I recently 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 Adjunct Assistant Professor of mathematics at ArtCenter College of Design in Pasadena, California.
National and Institute Committees. I am the Past Section Chair of the Southern California-Nevada Section of the MAA, Associate Editor of the Anneli Lax New Mathematical Library, Member at Large of the AMS Committee on Meetings and Conferences, and Co-Organizer of the SLMath (formerly MSRI) May 12th Celebration of Women in Mathematics. I am the former Section Chair of the Southern California-Nevada Section of the MAA, the former Chair of the AWM-MAA Liaison Committee, former Member of the MathFest and SIGMAA MAA Committees, and former President of the AWM Chapter at UCR.
I am Chair of the Faculty Council at ArtCenter College of Design. I am a member of the Executive Cabinet's Strategic Plan Steering Committee. I am the creator of the Faculty Institute at ArtCenter College of Design, and the Co-Creator of the Redesigning the Future Series.
I am a Member of the 2025 Scientific Advisory Board at the Active Inference Institute. I was a Member of the 2024 Scientific Advisory Board at the Active Inference Institute.I am the creator and facilitator of the MathArt Conversations Educational Project.
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.
I am a Co-Organizer (with Dr. Igor Nikolaev) of the AMS Special Session on Representations of p-adic Groups and Noncommutative Geometry, for the AMS 2025 Fall Eastern Sectional Meeting.
I am the Lead Organizer of the AMS Special Session on New Horizons for Quantum Error Correction: Categorical Approaches to Topological Codes, for the AMS 2025 Fall Eastern Sectional Meeting.
I was the Lead Organizer of the JMM 2025 AMS Special Session: Rethinking Number Theory: Highlighting the Research of the RNT Workshops. I was the Lead Organizer of the JMM 2025 AWM Special Session: Exploring Mathematics through the Arts and Pedagogy in Creative Settings. I was a Co-Organizer of the 4th Applied Active Inference Symposium.
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]. UCR, eScholarship. (300 pages)
Chehade, Sarah, Dobson, Shanna, and Pandey, Tushar (2025). Topological Quantum Error Correction: Theory to Implementation. Research in the Mathematical Sciences. In preparation.
Cannizzo, Catherine, Dobson, Shanna, and Parker, Matthew (2024). Positionality in Research in Graduate Mathematics Education with an Application Toward Symplectic Geometry. For the Learning of Mathematics. 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). 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 (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/clrm-72
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.bridgesmathart.org/2024/bridges2024-581.html#gsc.tab=0
Dobson, Shanna (2024). Categorical Colors in Diamonds: Sight as Site: Categorical Ozma and Cinderella. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 159-171. (doi:10.1007/978-3-031-66402-1_1).
Manrique, Hector M., Dobson, Shanna, and Walker, Michael J. (2024). Time-warps, PsyArXiv. https://doi.org/10.31234/osf.io/2yvja
Dobson, Shanna, and Zhong Jim (2024). Categorical Mental Imagery: Visualizing the 4th Spatial Dimension. https://philarchive.org/rec/DOBVTT
Dobson, Shanna (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.plrev.2023.10.032
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. (doi:10.1007/978-3-031-66402-1_1).
Dobson, Shanna, and Prentner, Robert (2023). Artistic Mediation in Mathematical Phenomenology. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 81-92. (doi:10.1007/978-3-031-66402-1_1).
Dobson, Shanna, and Scaff, Julian (2023). Quantum Intrinsic Curiosity Algorithms, https://philarchive.org/rec/DOBQIC
Dobson, Shanna, and Fields, Chris (2022). Making Up Our Minds: Imaginative Deconstruction in MathArt, 1920 – Present. Women in MathArt: Research, Creativity, and Teaching (AWMS Vol. 34). Dobson, Shanna (Ed.) (2024). Springer, pp. 1-21. (doi:10.1007/978-3-031-66402-1_1).
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. (doi:10.1007/978-3-031-66402-1_1).
Dobson, Shanna (2021). Curating Metacognitive Conversations to Address Imposter Syndrome, Read to Learn Cal State LA Practitioner Perspectives https://readtolearn.calstate.edu/practitioner-perspectives.
Dobson, Shanna (2021). Sophie Germain: Revolutionary Mathematician, AWM Book Review.
Selected Talks
Diamonds in the Langlands Program, NSF-CBMS Conference: Representations of p-adic Groups and Noncommutative Geometry, June 9-13, 2025.
Fractal Cohomology of the Ternary Cantor Set, Light Condensed Fractal Cohomology, and Fractal Descent, Dissertation Defense, UCR, May 12, 2025.
Fractal Descent and Light Condensed Fractal Cohomology, AMS 2025 Spring Western Sectional Meeting Special Session: Fractal Geometry and Complex Dynamics, May 3, 2025
Fractal Cohomology of the Ternary Cantor Set, its Complete Characterization, and Fractal Descent, Fractal Dynamics & Mathematical Physics Seminar, UCR, April 24, 2025
Diamond Decembris + Mathart, Women's History Month: Women in Mathematics, Cal State LA, March 22, 2025 https://www.calstatela.edu/calendar/women-mathematics
Fractal Motive + Fractal Descent II, Fractal Dynamics & Mathematical Physics Seminar, UCR, March 14, 2025
Categorical Enhancement of Fractal Cohomology to Profinite Sets, Inland Empire Math Summit, California State University, San Bernadino, March 8, 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
Towards a Complete Condensed Characterization of Fractal Cohomology, Fractal Dynamics & Mathematical Physics Seminar, UCR, February 6, 2025
Fractal Descent I, Fractal Dynamics & Mathematical Physics Seminar, UCR, January 23, 2025
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 Phantasia, JMM 2025 AWM Special Session: Exploring Mathematics Through the Arts and Pedagogy in Creative Settings, January 9, 2025.
