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James Cummings is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University. He holds a Ph.D. in Mathematics from Cambridge University. His research primarily focuses on combinatorial set theory, particularly within the realm of combinatorial objects such as graphs, posets, and colorings within infinite set environments. His work is characterized by interests in singular cardinal combinatorics, and it has significant implications across various subfields, including set theory forcing, large cardinals, Ramsey theory, and PCF theory. Cummings has explored topics related to structure theory for linear orderings and posets, rainbow Ramsey theory, and strong forcing axioms, applying new forcing techniques to obtain consistency results in singular cardinal combinatorics. Additionally, he has made contributions to finite combinatorics using algebraic constructions and the flag algebra method to demonstrate asymptotic extremal results for colorings of finite complete graphs.
Carnegie Mellon University • Pittsburgh, PA
Teaching and researching in mathematics, focusing on combinatorial set theory.
Admission is extremely competitive with no strict GPA cut-offs; holistic review is used.