Dr Jesus Martinez-Garcia
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Email
jesus.martinez-garcia@essex.ac.uk -
Telephone
+44 (0) 1206 873620
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Location
STEM 5.9, Colchester Campus
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Academic support hours
Agreed with students at the start of the term. Check Moodle module page for specific times. For out of term, please e-mail me in advance to avoid disappointment.
Profile
Biography
I am a Senior Lecturer at the Department of Mathematical Sciences of the University of Essex. Previously I held postdoctoral positions at the University of Bath, the Max Planck Institute for Mathematics in Bonn (Germany), and the Johns Hopkins University (USA). You can find more details below, or at my website (linked at the bottom). My research is on algebraic and complex geometry, with focus on birational geometry of varieties of Fano type, moduli spaces and computational algebraic geometry. More specifically, I work on problems in the following areas: *) Existence of constant scalar curvature Kähler metrics (including Kähler-Einstein metrics) and its relation to K-stability. *) Classification of varieties of Fano type. *) Compactification of moduli spaces and geometric invariant theory. *) Computational algebraic geometry.
Qualifications
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PhD Mathematics University of Edinburgh, (2013)
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MASt Mathematics University of Cambridge, (2009)
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MEng Computer Engineering Universidad Autonoma de Madrid, (2008)
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MSci Mathematics Universidad Autonoma de Madrid, (2008)
Appointments
University of Essex
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Lecturer, Mathematical Sciences, University of Essex (1/8/2019 - present)
Other academic
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Research Associate, Mathematical Sciences, University of Bath (15/6/2017 - 31/7/2019)
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Postdoc, Max Planck Institute for Mathematics Bonn (24/7/2016 - 30/6/2017)
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J.J. Sylvester Assistant Professor (postdoctoral position), Johns Hopkins University (1/7/2013 - 30/6/2016)
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Adjunct professor, Korea University (23/6/2015 - 10/8/2015)
Research and professional activities
Research interests
Algebraic Geometry
Birational geometry and Fano varieties
Moduli spaces and geometric invariant theory
K-stability and canonical metrics
Teaching and supervision
Current teaching responsibilities
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Group Theory (MA301)
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Commutative Algebra (MA316)
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Research Skills (MA903)
Previous supervision
Degree subject: Mathematics
Degree type: Doctor of Philosophy
Awarded date: 14/4/2023
Publications
Publications (5)
Martinez-Garcia, J., (2024). Two remarks on asymptotically log Fano pairs
Martinez-Garcia, J., Papazachariou, TS. and Zhao, J., (2024). K-moduli of log del Pezzo pairs and variations of GIT
Cheltsov, I., Krylov, I., Martinez-Garcia, J. and Shinder, E., (2023). On maximally non-factorial nodal Fano threefolds
Abban, H., Cheltsov, I., Denisova, E., Etxabarri-Alberdi, E., Kaloghiros, A-S., Jiao, D., Martinez-Garcia, J. and Papazachariou, T., (2023). One-dimensional components in the K-moduli of smooth Fano 3-folds
Cheltsov, I., Guerreiro, TD., Fujita, K., Krylov, I. and Martinez-Garcia, J., (2023). K-stability of Casagrande-Druel varieties
Journal articles (14)
Gallardo, P., Martinez-Garcia, J. and Spotti, C., Applications of the moduli continuity method to log K-stable pairs. Journal of the London Mathematical Society. 0
Cheltsov, I., Krylov, I., Martinez-Garcia, J. and Shinder, E., (2024). On maximally non-factorial nodal Fano threefolds. Revista Matematica Iberoamericana. 40 (5), 1781-1798
Abban, H., Cheltsov, I., Denisova, E., Etxabarri-Alberdi, E., Kaloghiros, A-S., Jiao, D., Martinez-Garcia, J. and Papazachariou, T., (2024). One-dimensional components in the K-moduli of smooth Fano 3-folds. Journal of Algebraic Geometry
Ivan, C., Tiago, DG., Kento, F., Igor, K. and Martinez-Garcia, J., (2024). K-stability of Casagrande--Druel varieties. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal
Cascini, P., Martinez-Garcia, J. and Rubinstein, YA., (2023). On the body of ample angles of asymptotically log Fano varieties. Rendiconti del Circolo Matematico di Palermo Series 2. 72 (2), 773-790
Martinez-Garcia, J., (2021). Constant scalar curvature Kähler metrics on rational surfaces. Mathematische Nachrichten. 294 (8), 1547-1558
Gallardo, P., Martinez‐Garcia, J. and Spotti, C., (2021). Applications of the moduli continuity method to log K‐stable pairs. Journal of the London Mathematical Society. 103 (2), 729-759
Cheltsov, I. and Martinez-Garcia, J., (2020). Stable polarized del Pezzo surfaces. International Mathematics Research Notices. 2020 (18), 5477-5505
Gallardo, P. and Martinez-Garcia, J., (2019). Moduli of cubic surfaces and their anticanonical divisors. Revista Matemática Complutense. 32 (3), 853-873
Cheltsov, I. and Martinez-Garcia, J., (2019). Unstable polarized del Pezzo surfaces. Transactions of the American Mathematical Society. 372 (2019), 7255-7296
Gallardo, P., Martinez-Garcia, J. and Zhang, Z., (2018). Compactifications of the moduli space of plane quartics and two lines. European Journal of Mathematics. 4 (3), 1000-1034
Gallardo, P. and Martinez-Garcia, J., (2018). Variations of geometric invariant quotients for pairs, a computational approach. Proceedings of the American Mathematical Society. 146 (6), 2395-2408
Cheltsov, I. and Martinez-Garcia, J., (2016). Dynamic Alpha-invariants of Del Pezzo Surfaces. International Mathematics Research Notices. 2016 (10), 2994-3028
Martinez-Garcia, J., (2014). Log canonical thresholds of del Pezzo surfaces in characteristic p. Manuscripta Mathematica. 145 (1-2), 89-110
Books (1)
Araujo, C., Castravet, A-M., Cheltsov, I., Fujita, K., Kaloghiros, A-S., Martinez-Garcia, J., Shramov, C., Süss, H. and Viswanathan, N., (2023). The Calabi Problem for Fano Threefolds. Cambridge University Press. 9781009193399
Conferences (1)
Martinez-Garcia, J. and Spotti, C., (2023). Some observations on the dimension of Fano K-moduli
Thesis dissertation (1)
Martinez-Garcia, J., (2013). Dynamic alpha-invariants of del Pezzo surfaces with boundary
Grants and funding
2024
AGGITatE: A conference on Groups, Representations and Cohomology
The Heilbronn Institute for Mathematical Research (University of Bristol)
INI@Essex � Algebras, Groups, Geometry, Invariants and Related Topics
The Isaac Newton Institute for Mathematical Sciences (INI)
2023
AGGITATE 2023: A Workshop on Algebraic Groups and Cremona Transformations
Foundation Compositio Mathematica
2022
AGGITATE 2023: A WORKSHOP ON ALGEBRAIC GROUPS AND CREMONA TRANSFORMATIONS
London Mathematical Society
2021
The Calabi problem for smooth Fano threefolds
Engineering and Physical Sciences Research Council
2019
Support of collaborative research with Dr Patricio Gallardo at The University of Essex, Colchester.
London Mathematical Society
Algebraic Groups and Geometric Invariant Theory Day (Day1)
London Mathematical Society
Contact
Academic support hours:
Agreed with students at the start of the term. Check Moodle module page for specific times. For out of term, please e-mail me in advance to avoid disappointment.
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