cm.martineze (at) uniandes (dot) edu (dot) co
Department of Mathematics
Universidad de Los Andes
Cra 1 Nº 18A - 12
Tel: +57 1 339 4949 Ext. 5229
I am a Postdoctoral Researcher at Universidad de Los Andes. Before, I was a Visiting Assistant Professor at the University of California, Santa Barbara under David R. Morrison. I graduated from the University of Utah in May 2015 with a PhD in Mathematics. I wrote my dissertation in Algebraic Geometry under the supervision of Aaron Bertram.
I am interested in the study of moduli spaces of sheaves, in particular their birational geometry. This goes hand in hand with the study of derived categories of coherent sheaves and Bridgeland stability conditions.
Papers, preprints, and projects
With T. Stark. Projectivity of Bridgeland moduli spaces on Hirzebruch surfaces. Work in progress.
With B. Schmidt. Geometry of 1-dimensional space sheaves. Work in progress.
With B. Schmidt. Bridgeland stability on blow-ups and counterexamples (with an appendix by Omprokash Das). Mathematische Zeitschrift, 2018, DOI 10.1007/s00209-018-2149-3. arXiv.
Failure of the generalized Bogomolov-Gieseker type inequality on blowups (a more general result appears in the item above with Schmidt).
Duality, Bridgeland wall-crossing and flips of secant varieties. International Journal of Mathematics: Volume 28, Issue 2 (2017), Pages 1750011-40. arXiv.
With A. Bertram and J. Wang. The birational geometry of moduli spaces of sheaves on the projective plane. Geometriae Dedicata: Volume 173, Issue 1 (2014), Pages 37-64. arXiv.
Events at Uniandes
Algebraic Geometry Learning Seminar: Moduli spaces of plane sheaves.
Juan Pablo Zuñiga Valencia. Universidad de los Andes.
During Spring 2019 I will be teaching Cálculo Integral con Ecuaciones Diferenciales (magistral ). Students will have access to the course materials through Sicua.
The comprehensive MATE 1214 study guide.
These are some study guides for some courses I taught at UCSB: Complex Variables, Intro to Real Analysis, Intro to Real Analysis(2), Discrete Mathematics, How to prove it (basics), Vector Calculus, Differential Equations.
Tuesday, Wednesday, and Thursday 1:00-2:00pm.
Slides from some talks
( Washington University in St. Louis-Algebraic Geometry Seminar, Spring 2018)