Joseph Fluegemann

PhD Work

Main Documents

The following is a revised and cleaned up version of my Ph.D. thesis (August 2026)

In my thesis, I provided a formula for calculating the multiplicity of a positroid variety at a torus-fixed point and pointed to code in Macaulay2 that does the calculation. The scripts for the code are in the following folder:

Here are my notes for my qualifying exam presentation, which was a chalk talk.

I started typing them up into a presentation (but ended up only typing up part of the handwritten notes above)

Here is the research statement I used to apply for jobs in 2024.

Talks/Presentations

Talk at University of Waterloo (invited by Karen Yeats) October 2024:

Talk at Pennsylvania State University (invited by Jacob Bourjaily) December 2021. This was the place where I first presented the main result of my thesis:

My notes for a talk "What is a Leading Singularity?" at the Amplitudes and Combinatorics Synergy Event, Institute for Advanced Study, October 2024:

Here is my presentation from a 2-part talk I gave in the Zoom Amplitudes and Geometry Club in 2023 on "Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM" by Elvang, Huang, Keeler, Lam, Olson, Roland, and Speyer:

Slides from a talk I gave on basic quantum field theory and the positive Grassmannian, given at the Cornell Olivetti seminar on September 21, 2021. This was part 1 of 2 talks I gave at the Olivetti.

Part 2 was an introduction to the Amplituhedron on Feb 22, 2022.

An early talk (2019) I gave on characteristic classes at a reading group Allen Knutson formed for potential students:

Solutions

I received permission from Henriette Elvang to publicly post my solutions to the textbook "Scattering Amplitudes in Gauge Theory and Gravity" by Henriette Elvang and Yutin Huang (I used the print version, it's almost the same as the Arxiv doc: https://arxiv.org/pdf/1308.1697) Unfortunately, I never got the chance to finish all the problems, nor to clean up and type up the ones that I did. However, the problems I did work on (from chapters 1-9) are here:

It's a mix of problems I completed, some partially complete/incomplete, and some incorrect. I only managed to type up a few of them here (with a couple others in the GrassmannianIntegrals presentations):

Also, here are the problem sets from Nima Arkani-Hamed's Fall 2019 class at Harvard on Amplitudes:

as well as some of the work that I did on some of the problems in 2019: