**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 have done postdocs at the ICMAT (Marie Curie Fellow, Severo Ochoa Fellow--Nigel Hitchin Laboratory), at the Ã‰cole Polytechnique FÃ©dÃ©ral de Lausanne (Switzerland), at the Centre for Quantum Geometry of Moduli Spaces (Denmark) and at the Max Planck Institute for Mathematics (Germany). I obtained my PhD in 2009 at the Universidad AutÃ³noma de Madrid.

#### Research Interest

My research is in the areas of differential geometry and algebraic geometry, and has strong links with geometric analysis and mathematical physics. The main research line I have carried out is the study of geometric structures and moduli spaces.

Current projects 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), special holonomy and mirror symmetry (Calabi-Yau, G2 geometry, Strominger system, generalized geometry, T-duality, vertex algebras).

### 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

• 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

• Geometry: mathematical aspects of string model building, Mainz, September 2018.

• Seminar, UniversitÃ degli Studi di Torino, September 2018.

• POISSON 2018, Fields Institute, Toronto, July 2018.

• Institute of Mathematical Sciences, ShanghaiTech University, July 2018.

• VBAC 2018, Luminy, June 2018.

• Geometry and Quantum Theory Colloquium, De Poort, Holland, June 2018.

• Seminar and colloquium, Universitaet Hamburg, June 2018.

• BYMAT, Instituto de Ciencias MatemÃ¡ticas, Madrid, May 2018.

• Seminar Fields Strings and Geometry, Surrey, April 2018.

• Seminar, Universidad del PaÄ±s Vasco, Bilbao, March 2018.

• MIST 2018: Symposium on Geometric Analysis, Hong Kong, January 2018.

• Young Geometric Analystsâ€™ Forum, Tsinghua Sanya International Mathematics Forum, January 2018.

• Seventh Iberoamerican Congress on Geometry, Valladolid, January 2018.

• Gauge Theory and Special Holonomy, Imperial College London, January 2018.