# Tuomas Tajakka

Graduate student

Department of Mathematics

University of Washington

**Email:** ttajakka@uw.edu
**Office:** Padelford C-113

### Research

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

My advisor is 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. - Seshadri's First Main Lemma

In this short note, I strengthen the conclusion and simplify the proof of the "First Main Lemma" in Seshadri's paper*Vector Bundles on Curves*.

### Teaching

#### Current

- Math 308 B: Linear Algebra with Applications, Summer 2020

#### Past

- 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.

### Service and outreach

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'm currently a UAW 4121 steward for the UW math department together with Olivia Borghi and Amzi Jeffs.