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, Associate Editor of the Anneli Lax New
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, fractal cohomology, categorical methods in geometry, and topos theory.
Edited Volumes
Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer https://link.springer.com/
Cutting EDGE Mathematics: Celebrating the 25th Anniversary of the Enhancing Diversity in Graduate Education Program, a Special Collection in Research in the Mathematical Sciences. Dobson, Shanna, et al., (Eds.) (2025). Springer https://link.springer.com/
Local Langlands Conjectures and Noncommutative Geometry. In Contemporary Mathematics. (Proc. of the AMS Special Session on Local Langlands Conjectures and Noncommutative Geometry, JMM2026). Igor Nikolaev and Shanna Dobson (Eds.) (2026). American Mathematical Society. In preparation.
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
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 Representations of p-adic Groups and Noncommutative Geometry, AMS 2025 Fall Eastern Sectional Meeting; joint with Dr. Igor Nikolaev
Selected Articles
Shanna Dobson and Michel L. Lapidus (2025). Fractal Cohomology: Cross-Scales Paths & Cohomological Complex Dimensions of the Ternary Cantor Set. In preparation.
Shanna Dobson (2025). Fractal Cohomology of the Ternary Cantor Set, Light Condensed Fractal Cohomology, and Fractal Descent. [Doctoral dissertation, University of California, Riverside]. 300 pages.
Sarah Chehade, Shanna Dobson, and Tushar Pandey (2025). Topological Quantum Error Correction via Higher Categories. In preparation.
Shanna Dobson (2024). Diamonds in the Langlands Program: a Comprehensive Review. Ramanujan Journal, DOI 10.1007/s11139-024-00899-
Shanna Dobson (Ed.) (2024). Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Springer. https://link.springer.com/
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.
Shanna Dobson (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/
Shanna Dobson and E.R. Lutken (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.
Shanna Dobson (2024). Mathematical Graffiti: Bridges 2023 Clerihew Collection. Journal of Humanistic Mathematics. Volume 14: Issue 2 (July 2024), pages 602-611. https://scholarship.
Hector M. Manrique, Shanna, Dobson and Michael J. Walker (2024). Time-warps, PsyArXiv. https://doi.org/10.31234/osf.
Shanna Dobson (2023). Constructing Agentive Inference as a Universal property: Strange Functorial Things and Categorical Red Queen Dynamics: Comment on “Path integrals, particular kinds, and strange things” by K. Friston, L. Da Costa, D. Sakthivadivel, C. Heins, G. Pavliotis, M. Ramstead, and T. Parr. Physics of Life Reviews, 2023, ISSN 1571-0645. https://doi.org/10.1016/j.
Shanna Dobson and Chris Fields (2023). Constructing Condensed Memories in Functorial Time. Journal of Experimental & Theoretical Artificial Intelligence. DOI: 10.1080/0952813X.2023.
Shanna Dobson and Julian Scaff (2023). Qurio: Meta-Learning Curiosity Algorithm. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 249-263.
Shanna Dobson and Robert Prentner (2023). Artistic Mediation in Mathematical Phenomenology. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 81-92.
Shanna Dobson (2021). Efimov K-theory of Diamonds, 3rd BYMAT Conference Proceedings, TEMat Monograficos ISBN 2660-6003.
Shanna Dobson and Robert Prentner (2021). Perfectoid Diamonds and n-Awareness. A Meta-Model of Subjective Experience arXiv:2102.07620 [math.GM].
Shanna Dobson, and Gershom Spruijt (2022). Imagination as Mathematics. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 205-223.
Shanna Dobson (2021). Sophie Germain: Revolutionary Mathematician, AWM Book Review.
Selected Talks
Fractal Cohomology of the Ternary Cantor Set: Cohomological Zeta Functions, WiMSoCal 2026, Loyola Marymount University, February 21, 2026.
P-adic Geometry: Fargues-Scholze Program, Fractal Dynamics Seminar, UCR, January 22, 2026.
Diamond Topos and Diamond Moduli Stacks in Geometrization of Local Langlands, AMS Special Session on Local Langlands Conjectures and Noncommutive Geometry, 2026 JMM, Washington, D.C., January 6, 2026.
Imagining Topos as Mathematical Dance [Film], AWM Special Session on Exploring Mathematics Through the Arts and Pedagogy in Creative Settings, 2026 JMM, Washington, D.C., January 5, 2026
Diamond Stacks in the Langlands Program, AMS Special Session on Representations of p-adic Groups and Noncommutative Geometry, AMS 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
The Intersection of Mathematics + Graphic Design: a Conversation with Pamela Olecki and Shanna Dobson, ArtCenter College of Design, February 14, 2025. https://youtu.be/-B9V8ReZUx8
Light Condensed Fractal Cohomology, JMM 2025 AMS Special Session: Fractal Geometry: Analysis, Number Theory and Mathematical Physics, January 10, 2025
Descent Conditions on Phantasia, JMM 2025 AWM Special Session: Exploring Mathematics Through the Arts and Pedagogy in Creative Settings, January 9, 2025
Qurio: Quantum Thinking for Artists and Designers, AICAD Symposium 2024: “Teach for Tomorrow: ReDesigning the Future”, ArtCenter College of Design, November 14, 2024
Cohomological Infinitesimals as Condensed Sets, Fractal Dynamics Seminar, UCR, November 7, 2024
Phenomenology of Sick Spirit + p-adic Hyperphantasia (with Sonia de Jager), Too Mad to be True III: Paradoxes of Madness, October 31, 2024, Belgium
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
The Chronicles of Fractal Geometry: Fractal Strings, and Functorial Harps, Analysis Seminar, Pomona College, April 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.
Condensed Sets: a Comprehensive Review, Fractal Dynamics Seminar, UCR, 2022
Perfectoid Spaces: Review, Fractal Dynamics Seminar, UCR, 2021
Infinity Categories and Factorization Homology, Fractal Dynamics Seminar, UCR, 2021
Mathematical Poetry
© 2022 Shanna Dobson