## Cristian Martinez

martinez (at) math (dot) ucsb (dot) edu

Department of Mathematics

University of California

South Hall, Room 6607

Santa Barbara, CA 93106-3080

Office: South Hall 6503

I am a Visiting Assistant Professor at the University of California, Santa Barbara. My mentor is 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.

Curriculum Vitae

Research Statement

Teaching Statement

### 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.
My google Scholar page.

My articles on arXiv.

#### Papers:

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). Preprint. 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. Submitted. 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.

### Geometry at UCSB

Algebraic Geometry Seminar.

Kahler Geometry Learning Seminar.

Geometry, Topology and Physics Seminar

Differential Geometry Seminar

### Current Students

Starting this summer I am advising Talon Stark from CCS. His SURF project is titled "Projectivity of some Bridgeland moduli spaces on Hirzebruch surfaces"

### Teaching

During Fall 2017 I will be teaching MATH 34B. Students will have access to the course materials through GauchoSpace.

#### Notes:

These are some study guides for some courses I have taught at UCSB:
MATH 122A, MATH 117(1), MATH 117(2), MATH 8, MATH 8 (basics), MATH 6B, MATH 4B.

#### Office Hours:

Monday-Wednesday 11:00am-12:30pm SH 6503.

### Links

UCSB Mathematics Seminars.
University of Utah Algebraic Geometry Seminar.
ArXiv/AG/.
Southern California Algebraic Geometry Seminar.
WAGS.
Ravi Vakil's Algebraic Geometry conference list.