Emily Cairncross
I am a Mathematical Computer Science (MCS) doctoral candidate at the University of Illinois at Chicago (UIC). My Ph.D. advisor is Dhruv Mubayi. My academic CV can be found here, and I can be reached at emilyc10@uic.edu. My industry resume can be found here, and I can be reached at egcairncross@gmail.com. I expect to graduate in Spring 2026.
I co-organized the weekly Graduate Student Combinatorics, Algorithms, and Probability Seminar (GCAPS) with Clayton Mizgerd in 2024-2025, I have been a member of Symbols of Inclusion throughout my time at UIC, and I served as co-president of the Math Graduate Student Assocation (MGSA) in 2022-2023.
My office hours for Fall 2025 are 1-3pm on Wednesdays in the MSLC.
Research Interests
I am interested in extremal combinatorics, especially extremal graph theory and extremal set theory.
Papers and Preprints
- Inducibility of rainbow graphs, with Clayton Mizgerd, Dhruv Mubayi (27 pages), submitted.
- Ordered and colored subgraph density problems, with Dhruv Mubayi (17 pages), published in SIAM Journal on Discrete Mathematics, Vol. 39, No. 1 (2025).
- Nationwide cost and capacity estimates for sedimentary basin geothermal power and implications for geologic CO2 storage, with J. Ogland-Hand, B. Adams, R. Middleton (11 pages), published in Frontiers in Energy Research, Vol. 12 (2024).
- Throttling for standard zero forcing on directed graphs, with J. Carlson, P. Hollander, B. Kitchen, E. Lopez, A. Zhuang (27 pages), published in The Australasian Journal of Combinatorics, Vol. 84, Part 1 (2022).
- Classifying toric surface codes of dimension 7, with S. Ford, E. Garcia, K. Jabbusch (12 pages), published in Involve, Vol. 14, No. 4 (2021).
Teaching
- Fall 2025: MATH 160 Finite Math for Business
- Spring 2025: MCS 275 Programming Tools and File Management, MCS 360 Intro to Data Structures
- Fall 2024: MATH 160 Finite Math for Business
- Fall 2023: MATH 180 Calculus I
- Fall 2022: MATH 160 Finite Math for Business
- Spring 2022: MATH 110 College Algebra
- Fall 2021: MATH 160 Finite Math for Business
(Photo credit to Amelia Pompilio.)