Alexander Torres-Gomez

Hello, I am a mathematical physicist specializing in differential and algebraic geometry. I currently work as an Associate Professor at the Institute of Mathematics at the University of Antioquia in Medellín, Colombia.

My current research primarily centers around the following topics:
- Coherent sheaves on locally super-ringed spaces (super-geometry);- F-manifolds and Frobenius manifolds;- Topological string theory on singular toric Calabi-Yau varieties, quantum cohomology and quantum D-modules;- Deformation theory from differential graded Lie algebra point of view;- Topological quantum field theories.
More broadly, I am interested in areas of algebraic and differential geometry inspired by the geometrical and algebraic structures that arise in theoretical physics, especially gauge theory and string theory.

Publications

C∞-Superrings and C∞-Superschemes. C. D. Olarte, P. Rizzo and A. Torres-Gomez.

arXiv:2508.09900 [math.AG].

Valuations on Superrings. P. Rizzo, J. Torres del Valle and A. Torres-Gomez.

arXiv:2505.09842 [math.RA].

Double extension of flat pseudo-Riemannian F-Lie algebras. A. Torres-Gomez and F. Valencia

Journal of Algebra, Volume 666, 2025, Pages 1-27, https://doi.org/10.1016/j.jalgebra.2024.11.021 ; arXiv:2405.02130v2 [math.DG]

A Note on Unique Factorization in Superrings. P. Rizzo, J. Torres del Valle and A. Torres-Gomez.

Communications in Algebra, Pages 1-14, https://doi.org/10.1080/00927872.2025.2526107 ; arXiv:2402.07096 [math.RA].

Dedekind Superrings and Related Concepts. P. Rizzo, J. Torres del Valle and A. Torres-Gomez.

arXiv:2310.03822 [math.RA, math.QA, math.AG].

F-algebra–Rinehart Pairs and Super F-algebroids. J.A. Cruz Morales, J. Gutierrez and A. Torres-Gomez.

Sao Paulo J. Math. Sci. (2022), https://doi.org/10.1007/s40863-021-00277-6; arXiv:1904.04724 [math.DG, math.QA, math.AG].

On F-Algebroids and Dubrovin’s Duality. J.A. Cruz Morales and A. Torres-Gomez.

Archivum Mathematicum Volume 55 (2019), No. 2, pp. 109-122, https://www.emis.de/journals/AM/19-2/am3041.html; arXiv:1805.08086 [math.DG].

Topological String Partition Function on Generalised Conifolds. E. Gasparim, B. Suzuki, A. Torres-Gomez and C.A.B. Varea.

J. Math. Phys. 58, 042303 (2017), https://aip.scitation.org/doi/10.1063/1.4980013; arXiv:1603.06168 [hep-th, math.AG]

Differential Poisson Sigma Models with Extended Supersymmetry. C. Arias, P. Sundell and A. Torres-Gomez.

arXiv:1607.00727 [hep-th].

Action principles for higher and fractional spin gravities. C. Arias, R. Bonezzi, N. Boulanger, E. Sezgin, P. Sundell, A. Torres-Gomez and M. Valenzuela.

Chapter in the book: “Higher Spin Gauge Theories”, World Scientific Publishing, 2017, https://www.worldscientific.com/doi/10.1142/9789813144101_0012; arXiv:1603.04454 [hep-th].

2D Poisson Sigma Models with Gauged Vectorial Supersymmetry. R. Bonezzi, P. Sundell and A. Torres-Gomez.

JHEP 1508, 047 (2015), https://link.springer.com/article/10.1007/JHEP08(2015)047; arXiv:1505.04959 [hep-th].

2D sigma models and differential Poisson algebras. C. Arias, N. Boulanger, P. Sundell and A. Torres-Gomez.

JHEP 1508, 095 (2015), https://link.springer.com/article/10.1007/JHEP08(2015)095; arXiv:1503.05625 [hep-th].

Fermions via spinor-valued one-forms. A. Torres-Gomez and K. Krasnov.

Int. J. Mod. Phys. A 28, no. 24, 1350113 (2013), https://www.worldscientific.com/doi/abs/10.1142/S0217751X13501133, arXiv:1212.3452 [hep-th].

A Unified Theory of Non-Linear Electrodynamics and Gravity. A. Torres-Gomez, K. Krasnov and C. Scarinci.

Phys. Rev. D 83, 025023 (2011), https://journals.aps.org/prd/abstract/10.1103/PhysRevD.83.025023; arXiv:1011.3641 [gr-qc].

Gravity-Yang-Mills-Higgs unification by enlarging the gauge group. A. Torres-Gomez and K. Krasnov.

Phys. Rev. D 81, 085003 (2010), https://journals.aps.org/prd/abstract/10.1103/PhysRevD.81.085003; arXiv:0911.3793 [hep-th].

Remarks on Barbero-Immirzi parameter as a field. A. Torres-Gomez and K. Krasnov.

Phys. Rev. D 79, 104014 (2009), https://journals.aps.org/prd/abstract/10.1103/PhysRevD.79.104014; arXiv:0811.1998 [gr-qc].

On the embedding of space-time in five-dimensional Weyl spaces. F. Dahia, G.A.T. Gomez and C. Romero.

J. Math. Phys. 49, 102501 (2008), https://aip.scitation.org/doi/10.1063/1.3000049; arXiv:0711.2754 [gr-qc].

Get in touch at: galexander.torres@udea.edu.co

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