PhD Position in Number Theory and Formalization
Explore the formalization of number theory with proof assistants to tackle Diophantine problems. Join a dynamic team at Vrije Universiteit Amsterdam working at the intersection of pure and algorithmic mathematics.
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Project Description
Project Overview
The Department of Mathematics at Vrije Universiteit Amsterdam offers a 4-year PhD position focused on Number Theory and Formalization. Research involves developing and formalizing mathematical theories necessary for Diophantine problem-solving, primarily in effective and algorithmic number theory, with pure mathematical results also contributing. The project is supervised by Dr. Sander Dahmen and Assia Mahboubi, supported by an NWO-funded Vici project aiming to bridge the gap in formalized Diophantine research. The candidate will work within the Center for Topology, Algebra, and their Applications, joining an inclusive and interdisciplinary group committed to diversity and internationalism.
What You Will Do
Your duties include conducting original research aimed at a PhD thesis, using proof assistants such as Lean or Rocq to formalize number theory. You will also participate in teaching activities, including supervising exercise classes, which comprise roughly 15% of your working time.
Expected Outcomes
The research aims to advance the formalization and algorithmic understanding of number theory relevant to Diophantine problems, contributing novel mathematical insights and proof formalizations. The position combines theoretical and computational approaches within an international research environment.
Why This Matters
Formalizing number theory using modern proof assistants enhances mathematical rigor and accessibility, fosters reproducibility, and facilitates complex problem-solving in mathematics. The research supports developments in both pure and effective number theory, with potential applications in cryptography, algorithm design, and mathematical logic.
Entry Requirements
Eligibility
Supervisor Profile
Dr. Sander Dahmen is a researcher in number theory and formalization at Vrije Universiteit Amsterdam. He focuses on bridging formalized mathematics and classical mathematical problems such as those in Diophantine equations, using tools like Lean. He leads the NWO-funded Vici project aimed at advancing formalized Diophantine research and is deeply involved in computational approaches to pure mathematics.