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Mario Garcia-Fernandez

Institution: Universidad Autónoma de Madrid

Position: Profesor Ayudante Doctor (Assistant Professor)

Office: 316        Phone:+34 912999 776

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

Personal Webpage

 

Biographical Review

I am an Assistant Professor (Profesor Ayudante Doctor) at the Universidad Autónoma de Madrid, from September 2017. Previously, I have done postdocs at the ICMAT (Marie Curie Fellow, Severo Ochoa Fellow--Nigel Hitchin Laboratory), at the École Polytechnique Fédéral 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 Autónoma 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 Kähler geometry (constant scalar curvature Kähler, 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) 539–-595.

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

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

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

• Lectures on the Strominger system, Travaux Mathématiques, 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 Kähler–Yang–Mills equations, (with C. Tipler) J. London Math. Soc. 89 (2014) 779-–796.

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

• Coupled equations for Kähler metrics and Yang–Mills connections, (with L. Álvarez-Cónsul and O. García-Prada) Geometry and Topology 17 (2013) 2731–-2812.

• Heterotic Non-Kähler Geometries via polystable bundles on Calabi-Yau threefolds, (with B. Andreas) J. Geom. Phys. 62 (2012) 183-–188.

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

 

Preprints

• The Kähler-Yang-Mills-Higgs equations, (with L. Álvarez-Cónsul and O. García-Prada), to appear (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. Álvarez-Cónsul, O. García-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, Università 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 Matemáticas, Madrid, May 2018.

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

• Seminar, Universidad del Paıs Vasco, Bilbao, March 2018.

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

• Young Geometric Analysts’ 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.