James Cummings

James Cummings is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University (CMU), part of the Mellon College of Science. He holds a Ph.D. in Mathematics from Cambridge University and has held postdoctoral appointments at the Mathematical Sciences Research Institute, MIT, Dartmouth College, and the Hebrew University of Jerusalem.

His research focuses on combinatorial set theory, particularly singular cardinal combinatorics, and explores topics such as forcing axioms, Ramsey theory, PCF theory, and linear orderings. He also investigates finite combinatorics using algebraic and flag algebra methods. His work bridges foundational set-theoretic questions with applications in logic and discrete mathematics.

Recent publications address areas like Dowker filters, forcing constructions at singular cardinals, stationary reflection, and monochromatic graph colourings. His research emphasizes consistency results, combinatorial frameworks, and asymptotic extremal problems.

Cummings has advised Ph.D. students (names not listed here) and contributed to the academic community through his postdoctoral collaborations and teaching at CMU. His work is supported by grants and institutional resources at the Mellon College of Science.