Joshua Fitzgerald Email & Phone Number

I research and apply novel techniques for auditing arithmetic circuits and ZK libraries for security and efficiency.

At Lagrange Labs I researched expressing SQL queries efficiently as recursive arithmetic circuits in a MapReduce-inspired framework. I designed a novel hash-to-curve circuit designed to be efficient on "double-odd" elliptic curves and researched SNARK-friendly accumulation schemes.

Internet, Oo

I researched the Plonk and Plookup schemes and represented Heliax in a multi-company collaboration building an open source library (ZkGarage/plonk) implementing these schemes. I co-wrote a research paper on our techniques for combining the schemes, which we called Plonkup, and presented it on the ZKStudyClub YouTube series and as a workshop the for the first ever ZKHack competition, for which I wrote one of Heliax's challenges.I contributed to the Anoma protocol by designing a proof-system-agnostic language for arithmetic circuits called Vamp-IR. Then I led a team implementing its Rust-based compiler. I presented Vamp-IR at ZKSummit 7, EthCC 5, ZKSummit 9, and EthCC 6.

At Metastate I researched the Plonk zk-SNARK proving system and ways to efficiently adapt the company's prior work into this new system. I published a series of introductory articles on Plonk titled PLONK by Hand. I also began work collaborating on an implementation of Plonk with Plookup using the Arkworks backend.

I write creative mathematics questions for competitive events and online resources.

Fort Wayne, Indiana, Us

I managed the technology needs of students, teachers, and staff.This role required timely and prudent solutions to technical issues in the school building while keeping disruptions to the learning environment to a minimum. I regularly and kindly communicated with teachers and staff about problems or deficiencies they experienced with school devices, developed a plan of action, and followed through to remedy any issues affecting the learning environment.I performed troubleshooting, installation, repairs, and replacement on school equipment including network infrastructure, Windows servers, classroom workstations, staff laptops, iPads, thin clients, smart boards, printers, IP phones, projectors, and peripherals.I kept school software secure, up-to-date, and consistent by installing and updating operating systems, applications, and drivers.I also trained faculty and staff on safely using the school's digital resources and software.After a lightning strike damaged an unknown amount of school equipment in 2018 I learned how to make quick assessments to eliminate functional equipment from consideration and zero in on faulty devices, sometimes triaging multiple concurrent equipment failures. I had to think on my feet, manage stress, and learn troubleshooting procedures while on the go.

Fort Wayne, Indiana, Us

I taught Mathematics (8th grade) from 2018 to 2020, Physical Education (grades K-8) from 2018 to 2019, and Technology (grades K-8) from 2019 to 2020.As a math teacher I incorporated 8th-grade accessible elements of higher math concepts like Group Theory and Cryptography into the curriculum as enrichment activities and utilized the gymnasium to bring a kinesthetic aspect to some lessons.As a technology teacher I developed the first-ever technology curriculum for St. Peter's, which included art projects, web design, and programming as well as training in word processing, spreadsheet, and slide presentation software.My physical education classes emphasized safety, teamwork, sportsmanship, and fun.

I applied zero-knowledge proofs to Statebox's category-theoretic approach to visual programming for a grant received from the Ethereum Foundation. I used the Libsnark library to create and verify proofs of boolean circuit satisfaction and wrote a verifier contract for boolean circuit SNARKs in Solidity. I also wrote blog posts explaining some aspects of Statebox's work.

Oxford, Oh, Us

I write and deliver lectures. I coach students. I design curriculum materials in LaTeX. I collaborate with colleagues to develop teaching methods. I assess student performance and provide timely feedback.

Oxford, Oh, Us

I assess each the current knowledge and ability of each tutee, suggesting tasks to address any deficiencies and providing individualized alternative understandings of curriculum content.

Huntington, In, Us

I wrote creative and challenging math activities for individual and team-based competition. I organized all material, oversaw student volunteers, communicated with teachers and parents, and hosted the competition.

Master Of Science, Mathematics

Bachelor Of Science - Bs, Mathematics Education

Bachelor Of Science, Mathematics Education

Bachelor Of Science - Bs, Mathematics Teacher Education

Bachelor Of Science, Mathematics Education

Master Of Science, Mathematics

Education record