About me

I am a Research Associate at the Department of Mathematical Sciences of the University of Bath. My position is funded through the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics. My mentor is Johannes Nordström.

Previously I was postdoc fellow at the Max Planck Institute for Mathematics in Bonn and a J.J. Sylvester Assistant Professor (postdoctoral position) of the Department of Mathematics of Johns Hopkins University. I obtained my PhD at the School of Mathematics of the University of Edinburgh in June 2013 under the supervision of Prof. Ivan Cheltsov.

My research interests include the existence of costant scalar curvature Kähler metrics (including K\ähler-Einstein metrics), (log) K-stability, (log) Fano varieties, minimal model program techniques, Geometric Invariant Theory and applications to the study of moduli spaces, alpha-invariants, classification problems or log canonical thresolds. While these are mainly Birational and Algebraic Geometry topics, I have a fairly good background in Complex Differential Geometry and my work has applications to the existence of canonical metrics and the study of their moduli. Due to my additional background as a Computer Engineering I find easy to turn problmes into a language that allows for a computational solution. Recently I have developed an interest on the construction of manifolds with special holonomy using Fano threefolds.

New (02/2019): Our paper Moduli of cubic surfaces and their anticanonical divisors, joint with Patricio Gallardo has been accepted for publication in Rev. Mat. Complut.

New (12/2018): Our paper Applications of the moduli continuity method to log K-stable pairs, joint with Patricio Gallardo and Cristiano Spotti, is on the ArXiv (actually for almost 2 months but I did not have time to update my web yet). It is the culmination of a long term project to produce explicit examples of variations of compact moduli of log Fano pairs and it builds up on our framework construction of GIT for log pairs of Fano hypersurfaces and hyperplane sections, and its sequel on the classification of all GIT compactifications for log pairs formed by a cubic surface and an anti-canonical section.

Contact

E-mail: J (dot) Martinez (dot) Garcia (at) bath (dot) ac (dot) uk
Office: 4 West 5.5
Address: Dr Jesus Martinez Garcia
4 West 5.5
Dept of Mathematical Sciences
University of Bath
Bath
BA2 7AY
United Kingdom
Phone: +44 (0) 1225 385633
Jesus

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