Quantum Weirdness, Palm Springs Art Museum: Mixed Feelings Public Lecture Series, December 7, 2024
Hyperphantasia and Categorical Surprisal, 4th Applied Active Inference Symposium, Active Inference Institute, November 14, 2024. https://www.youtube.com/watch?
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 & Mathematical Physics Seminar, UCR, November 7, 2024
Condensed Fractality + Fractal Cohomology, Pitzer College: MAA SoCal-Nevada Fall Sectional Meeting CPS, October 5, 2024
Condensed Enhancement of the Extended Theory of Fractality, Fractal Dynamics Seminar, UCR, October 3, 2024
Mathematical Creativity, Research in Graduate Mathematics Education Seminar, Virginia Tech, July 29, 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
MathArt Conversations: MathArt Streams 1-8, Active Inference Institute, May 17, 2024 - December 31, 2024
https://www.youtube.com/watch?v=9DNxiBDYLzg&list=PLNm0u2n1Iwdp8i_e24LKV2DJWZKfW9Jrl&index=7
Functorial Harp and 2-Category of Complex Dimensions, Fractal Dynamics & Mathematical Physics Seminar, UCR, May 2024
The Chronicles of Fractal Geometry: Fractal Strings, and Functorial Harps, Claremont Colleges Analysis Seminar, Pomona College, April 2024
Diamond Fractal, WiMSoCal 2024, Pomona College, the Claremont Colleges, February 2024
Intuition and MathArt in Mathematics Graduate Curriculum: Multimodal Learning, Research in Graduate Mathematics Education Conference, February 2024
Diamond Fractal & the Moduli Space of Fractals, Fractal Dynamics & Mathematical Physics Seminar, UCR, January 2024
K-Theoretic Time Crystals, JMM 2024 AMS Special Session: Mathematical Physics & Future Directions, January 2024
Diamond Fractal: Geometric Oscillations as Profinite Reflections, Dynamics & Mathematical Physics Seminar, UCR, 2023
Six Operations on Topos and Infinity-Categorical Adjunction Theorem for Topoi, Fractal Dynamics Seminar, UCR, 2023
Moduli Space of Fractals and Modular Flow of Zeta Functions: a Comprehensive Review, Fractal Dynamics Seminar, UCR, 2023
Six Operations on Diamond Topos, JMM 2023 AMS Special Session: Langlands Program
Coniveau Spectral Sequence, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2023
MathArt Deconstruction, Active Inference Institute https://www.youtube.com/watch?
K-Theory of Schemes, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2023
Special Primes, Rethinking Number Theory, 2023
Diamond Langlands Functoriality, UCR Grad Slam Competition https://www.youtube.com/watch?
Six Operations on Topos, West Coast Number Theory, 2022
Langlands Correspondence and Conformal Field Theory: A Comprehensive Review, Fractal Dynamics Seminar, UCR, 2022
Geometric Langlands and Geometric Stake Equivalence: A Comprehensive Review, Fractal Dynamics Seminar, UCR, 2022
Modular Curves at Infinite Level and Perfectoid Modular Curves, Fractal Dynamics Seminar, UCR, 2022
Condensed Sets: a Comprehensive Review, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2022
Perfectoid Spaces: a Comprehensive Review, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2021
M-Theory and F-Theory: a Review, Fractal Dynamics & Mathematical Physics Seminar, UCR
Motivic Homotopy Theory: a Review, Fractal Dynamics & Mathematical Physics Seminar, UCR
Geometric Langlands and Mirror Symmetry: a Comprehensive Review, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2021
Infinity Categories and Factorization Homology: a Comprehensive Review, Fractal Dynamics & Mathematical Physics Seminar, UCR, 2021
Crystalline Topos + Fargues-Fontaine Curve, Women in Mathematics CSUCI https://www.youtube.com/watch?
Selected MathArt Works
Mathematical Poetry
Time's Homeomorphism @Shanna Dobson 2022
Mathematical Clerihews @Shanna Dobson 2023
Alexander Grothendieck
Crystalline motivic chic
Became a universal topos
Dandelion erose
My Mobius Poem
© 2022 Shanna Dobson
My Klein Bottle Poem
© 2022 Shanna Dobson
The concept of sidedness
Enchants my mindedness
Must language have a side?
I am enchanted by
Dimensionality.
How wonderfully peculiar it must be
To be realized a dimension higher.
Fantastical Fiction Novels
The Artemis Chronicles of Imaginarium @Shanna Dobson 2021 - 2024
Mathematical Plays
A Unicorn's Infinity-Christmas: Christmas Eve at the Imaginarium Institute, @Shanna Dobson 2021
Cinderella Ozma @Shanna Dobson 2021
Community Events
5/10/24: SL Math Celebration of Women in Mathematics
1/21/24: SoCal-Nevada MAA Section: Welcome Back Event at the American Institute of Mathematics (AIM Caltech)
12/13/23: A Winter Evening of Mathematical Holiday Poetry