs for non-commutative resolutions and propose they can be used to study a class of recently discovered mirror pairs of singular CY varieties. Our main result shows that the hemisphere partition functions (a.k.a.~$A$-periods) in the new GLSM are in fact period integrals (a.k.a.~$B$-periods) of the singular CY varieties. We conjecture that the two are completely equivalent: $B$-periods are the same as $A$-periods. We give some examples to support this conjecture and formulate some expected homological mirror symmetry (HMS) relation between the GLSM theory and the CY. As shown in arXiv:2003.07148, the $B$-periods in this case are precisely given by a certain fractional version of the $B$-series of arXiv:alg-geom/9511001. Since a hemisphere partition function is defined as a contour integral in a cone in the complexified secondary fan (or FI-theta parameter space) arXiv:1308.2438, it can be reduced to a sum of residues (by theorems of Passare-Tsikh-Zhdanov and Tsikh-Zhdanov). Our conjecture shows that this residue sum may now be amenable to computations in terms of the $B$-series.
- 17 November 2022
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 112 (6) , 1-57
Hybrid models for homological projective duals and noncommutative resolutions
- 17 November 2022
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 112 (6) , 1-57
Hybrid models for homological projective duals and noncommutative resolutions
- 5 November 2022
- Published by Springer Nature in Annales Henri Poincare
- Vol. 24 (4) , 1077-1136
A-branes, Foliations and Localization
- 5 November 2022
- Published by Springer Nature in Annales Henri Poincare
- Vol. 24 (4) , 1077-1136
A-branes, Foliations and Localization
- Open Access
Hybrid models for homological projective duals and noncommutative resolutions
We study hybrid models arising as homological projective duals (HPD) of certain projective embeddings $f:X\rightarrow\mathbb{P}(V)$ of Fano manifolds $X$. More precisely, the category of B-branes of such hybrid models corresponds to the HPD category of the embedding $f$. B-branes on these hybrid models can be seen as global matrix factorizations over some compact space $B$ or, equivalently, as the derived category of the sheaf of $\mathcal{A}$-modules on $B$, where $\mathcal{A}$ is an $A_{\infty}$ algebra. This latter interpretation corresponds to a noncommutative resolution of $B$. We compute explicitly the algebra $\mathcal{A}$ by several methods, for some specific class of hybrid models, and find that in general it takes the form of a smash product of an $A_{\infty}$ algebra with a cyclic group. Then we apply our results to the HPD of $f$ corresponding to a Veronese embedding of projective space and the projective embedding of Fano complete intersections in $\mathbb{P}^{n}$.Open AccessHybrid models for homological projective duals and noncommutative resolutions
We study hybrid models arising as homological projective duals (HPD) of certain projective embeddings $f:X\rightarrow\mathbb{P}(V)$ of Fano manifolds $X$. More precisely, the category of B-branes of such hybrid models corresponds to the HPD category of the embedding $f$. B-branes on these hybrid models can be seen as global matrix factorizations over some compact space $B$ or, equivalently, as the derived category of the sheaf of $\mathcal{A}$-modules on $B$, where $\mathcal{A}$ is an $A_{\infty}$ algebra. This latter interpretation corresponds to a noncommutative resolution of $B$. We compute explicitly the algebra $\mathcal{A}$ by several methods, for some specific class of hybrid models, and find that in general it takes the form of a smash product of an $A_{\infty}$ algebra with a cyclic group. Then we apply our results to the HPD of $f$ corresponding to a Veronese embedding of projective space and the projective embedding of Fano complete intersections in $\mathbb{P}^{n}$. - 8 May 2022
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 394 (1) , 355-407
A GLSM View on Homological Projective Duality
- 8 May 2022
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 394 (1) , 355-407
A GLSM View on Homological Projective Duality
- Open Access
A GLSM view on Homological Projective Duality
Given a gauged linear sigma model (GLSM) $\mathcal{T}_{X}$ realizing a projective variety $X$ in one of its phases, i.e. its quantum K\"ahler moduli has a maximally unipotent point, we propose an \emph{extended} GLSM $\mathcal{T}_{\mathcal{X}}$ realizing the homological projective dual category $\mathcal{C}$ to $D^{b}Coh(X)$ as the category of B-branes of the Higgs branch of one of its phases. In most of the cases, the models $\mathcal{T}_{X}$ and $\mathcal{T}_{\mathcal{X}}$ are anomalous and the analysis of their Coulomb and mixed Coulomb-Higgs branches gives information on the semiorthogonal/Lefschetz decompositions of $\mathcal{C}$ and $D^{b}Coh(X)$. We also study the models $\mathcal{T}_{X_{L}}$ and $\mathcal{T}_{\mathcal{X}_{L}}$ that correspond to homological projective duality of linear sections $X_{L}$ of $X$. This explains why, in many cases, two phases of a GLSM are related by homological projective duality. We study mostly abelian examples: linear and Veronese embeddings of $\mathbb{P}^{n}$ and Fano complete intersections in $\mathbb{P}^{n}$. In such cases, we are able to reproduce known results as well as produce some new conjectures. In addition, we comment on the construction of the HPD to a nonabelian GLSM for the Pl\"ucker embedding of the Grassmannian $G(k,N)$.Open AccessA GLSM view on Homological Projective Duality
Given a gauged linear sigma model (GLSM) $\mathcal{T}_{X}$ realizing a projective variety $X$ in one of its phases, i.e. its quantum K\"ahler moduli has a maximally unipotent point, we propose an \emph{extended} GLSM $\mathcal{T}_{\mathcal{X}}$ realizing the homological projective dual category $\mathcal{C}$ to $D^{b}Coh(X)$ as the category of B-branes of the Higgs branch of one of its phases. In most of the cases, the models $\mathcal{T}_{X}$ and $\mathcal{T}_{\mathcal{X}}$ are anomalous and the analysis of their Coulomb and mixed Coulomb-Higgs branches gives information on the semiorthogonal/Lefschetz decompositions of $\mathcal{C}$ and $D^{b}Coh(X)$. We also study the models $\mathcal{T}_{X_{L}}$ and $\mathcal{T}_{\mathcal{X}_{L}}$ that correspond to homological projective duality of linear sections $X_{L}$ of $X$. This explains why, in many cases, two phases of a GLSM are related by homological projective duality. We study mostly abelian examples: linear and Veronese embeddings of $\mathbb{P}^{n}$ and Fano complete intersections in $\mathbb{P}^{n}$. In such cases, we are able to reproduce known results as well as produce some new conjectures. In addition, we comment on the construction of the HPD to a nonabelian GLSM for the Pl\"ucker embedding of the Grassmannian $G(k,N)$.