**Institution**: Universidad AutÃ³noma de Madrid

**Position**: Profesor Ayudante Doctor (Assistant Professor)

**Office**: 316 **Phone**:+34 912999 776

**E-mail**: mario.garcia()icmat.es

#### Biographical Review

I am an Assistant Professor (Profesor Ayudante Doctor) at the Universidad AutÃ³noma de Madrid, from September 2017. Previously, I was a Marie Sklodowska-Curie Individual Fellow at the Instituto de Ciencias MatemÃ¡ticas (ICMAT) in Madrid (2015-2017), and had postdoctoral appointments at the Nigel Hitchin Laboratory of ICMAT (2014-2015), the Ã‰cole Polytechnique Federal de Lausanne (2013-2014), and the Centre for Quantum Geometry of Moduli Spaces (Aarhus, 2010-2012). I have also held visiting positions at the Max Planck Institute for Mathematics (Bonn), at the Humboldt University (Berlin), and at the Hausdorff Research Institute for Mathematics (Bonn). I obtained my PhD in 2009 at the Universidad AutÃ³noma de Madrid.

#### Research Interests

My research is in the areas of differential geometry and algebraic geometry, and has strong links with geometric analysis and mathematical physics. The main projects I have carried out include special metrics and connections in KÃ¤hler geometry (constant scalar curvature KÃ¤hler, Hermite-Yang-Mills, vortices, Hitchin equations) and their relation to stability conditions in algebraic geometry (GIT), moduli spaces (bundles and varieties, Higgs bundles, wall-crossing in DT-Theory), special holonomy and mirror symmetry (Calabi-Yau, G2 geometry, Hull-Strominger system, spin geometry, generalized geometry, T-duality).

My current main research interests are complex non-KÃ¤hler geometry, special holonomy with torsion, and vertex algebras. In my work I transfer techniques from KÃ¤hler geometry to address problems in complex non-KÃ¤hler geometry, using the theory of Courant algebroids and other objects reminiscent from higher gauge theory. My research builds towards providing mathematical underpinnings for the interesting phenomenon of (0,2)-mirror symmetry, using special holonomy with torsion and the theory of vertex algebras. In particular, in the last 8 years I have extensively studied the Hull-Strominger system of partial differential equations, which provides a common ground for these three topics.

### Publications

• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry, (with R. Rubio and C. Tipler) Mathematische Annalen 369 (2017) 539â€“-595.

• Stability data, irregular connections and tropical curves, (with S. Filippini and J. Stoppa) Selecta Mathematica New Ser. 23 (2) (2017) 1355â€“-1418.

• Gravitating vortices, cosmic strings and the Kähler-Yang-Mills equations, (with L. Ãlvarez-CÃ³nsul and O. GarcÃa-Prada) Comm. Math. Phys. 351 (1) (2017) 361--385.

• Balanced metrics on twisted Higgs bundles, (with J. Ross) Mathematische Annalen 367 (3) (2017) 1429-â€“1471.

• Lectures on the Strominger system, Travaux MathÃ©matiques, Special Issue: School GEOQUANT at the ICMAT, Vol. XXIV (2016) 7--61, arXiv:1609.02615.

• Note on Solutions of the Strominger System from Unitary Representations of cocompact lattices of SL(2;C), (with B. Andreas) Comm. Math. Phys. 332 (2014) 1381--1383.

• Torsion-free generalized connections and Heterotic Supergravity, Comm. Math. Phys. 332 (2014) 89--115.

• Deformation of complex structures and the Coupled KÃ¤hlerâ€“Yangâ€“Mills equations, (with C. Tipler) J. London Math. Soc. 89 (2014) 779-â€“796.

• Balanced metrics on vector bundles and polarised manifolds, (with J. Ross) Proc. London Math. Soc. 106 (2013) 1143â€“-1156.

• Coupled equations for Kähler metrics and Yangâ€“Mills connections, (with L. Ãlvarez-CÃ³nsul and O. GarcÃa-Prada) Geometry and Topology 17 (2013) 2731â€“-2812.

• Heterotic Non-KÃ¤hler Geometries via polystable bundles on Calabi-Yau threefolds, (with B. Andreas) J. Geom. Phys. 62 (2012) 183-â€“188.

• Solutions of the Strominger System via stable bundles on Calabi-Yau threefolds, (with B. Andreas) Comm. Math. Phys. (1) 315 (2012) 153-â€“168.

### Preprints

• T-dual solutions of the Hull-Strominger system on non-KÃ¤hler threefolds, arXiv:1810.04740 (2018).

• Holomorphic string algebroids, (with R. Rubio and C. Tipler) arXiv:1807.10329 (2018).

• On the Kähler-Yang-Mills-Higgs equations, (with L. Ãlvarez-CÃ³nsul and O. GarcÃa-Prada), arXiv:1807.10691 (2018).

• Canonical metrics on holomorphic Courant algebroids, (with R. Rubio, C. Tipler and C. Shahbazi) arXiv:1803.01873 (2018).

• Ricci flow, Killing spinors, and T-duality in generalized geometry, arXiv:1611.08926 (2016).

• Moduli of G2 structures and the Strominger system in dimension 7, (with A. Clarke and C. Tipler) arXiv:1607.01219 (2016).

• Gravitating vortices and the Einstein-Bogomol'nyi equations, (with L. Ãlvarez-CÃ³nsul, O. GarcÃa-Prada, and V. Pingali) arXiv:1606.07699 (2016).

• Quantization of Hitchin's equations for Higgs bundles I, (with J. Keller and J. Ross) arXiv:1601.04960 (2016).

• Self-dual generalized metrics for pure N=1 six-dimensional Supergravity, (with C. S. Shahbazi) arXiv:1505.03088 (2015).

### Some recent and forthcoming activities

• SISSA, Trieste, Italy, June 2020.

• Bridging the gap between KÃ¤hler and non-KÃ¤hler complex geometry, BIRS, Banff, October 2019.

• UniversitÃ© de Bretagne Occidentale, June-July 2019.

• UniversitÃ di Firenze, May 2019.

• MIST 2019, Hong Kong, January 2019.

• School and Workshop on Special Metrics and Gauge Theory, ICMAT, December 2018.

• School and Workshop on New Trends in Higgs Bundle Theory, ICMAT, November 2018.

• Group actions in algebraic and symplectic geometry, ICMAT, October 2018.

• Trimester on Moduli Spaces, ICMAT, September-December 2018.