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**Emily Riehl** is an American mathematician who has contributed to higher category theory and homotopy theory. Much of her work, including her PhD thesis,^{[1]} concerns model structures and more recently the foundations of infinity-categories.^{[2]}^{[3]} She is the author of two textbooks^{[4]}^{[5]} and serves on the editorial boards of three journals.^{[6]}

Emily Riehl | |
---|---|

Born | Thousand Oaks, California, US |

Alma mater | |

Scientific career | |

Fields | Mathematics |

Institutions | |

Thesis | Algebraic model structures (2011) |

Doctoral advisor | J. Peter May |

Riehl grew up in Bloomington-Normal, Illinois.^{[7]}
As a high school student at University High School in Normal in 2002, she won third place in the national Intel Science Talent Search for a project in mathematics entitled "On the Properties of Tits Graphs".^{[8]}

Riehl attended Harvard University as an undergraduate; with Benedict Gross as a mentor, she wrote a senior thesis on local class field theory. She also headed the school rugby team and played viola in the Harvard–Radcliffe Orchestra.^{[9]} After Harvard, she completed part III of the Maths Tripos at Cambridge.^{[4]} She defended her doctoral dissertation, *Algebraic model structures*, at the University of Chicago in 2011, supervised by J. Peter May.^{[10]}

Between 2011 and 2015, Riehl held a position at Harvard University as a Benjamin Peirce Postdoctoral Fellow. Since 2015, she has been employed at Johns Hopkins University, where she became an associate professor in 2019. In addition, she teaches on edX and has hosted videos for Numberphile.^{[11]}^{[12]} Along with Benedict Gross and Joe Harris, she developed a Harvard course on edX titled "Fat Chance: Probability from the Ground Up".^{[13]}

In January 2020, Riehl received the JHU President's Frontier Award, a $250,000 award that "supports individuals at Johns Hopkins who are breaking new ground and poised to become leaders in their field". She is the sixth JHU faculty member to receive the award.^{[14]}

Riehl was awarded the 2021 AWM Joan & Joseph Birman Research Prize "for her deep and foundational work in category theory and homotopy theory."^{[15]}^{[16]} She is the fourth winner of this prize. She was named a Fellow of the American Mathematical Society, in the 2022 class of fellows, "for contributions to research, exposition, and communication in higher category theory".^{[17]} In 2022 she was awarded a Simons Fellowship.^{[18]}

Riehl is a host of the n-Category Café, a blog on subjects related to category theory in mathematics, physics, and philosophy.^{[19]} She was a board member of the LGBT mathematical association Spectra.^{[20]}

In addition to her mathematical work, Riehl has competed on the United States women's national Australian rules football team at the Australian Football International Cup,^{[2]}^{[21]} and was vice captain of the team at the 2017 cup.^{[22]}

While working as a postdoctoral researcher at Harvard, she played electric bass in the band Unstraight.^{[2]}^{[23]} She has also written about "unstraightening" in her mathematical research.^{[24]}

Riehl is the author of three books, with a fourth in preparation:

*Categorical Homotopy Theory*(2014)^{[25]}*Category Theory in Context*(2016)^{[26]}*Fat Chance: Probability from 0 to 1*, with Benedict Gross and Joe Harris (2019)^{[27]}*Elements of ∞-Category Theory*, with Dominic Verity, online draft.

**^**Riehl, Emily (2011). "Algebraic model structures" (PDF).*The New York Journal of Mathematics*.**17**: 173–231. MR 2781914.- ^
^{a}^{b}^{c}Malmskog, Beth (August 19, 2017). "Category Theory and Context: An Interview with Emily Riehl".*AMS Blogs*. Archived from the original on March 8, 2018. Retrieved March 8, 2018. **^**Young, Lauren J. (2017-11-17). "The Women Taking Math To The Next Dimension".*Science Friday*. Retrieved 2018-03-08.- ^
^{a}^{b}Readdy, Margaret; Taylor, Christine (March 2018). "Women's History Month".*Notices of the American Mathematical Society*.**65**(3): 248–303. doi:10.1090/noti1653. **^**Baez, John C. (2016-01-02). "How to Learn Math and Physics".*University of California, Riverside*. Retrieved 2018-03-08.**^**"Editorial board".*Journal of Homotopy and Related Structures*. Springer. Retrieved 2018-03-08.

"Editorial board".*Homology, Homotopy and Applications*. Retrieved 2018-03-08.

