Emily Riehl

Emily Riehl is an American mathematician specializing in homotopy theory, category theory, and higher category theory. She has held faculty positions at Johns Hopkins University and Washington University in St. Louis, and is known for contributions to model categories, higher categorical structures, and mathematical exposition. Her research intersects with work by figures and institutions such as Jacob Lurie, J. Peter May, Quillen, Boardman–Vogt, and centers such as the Institute for Advanced Study, MSRI, and Simons Foundation.

Early life and education

Riehl grew up in the United States and pursued undergraduate studies before entering graduate school at University of Chicago where she completed doctoral work under J. Peter May. Her dissertation built on foundations connected to Daniel Quillen's concepts and the tradition of homotopical algebra influenced by Category theory pioneers such as Saunders Mac Lane and Samuel Eilenberg. She later held postdoctoral positions and research affiliations with institutions including Institute for Advanced Study, MSRI, and collaborative groups associated with Simons Foundation programs and workshops led by scholars like Jacob Lurie and Clark Barwick.

Career and research

Riehl's research program centers on structural questions in homotopy theory and higher category theory, addressing problems related to model category structures, enriched category theory, and the formalization of higher categorical limits and colimits. She has developed perspectives informed by the work of Quillen, Grothendieck, Street, Hovey, and Bousfield, and has engaged with frameworks advanced by Joyal and Lurie for ∞-categories. Her papers analyze interactions among simplicial sets, model categories, and notions of equivalence that trace back to research by Boardman, Vogt, and May; she has contributed to clarifying coherence results and lifting problems that connect to applications studied at venues like ICM sessions and workshops at Banff Centre.

Beyond technical results, she is recognized for clear exposition and synthesis, producing monographs and textbooks that situate topics alongside classical treatments by Mac Lane, May, Weibel, and Hatcher. Her collaborations and seminars often include participation with researchers such as Emily Noether-inspired programs, organizers from AMS meetings, and colleagues at Harvard University, Princeton University, and MIT who work on related categorical and homotopical problems. Her influence extends through lecture series at Oberwolfach, courses at MSRI, and invited talks at conferences like Joint Mathematics Meetings and ICM satellite events.

Awards and honors

Riehl has received recognition from mathematical societies and foundations, including early-career fellowships and awards associated with organizations such as the American Mathematical Society, Simons Foundation, and national research fellowships that support work at centers like MSRI and the Institute for Advanced Study. She has been invited to serve on editorial boards for journals linked to publishing houses and societies such as Springer, Cambridge University Press, and the American Mathematical Society, and has been named to program committees and prize selection panels alongside scholars from Princeton University, Harvard University, and University of Chicago.

Selected publications

- Monograph and textbook expositions that present higher category theory and model categories in the tradition of Mac Lane and May, used in graduate courses at Johns Hopkins University and Washington University in St. Louis. - Research articles on model structures, enriched categories, and homotopical coherence connecting to work by Quillen, Hovey, Joyal, and Lurie, published in journals associated with AMS and international publishers such as Springer and Cambridge University Press. - Survey papers and lecture notes for summer schools and programs at MSRI, Oberwolfach, and thematic programs funded by the Simons Foundation.

Teaching and mentorship

As a faculty member at Johns Hopkins University and later at Washington University in St. Louis, she has taught graduate courses in category theory, algebraic topology, and homotopy theory, supervising Ph.D. students whose work engages with frameworks developed by Quillen, Mac Lane, May, and Lurie. Her mentorship includes advising students and postdoctoral researchers who have gone on to positions at institutions such as Princeton University, Harvard University, MIT, University of Chicago, and faculty roles supported by grants from bodies like the National Science Foundation and the Simons Foundation. She has organized workshops and reading groups in collaboration with departments at Johns Hopkins University, Washington University in St. Louis, and research centers including MSRI and the Institute for Advanced Study.

Category:American mathematicians Category:Category theorists Category:Algebraic topologists