
I am a postdoc at UC Berkeley, where I work on computability theory and descriptive set theory. Here is my CV.
Office: 987 Evans Hall
Email: pglutz “at” berkeley.edu
BA: Mathematics, UC Berkeley, 2012-2016
PhD: Mathematics, UC Berkeley, 2016-2021
Seminars
David Gonzalez and I are organizing a seminar on higher order reverse math.
Research

Here is a list of research questions which I think are interesting.
Papers (published/submitted)
Preprints
- A note on a conjecture of Sacks
with Kojiro Higuchi [arXiv] [slides]
In preparation
- Local Martin’s conjecture, revisited
with Vittorio Bard
- Counterexamples concerning the Hausdorff dimension of continuous images
with Joe Miller [slides]
- Complexity of oracles for packing dimension
- Measure hyperfiniteness and lossless expansion
with Jan Grebík [slides]
Theses
- Results on Martin’s conjecture
PhD thesis, UC Berkeley 2021 [pdf]
Comment: Liang Yu has found a counterexample to Conjecture 5.36 (a.k.a. question 9.10)
Other slides
Expository
Here are some expository documents I’ve written. I hope to add more soon.
- How to use Steel forcing
[notes]
- A different kind of fixed point theorem
A talk I gave about Kleene’s fixed point theorem for an audience of undergraduate students
[slides]
Teaching
Current teaching: Math 125A, Mathematical Logic
Past teaching: Here is a list of courses I’ve taught in the past.
Teaching materials: For two of the courses I taught at UCLA, I compiled handwritten notes:
Course websites: Here are websites I made for some of the courses I have taught.