I am a Mathematics Lecturer at Cal State LA and Assistant Professor at ArtCenter College of Design in Pasadena, California. I am the Section Chair-Elect of the SoCal-Nevada Section of the MAA, and Co-Organizer of the SLMath May 12th Celebration of Women in Mathematics.
My graduate research was generously supported by an NSF Mathematical Sciences Graduate Research Fellowship. I was a participant in the Institute for Advanced Study Women and Mathematics Program, and Ambassadorship.
I received my PhD in Mathematics (Summa cum laude) from the University of California, Riverside. My doctoral advisor is Dr. Michel L. Lapidus, Distinguished Professor of Mathematics.
Research Interests. Fractal and Arithmetic Geometry, and Topos Theory.
Editor. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer https://link.springer.com/book/10.1007/978-3-031-66402-1
Lead Guest Editor. Cutting EDGE Mathematics: Celebrating the 25th Anniversary of the Enhancing Diversity in Graduate Education Program, a Special Collection in Research in the Mathematical Sciences (Springer). 2025. https://link.springer.com/collections/fgdhfbhbij
Pedagogy and Scholarship. My work champions the principles of Universal Design for Learning and multimodal pedagogy to create accessible mathematics instruction that honors and is responsive to the unique life circumstances of all learners.
MathArt. I created the Women, Art, and Mathematics AWM Research Network to amplify variations in mathematical thinking, and highlight research and pedagogy at the intersections of mathematics and the arts.
My scholarly interests explore the application of creativity and innovation in the Scholarship of Teaching and Learning. I examine the intersections of mathematics with continental philosophy, neuroscience, and the arts.
Mathematics is an Imaginiarium .
Organization: Upcoming Conferences
AMS Special Session on Local Langlands Conjectures and Noncommutative Geometry, JMM 2026; joint with Dr. Igor Nikolaev
AWM Special Session on Exploring Mathematics through the Arts and Pedagogy in Creative Settings, JMM 2026 Meeting; lead
AMS Special Session on New Horizons for Quantum Error Correction: Categorical Approaches to Topological Codes, AMS 2025 Fall Eastern Sectional Meeting; lead
AMS Special Session on Representations of p-adic Groups and Noncommutative Geometry, AMS 2025 Fall Eastern Sectional Meeting; joint with Dr. Igor Nikolaev
Selected Articles/Preprints
Dobson, Shanna and Lapidus, Michel (2025). Cohomological Complex Dimensions of the Ternary Cantor Set. In preparation.
Dobson, Shanna (2025). Fractal Cohomology of the Ternary Cantor Set, Light Condensed Fractal Cohomology, and Fractal Descent. [Doctoral dissertation, University of California, Riverside]. 300 pages.
Chehade, Sarah, Dobson, Shanna, and Pandey, Tushar (2025). Topological Quantum Error Correction via Higher Categories: Theory to Implementation. Research in the Mathematical Sciences. In preparation.
Dobson, Shanna (2024). Diamonds in the Langlands Program: a Comprehensive Review. Ramanujan Journal, DOI 10.1007/s11139-024-00899-2, https://doi.org/10.1007/s11139-024-00899-2.
Dobson, Shanna (Ed.) (2024). Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Springer. https://link.springer.com/book/10.1007/978-3-031-66402-1
John Cullinan, Shanna Dobson, Linda Frey, Asimina Hamakiotes, Roberto Hernandez, Nathan Kaplan, Jorge Mello, and Gabrielle Scullard (2024). The Probability of Non-Isomorphic Group Structures of Isogenous Elliptic Curves in Finite Field Extensions, II. Journal of Number Theory, Volume 266, Pages 131-165, ISSN 0022-314X, https://doi.org/10.1016/j.jnt.2024.07.013. https://www.sciencedirect.com/science/article/pii/S0022314X24001720
Dobson, Shanna (2024). Literary Incarnations of Topology. Teaching Mathematics Through Cross-Curricular Projects, AMS/MAA Classroom Resource Materials, American Mathematical Society, MAA Press. Volume 72: Chapter 7. https://bookstore.ams.org/
Dobson, Shanna, and Lutken E.R. (2024). To Look on Beauty Bare: Mathematics as Metaphor in Poetry. Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture. Pages 581 - 586. https://archive.
