I completed my PhD in Mathematics (Summa cum laude) at the University of California, Riverside. My doctoral advisor is Dr. Michel L. Lapidus, Distinguished Professor of Mathematics at the University of California, Riverside.
I am an NSF Mathematical Sciences Graduate Research Fellow, UCR Chancellor Distinguished Fellow, Campbell Dissertation Scholar, Caltech SURF Fellow, Institute for Advanced Study Women and Mathematics Ambassador, Associate Member of the Sigma Xi Scientific Research Honor Society, USC CUE & CETL Faculty Equity Fellow, and Mellon Foundation grantee.
Research Interests. Arithmetic Geometry, Topos Theory
Professional Appointments. I am a mathematics lecturer at California State University, Los Angeles. I am an Assistant Professor at ArtCenter College of Design in Pasadena, California.
National and Institute Committees. I am the Section Chair-Elect of the Southern California-Nevada Section of the MAA, and Co-Organizer of the SLMath (formerly MSRI) May 12th Celebration of Women in Mathematics.
Editor. I am the Editor of the Springer-Volume: Women in MathArt: Research, Creativity, and Teaching (AWMS, Volume 34).(2024). Springer. https://link.springer.com/book/10.1007/978-3-031-66402-1
Guest Editor. I am the Lead Guest Editor of the EDGE Special Collection, Cutting EDGE Mathematics: Celebrating the 25th Anniversary of the Enhancing Diversity in Graduate Education Program, to appear in the Springer Journal, Research in the Mathematical Sciences.
Pedagogy and Scholarship. I am a strong advocate of multimodal learning, Universal Design for Learning, and making mathematics instruction universally accessible to all learners in a way that compliments their unique life circumstances, at the undergraduate and graduate level.
MathArt. I am the creator of Women, Art, and Mathematics (WAAM), a new AWM Research Network. The aim of the network is to amplify variations in mathematical thinking, and highlight research and pedagogy at the intersections of mathematics and the arts.
I explore creativity and innovation in the scholarship of teaching and learning. I survey the intersections of mathematics and continental philosophy, mathematics and neuroscience, and mathematics and the arts, primarily the literary 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
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 (2025). Fractal Cohomology of the Ternary Cantor Set, Light Condensed Fractal Cohomology, and Fractal Descent. [Doctoral dissertation, University of California, Riverside]. 300 pages.
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). 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
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://www.youtube.com/watch?v=W4lw98mVLOU
Light Condensed Fractal Cohomology, JMM 2025 AMS Special Session: Fractal Geometry with Applications to Analysis, Number Theory and Mathematical Physics, January 10, 2025
Hyperphantasia and Categorical Surprisal, 4th Applied Active Inference Symposium, Active Inference Institute, November 14, 2024. https://www.youtube.com/watch?
Phenomenology of Sick Spirit + p-adic Hyperphantasia (joint with Sonia de Jager), Too Mad to be True III: Paradoxes of Madness, October 31, 2024, Dr. Guislain Museum, Ghent, Belgium
Condensed Fractality + Fractal Cohomology, Pitzer College: MAA SoCal-Nevada Fall Sectional Meeting CPS, October 5, 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, JMM 2023 AMS Special Session: Langlands Program
Time's Homeomorphism, Bridges Math Art Poetry Reading, August 4, 2022
Geometric Langlands and Geometric Stake Equivalence, Fractal Dynamics Seminar, UCR, 2022
Condensed Sets, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2022
Perfectoid Spaces, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2021
Motivic Homotopy Theory, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2021
Infinity Categories and Factorization Homology, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2021
Crystalline Topos + Fargues-Fontaine Curve, Women in Mathematics CSUCI, September 28, 2019
My Mobius Poem
© 2022 Shanna Dobson