cm.martineze (at) uniandes (dot) edu (dot) co

Department of Mathematics

Universidad de Los Andes

Cra 1 Nº 18A - 12

Bogotá, Colombia

Office: H-001

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.

### Research

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).

With A. Bertram. Change of polarization for moduli of sheaves on surfaces as Bridgeland wall-crossing. International Mathematics Research Notices, rny065, Journal link . arXiv.

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.

### Students

Juan Pablo Zuñiga Valencia. Universidad de los Andes.

Talon Stark. College of Creative Studies at UCSB. Thesis: "Towards Projectivity of some Bridgeland moduli spaces on Hirzebruch surfaces". Now a graduate student at UCLA.

### Teaching

During Spring 2019 I will be teaching Cálculo Integral con Ecuaciones Diferenciales (magistral ). Students will have access to the course materials through Sicua.

Notes:

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.

Office Hours:

Tuesday, Wednesday, and Thursday 1:00-2:00pm.

### Slides from some talks

Universidad de los Andes Colloquium, Fall 2018

Encuentro SCM-SMM, Spring 2018

AMS Sectional Meeting-Portland State University, Spring 2018.

( Washington University in St. Louis-Algebraic Geometry Seminar, Spring 2018)

AMS Sectional Meeting -UGA, Spring 2016

AMS Summer Institute in Algebraic Geometry, Salt Lake City 2015

### Links

University of Utah Algebraic Geometry Seminar.

Southern California Algebraic Geometry Seminar.

WAGS.