Dobson, Shanna (2024). Mathematical Graffiti: Bridges 2023 Clerihew Collection. Journal of Humanistic Mathematics. Volume 14: Issue 2 (July 2024), pages 602-611. https://scholarship.claremont.edu/jhm/vol14/iss2/22
Dobson, Shanna, and Fields, Chris (2023). Constructing Condensed Memories in Functorial Time. Journal of Experimental & Theoretical Artificial Intelligence. DOI: 10.1080/0952813X.2023.222237
Dobson, Shanna (2023). Dark Imaginarium: Infinity-Curiosity. https://philpapers.org/rec/DOBDII
Dobson, Shanna, and Scaff, Julian (2023). Qurio: Meta-Learning Curiosity Algorithm. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 249-263.
Dobson, Shanna (2021). Efimov K-theory of Diamonds, 3rd BYMAT Conference Proceedings, TEMat Monograficos ISBN 2660-6003.
Dobson, Shanna and Prentner, Robert (2021). Perfectoid Diamonds and n-Awareness. A Meta-Model of Subjective Experience arXiv:2102.07620 [math.GM].
Dobson, Shanna, and Spruijt, Gershom (2022). Imagination as Mathematics. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 205-223.
Dobson, Shanna (2021). Sophie Germain: Revolutionary Mathematician, AWM Book Review.
Selected Recent Talks
Diamond Stacks in Local Langlands, AMS Special Session on Local Langlands Conjectures and Noncommutive Geometry, 2026 JMM, Washington, D.C., January 6, 2025
Imagining and Constructing Topos as Mathematical Dance, AWM Special Session on Exploring Mathematics Through the Arts and Pedagogy in Creative Settings, 2026 JMM, Washington, D.C., January 5, 2025
Topological Phase Transitions via Topoi and Functorial Wormholes, AMS Special Session on Advances in Quantum Topology, Tensor Categories, and Diagrammatic Algebras, 2025 Fall Eastern Sectional Meeting, October 25, 2025
Diamond Stacks in the Langlands Program, AMS Special Session on Representations of p-adic Groups and Noncommutative Geometry, 2025 Fall Eastern Sectional Meeting, October 25, 2025
Diamonds in the Langlands Program, NSF-CBMS Conference: Representations of p-adic Groups, June 9-13, 2025
Light Condensed Fractal Cohomology and Fractal Descent, UC Santa Barbara: Graduate Mathematics Colloquium, June 5, 2025
Fractal Descent and Light Condensed Fractal Cohomology, AMS 2025 Spring Western Sectional Meeting Special Session: Fractal Geometry and Complex Dynamics, May 3, 2025
The Intersection of Mathematics + Graphic Design: a Conversation with Pamela Olecki and Shanna Dobson, ArtCenter College of Design, February 14, 2025. https://lib.artcenter.edu/news/faculty-dialogues-olecki-dobson
Light Condensed Fractal Cohomology, JMM 2025 AMS Special Session: Fractal Geometry with Applications to Analysis, Number Theory and Mathematical Physics, January 10, 2025
Descent Conditions on Hyperphantasia, 4th Applied Active Inference Symposium, Active Inference Institute, November 14, 2024.
Particles and Waves: Southern California Abstraction and Science, 1945 - 1990, Palm Springs Art Museum: Getty Museum Pacific Standard Time ART Initiative: Art & Science Collide, May 31, 2024
Diamond Fractal, WiMSoCal 2024, Pomona College, the Claremont Colleges, February 2024
Six Operations on Diamond Topos, AMS Special Session: Langlands Program, JMM 2023
Geometric Langlands and Geometric Stake Equivalence, Fractal Dynamics Seminar, UCR, 2022
Time's Homeomorphism, Mathematical Poetry at Bridges, Bridges Aalto, Aalto University, Helsinki and Espoo, Finland, August 2022.
Mathematical Poetry.
© 2022 Shanna Dobson