"Editorial Board".*Cahiers de Topologie et Géométrie Différentielle Catégoriques*. Retrieved 2018-03-08.**^**Perkins, S. (16 March 2002). "Science Smarts".*Science News*.**161**(11): 165–166. doi:10.2307/4013075. JSTOR 4013075.**^**"Students Awarded $530,000 At Intel Science Talent Search". Intel. March 11, 2002. Retrieved March 8, 2018.**^**Widdicombe, Elizabeth S. (May–June 2006). "Emily Riehl". Stellar Seniors.*Harvard Magazine*.**^**Emily Riehl at the Mathematics Genealogy Project**^**"Emily Riehl, Harvard Online Learning Portal".*Harvard University*. 28 February 2018. Retrieved 2018-03-08.**^**"Numberphile – Videos about Numbers and Stuff".*Numberphile*. Archived from the original on 2018-07-15. Retrieved 2018-03-08.

"Stable Marriage Problem – Numberphile".*YouTube*. 2014-09-04. Retrieved 2018-03-08.**^**"Fat Chance: Probability from the Ground Up".*edX*. Retrieved 2020-07-29.**^**Sandy Alexander (January 16, 2020). "Mathematician Emily Riehl earns President's Frontier Award". Hub –Johns Hopkins University.**^**"AWM Joan & Joseph Birman Research Prizes".**^**"Joan and Joseph Birman Research Prize 2021".**^**"2022 Class of Fellows of the AMS". American Mathematical Society. Retrieved 2021-11-05.**^**"2022 Simons Fellows in Mathematics and Theoretical Physics Announced".*Simons Foundation*. 2022-02-18. Retrieved 2022-07-04.**^**"The n-Category Café". Retrieved 7 October 2019.**^**"Spectra: The Association for LGBT Mathematicians". Retrieved 20 August 2022.**^**Holt, Stephanie (2013-05-17). "Footy Town: Kick like a girl, score like a lady".*The Footy Almanac*. Retrieved 2018-03-08.**^**Barrish, Brian (July 31, 2017). "Freedom Captains Ready for IC Challenge". United States Australian Football League.**^**"Interview: LGBT movement and feminism with queer band Unstraight".*Highclouds*. 2017-02-15. Retrieved 2018-03-08.**^**Riehl, Emily; Verity, Dominic (2018). "The comprehension construction".*Higher Structures*.**2**(1): 116–190. arXiv:1706.10023. Bibcode:2017arXiv170610023R. doi:10.21136/HS.2018.05. MR 3917428. S2CID 51758720. Archived from the original on 2020-08-28. Retrieved 2019-06-26.**^**Riehl, Emily (2014).*Categorical Homotopy Theory*. New Mathematical Monographs. Vol. 24. Cambridge: Cambridge University Press. ISBN 978-1-107-04845-4. OCLC 891831279. (book website with downloadable pdf). Reviews:- Scherer, Jérôme.
*zbMATH*. Zbl 1317.18001.`{{cite journal}}`

: CS1 maint: untitled periodical (link) - Blanc, David A.
*Mathematical Reviews*. MR 3221774.`{{cite journal}}`

: CS1 maint: untitled periodical (link) - Weiss, Ittay (July 2014). "Review".
*MAA Reviews*. Mathematical Association of America.

- Scherer, Jérôme.
**^**Riehl, Emily (2016).*Category Theory in Context*. Courier Dover Publications. ISBN 978-0-486-80903-8. OCLC 1006743127. (book website with downloadable pdf). Review:- Weiss, Ittay (April 2018). "Review".
*MAA Reviews*. Mathematical Association of America.

- Weiss, Ittay (April 2018). "Review".
**^**Gross, Benedict; Harris, Joe; Riehl, Emily (2019).*Fat Chance: Probability from 0 to 1*. Cambridge University Press. Reviews:- Bollman, Mark.
*Mathematical Reviews*. MR 3931738.`{{cite journal}}`

: CS1 maint: untitled periodical (link) - Paditz, Ludwig.
*zbMATH*. Zbl 1423.00005.`{{cite journal}}`

: CS1 maint: untitled periodical (link) - Nespolo, Massimo (November 2019).
*Journal of Applied Crystallography*.**52**(6): 1467–1468. doi:10.1107/s1600576719014055.`{{cite journal}}`

: CS1 maint: untitled periodical (link)

- Bollman, Mark.

- "Emily Riehl's homepage".