Tuomas Tajakka

My research focuses on algebraic geometry. In particular, I'm interested in moduli spaces of sheaves and complexes on varieties.

My postdoctoral mentor is Sofia Tirabassi. I did my PhD at the University of Washington, where my advisor was Jarod Alper.

• Uhlenbeck Compactification as a Bridgeland Moduli Space
  In this paper I prove that certain Bridgeland moduli spaces on surfaces are projective, and compare these moduli spaces to the Uhlenbeck compactification.
• Projective moduli spaces of complexes of sheaves
  My PhD thesis.
• Projectivity of the moduli space of vector bundles on a curve
  Contribution to the Stacks Project Expository Collection (SPEC), with J. Alper, P. Belmans, D. Bragg, and J. Liang.

Current

• I'm not teaching a class currently. In the spring of 2022, I will be teaching Mathematics of Cryptography at Stockholm University.

Past

• Math 308 B: Linear Algebra with Applications, Summer 2020
• Math 308 I: Linear Algebra with Applications, Spring 2020
• Math 309 C: Linear Analysis, Summer 2019
• Math 309 A: Linear Analysis, Summer 2017

Notes

• Lecture notes I wrote for Math 309. Topics cover systems of ordinary differential equations, Fourier series, and an introduction to partial differential equations.

Here are some ways I've engaged with the broader community:

• I was the graduate student mentor for the WXML project Orbit Structures of Crystal Operators led by Jake Levinson in Winter and Spring 2018.
• I mentored a WDRP reading project on Galois theory in Spring 2019.
• I volunteered as a FEPPS study hall tutor at Washington Corrections Center for Women in Winter 2019.
• I was a UAW 4121 steward for the UW math department together with Olivia Borghi and Amzi Jeffs.