Thomas Scanlon

Thomas Scanlon is Professor of Mathematics at the University of California, Berkeley and serves as Vice-Chair for Graduate Affairs in the Berkeley Senate. He is additionally affiliated with the campus-wide Group in Logic and the Methodology of Science. His research lies at the intersection of mathematical logic and number theory, with a focus on model theory and its applications to diophantine geometry, difference and differential algebra, and arithmetic dynamics.

Education

• S.B., University of Chicago, 1993
• Ph.D., Harvard University, 1997

Research Interests
Scanlon’s work centers on model theory, especially o-minimality, stability theory, and geometric model theory. He applies these logical tools to problems in diophantine geometry such as the André–Oort and Zilber–Pink conjectures, studies difference and differential algebraic structures, and investigates arithmetic dynamics of rational maps and Drinfeld modules.

Publications Overview
Since 1997 he has authored or co-authored more than sixty research papers. Recurring themes include the model theory of valued and difference fields, jet and prolongation spaces, effective bounds in diophantine problems, and functional transcendence results. Recent work (2018-2025) explores differential Chow varieties, strong minimality of modular functions, effective elimination procedures for differential-difference equations, and uniformity questions in diophantine geometry.

Doctoral Supervision
Scanlon has supervised at least sixteen Ph.D. theses at UC Berkeley, covering pure model theory, diophantine geometry, differential algebra, and stability theory. Students graduated between 2002 and 2022 include Alice Medvedev, Dragos Ghioca, Alex Kruckman, and Benjamin Castle.

Contact & Office

• Email: scanlon@math.berkeley.edu
• Office: 723 Evans Hall, UC Berkeley
• Phone: (510) 642-3665