I am a postdoc at UCLA, where I work on computability theory and descriptive set theory.

**Office:** MS 7336

**Email:** pglutz “at” berkeley “dot” edu

**BA:** Mathematics, UC Berkeley, 2012-2016

**PhD:** Mathematics, UC Berkeley, 2016-2021

Currently I’m mostly working on questions related to Martin’s conjecture, but I’m interested much more generally in logic and foundations of math. My goal is to work on problems that are both mathematically appealing and philosophically significant.

**Incompleteness and jump hierarchies**

with James Walsh [arXiv] [journal]**Local Martin’s conjecture, revisited**

with Vittorio Bard [in preparation]**Part 1 of Martin’s conjecture for order preserving functions**

with Benny Siskind [draft available on request]**Martin’s conjecture for regressive functions on the hyperarithmetic degrees**

[draft]**A note on a question of Sacks**

with Kojiro Higuchi [draft]**Conway can divide by three, but I can’t**

[draft]**Formalizing Galois theory**

with Thomas Browning [arXiv]

**Results on Martin’s conjecture**

PhD thesis, UC Berkeley 2021 [pdf]

*Comment:*Liang Yu has recently found a counterexample to Conjecture 5.36 (a.k.a. question 9.10)

**Survey of some recent work on Martin’s conjecture**

[Survey]**Part 1 of Martin’s conjecture for measure preserving functions and order preserving functions**

[Overview] [Measure preserving functions] [Ultrafilters on the Turing degrees] [Order preserving implies measure preserving]**Embedding partial orders into the Turing degrees: Height 2 vs. height 3 partial orders**

[Overview]**Division by two without choice**

[Sock division vs. shoe division]**Formalizing Galois theory in Lean**

[Progress report from January 2021]

**Berkeley Lean Seminar**

During Summer 2020, Thomas Browning, Rahul Dalal and I organized a seminar on the Lean proof assistant. The website for the seminar is here.**Galois theory in Lean**

Thomas Browning, Jordan Brown and I formalized various parts of Galois Theory in Lean. This culminated in a formalization of the Abel-Ruffini theorem on the unsolvability of the quintic (though I dropped out of this effort partway through to work on my thesis).**The Qual**

Once upon a time I took a qualifying exam and wrote up (most of) a transcript. I’m mostly proud of the picture I made to accompany it (and not so proud of the silly things I said during my qual).

**Current Teaching:** Math 182, Algorithms

**Past Teaching:** Here is a list of courses I’ve taught in the past. Also, here are websites I made for some of those classes:

**Spring 2021:**Math 54, Linear Algebra and Differential Equations**Spring 2018:**Math 10B, Math for Biology Majors**Summer 2017:**Math 54, Linear Algebra and Differential Equations**Spring 2017:**Math 10B, Math for Biology Majors**Fall 2016:**Math 54, Linear Algebra and Differential Equations