People

Dr Jesus Martinez-Garcia

Senior Lecturer
School of Mathematics, Statistics and Actuarial Science (SMSAS)
Dr Jesus Martinez-Garcia
  • Email

  • Telephone

    +44 (0) 1206 873620

  • Location

    STEM 5.9, Colchester Campus

  • 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

  • PhD Mathematics University of Edinburgh, (2013)

  • MASt Mathematics University of Cambridge, (2009)

  • MEng Computer Engineering Universidad Autonoma de Madrid, (2008)

  • MSci Mathematics Universidad Autonoma de Madrid, (2008)

Appointments

University of Essex

  • Lecturer, Mathematical Sciences, University of Essex (1/8/2019 - present)

Other academic

  • Research Associate, Mathematical Sciences, University of Bath (15/6/2017 - 31/7/2019)

  • Postdoc, Max Planck Institute for Mathematics Bonn (24/7/2016 - 30/6/2017)

  • J.J. Sylvester Assistant Professor (postdoctoral position), Johns Hopkins University (1/7/2013 - 30/6/2016)

  • Adjunct professor, Korea University (23/6/2015 - 10/8/2015)

Research and professional activities

Research interests

Algebraic Geometry

Key words: Moduli Spaces
Open to supervise

Birational geometry and Fano varieties

Open to supervise

Moduli spaces and geometric invariant theory

Open to supervise

K-stability and canonical metrics

Open to supervise

Teaching and supervision

Current teaching responsibilities

  • Group Theory (MA301)

  • Commutative Algebra (MA316)

  • Research Skills (MA903)

Previous supervision

Theodoros Stylianos Papazachariou
Theodoros Stylianos Papazachariou
Thesis title: K-Moduli of Log Fano Complete Intersections
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

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

jesus.martinez-garcia@essex.ac.uk
+44 (0) 1206 873620

Location:

STEM 5.9, Colchester Campus

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.

More about me