THE SHAPE OF A SOLUTION

Tyson Klingner

is an inquisitive scholar obsessed with abstract patterns that permeate the natural world. He completed a Bachelor of Mathematical Sciences (Advanced) degree in 2020, majoring in pure mathematics, then a Master of Philosophy degree in Pure Mathematics at the University of Adelaide. He is researching Higgs bundles, which are rich geometric objects relevant to different areas of mathematics and physics.

As a 2023 Fulbright Future Scholar, Tyson will pursue a PhD at the University of Washington, aiming to explore further algebrogeometric aspects of his current work.

Tyson, what does an "Algebraic Geometer" do?

In Layperson's terms, algebraic geometers study the geometry of solutions to algebraic equations. In particular, the algebraic equations may arise from physics, allowing us to view a physics problem through a dfferent lens, or the equation may be related to computing and coding.

Regardless of the origin of the equations studied, algebraic geometry is an active eld pioneering more areas than just abstract mathematics. As to what I wish to achieve, my avour of algebraic geometry lives on the physics side of the coin, so I hope to continue my current work to further research in algebraic geometry related to mathematical physics.

What do you enjoy most about your work?

I believe mathematics is the most fascinating discipline ever explored and pioneered by humanity. I enjoy playing a tiny, minuscule part in its development. Besides the beauty of the subject, I love the struggle.

Researching mathematics is not easy, but it makes for a stronger euphoric feeling when you begin converging on a solution to a research problem. Altogether, I find my work incredibly rewarding, and that is what I most enjoy.

How is Fulbright helping you?

Besides funding my PhD in the US, Fulbright enables me access to a vast network of talented individuals across all disciplines of academia. For instance, a few weeks ago, a Fulbright-funded law professor Marc Edelman visited the University of Adelaide and contacted me. We went out for lunch, and he gave me a rundown of every university I was considering and provided an overview of the cities, which aided me immensely in selecting a PhD program. Also, having the Fulbright Scholarship gives visibility in various domains, given its reputation.

What are you most looking forward to about studying in the US?

Academically, I think US mathematics programs are much stronger than those in Australian. My lecturers in Adelaide all encouraged me to pursue my PhD in the US. Outside of the technical aspect, I am excited about being in a new environment, meeting new people, and experiencing a new culture. I hope to immerse myself in whatever opportunities present themselves, whether it be professional or personal.

Also, I am keen to travel to different parts of the States and Canada, and see a new area of the world that I may not have had the opportunity to otherwise.

Can you tell us about your decision to do your PhD at the University of Washington?

Besides the University of Washington, I was also considering the University of Maryland, and I was in consideration at Columbia. In the end, it was an easy decision to make. I had a Zoom call with my supervisor Dr David Baraglia, and an Emeritus Professor, Mike Eastwood.

We studied the programs in depth and looked at the courses, seminar series, and papers of the mathematicians in the different departments. By the end of the call, we unanimously agreed that Washington was the best program for my area. Regarding the faculty at UW, the algebraic geometry research group as a whole stood out. The group consists of outstanding individuals, including Sandor Kovacs, Max Lieblich, and Jason Alper..

What would you say to aspiring students hoping to go onto further tertiary studies in the coming years?

Opportunities come to those who knock. If you want to use your studies to improve your quality of life, put yourself out there. For example, pursue an internship in a field you are interested in or conduct a research project with peers on a new topic. Also, there is no such thing as too many questions. Never feel afraid to ask someone that you admire for advice or help. Asking them may be the catalyst for a new endeavour you never envisioned. I am only in the position that I am in because I asked older students and lecturers questions and gauged what was out there. Be ambitious but also flexible.

My favourite “quote” from my dear friend Isaac: “if you shoot for the stars and you land on the moon, you have done an outstanding job and don't let anyone take that away from you” (which, it turns out, is a misquote from the famous Norman Vincent Peale)