معرفی
Peter Cholak is a Professor and Associate Chair in the Department of Mathematics at the University of Notre Dame. He holds a B.S. from Union College (1984), and M.S., M.A., and Ph.D. from the University of Wisconsin (1988, 1991). His research group specializes in logic and computability theory.
Cholak's research explores the relationship between computability and definability, with focus areas including automorphisms of computably enumerable sets, Ramsey theory, reverse mathematics, and algorithmic randomness. His work establishes deep connections between computational complexity and definability in arithmetic, such as the classification of orbits in c.e. sets and the computational strength of combinatorial principles.
His publications demonstrate consistent focus on computability-theoretic problems with recent expansions into machine learning theory. Key trends include definability in c.e. sets, reverse mathematics of combinatorial theorems, and computational aspects of geometric measure theory. Unifying themes include lattice automorphisms, degree structures, and the limits of formal systems.
He has supervised 12 doctoral dissertations in computability theory and related areas. Students have explored topics including algorithmic randomness, lattice embeddings, reverse mathematics, and applications to computer science.
Cholak leads the Logic Research Group at Notre Dame, collaborating with researchers globally on problems at the intersection of computability, combinatorics, and foundations of mathematics. Recent work includes computability-theoretic analysis of geometric projections and transformer network expressivity.
