I am a PhD Candidate in Mathematics 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, 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, Category Theory, 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 of the Southern California-Nevada Section of the MAA, Associate Editor of the Anneli Lax New Mathematical Library, President of the AWM Chapter at UCR, 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 Chair of the AWM-MAA Liaison Committee, and former Member of the MathFest and SIGMAA MAA Committees.
I am Chair of the Faculty Council Committee at ArtCenter College of Design. I am the Co-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 2024 Scientific Advisory Board at the Active Inference Institute. I am the creator and facilitator of the MathArt Conversations Educational Project.
Pedagogy and Scholarship I am a strong advocate of multimodal learning, UDL, 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 a new AWM Research Network called Women, Art, and Mathematics (WAAM). 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.
Organization: Upcoming Conferences Lead Organizer: JMM 2025 AMS Special Session: Rethinking Number Theory: Highlighting the Research of the RNT Workshops; Lead Organizer: JMM 2025 AWM Special Session: Exploring Mathematics through the Arts and Pedagogy in Creative Settings
Selected Articles/Preprints
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.
Manrique, Hector M., Dobson, Shanna, and Walker, Michael J. (2024). "Time-warps," PsyArXiv. https://doi.org/10.31234/osf.io/2yvja
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. In press. arXiv:2401.06250 [math.NT]
Dobson, Shanna (2024). Categorical Colors in Diamonds: Sight as Site: Categorical Ozma and Cinderella, Women in MathArt, Springer. In press. https://philpapers.org/rec/DOBCCI
Dobson, Shanna (2024). Mathematical Clerihews, Bridges Clerihew Collection: Journal of Humanistic Mathematics. In press.
Dobson, Shanna, Lutken E.R. (2024). To Look on Beauty Bare: Mathematics as Metaphor in Poetry, Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture.
Dobson, Shanna, 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). Literary Incarnations of Topology, Cross-Curricular Pure Math Applications, MAA Notes.
Dobson, Shanna (2023). Dark Imaginarium: Infinity-Curiosity, https://philpapers.org/rec/DOBDII
Dobson, Shanna, and Scaff, Julian (2023). Qurio: Meta-Learning Curiosity Algorithm and Agentive AI Tutor: Women in MathArt, Springer. In press.
Dobson, Shanna, and Prentner, Robert (2023). Artistic Mediation in Mathematical Phenomenology: Women in MathArt, Springer. In press.
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, Springer. In press.
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, Springer. In press.
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
Derived Enhancement of Fractal Geometry, JMM 2025 AMS Special Session: Fractal Geometry with Applications to Analysis, Number Theory and Mathematical Physics, January 10, 2025
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 Stream 1, Active Inference Institute, May 17, 2024 https://www.youtube.com/watch?v=9DNxiBDYLzg
MathArt Conversations: MathArt Stream 2, Active Inference Institute, May 24, 2024 https://www.youtube.com/watch?v=XQKjFV-pCXQ&t=3s
MathArt Conversations: MathArt Stream 3, Active Inference Institute, May 31, 2024 https://www.youtube.com/watch?v=WnC3mZ1TAxk
MathArt Conversations: MathArt Stream 5, Active Inference Institute, July 26, 2024 https://www.youtube.com/watch?v=MUcsN43HPoI
MathArt Conversations: MathArt Stream 6, Active Inference Institute, August 2, 2024 https://www.youtube.com/watch?v=qDilepcGCNs
Functorial Harp and 2-Category of Complex Dimensions, Fractal Analysis & Mathematical Physics Seminar, UCR, May 2024
The Chronicles of Fractal Geometry: Fractal Strings, and Functorial Harps, Pomona College, Claremont Colleges, April 2024
Diamond Fractal, WiMSoCal 2024, Pomona College, the Claremont Colleges, February 2024
Intuition and MathArt in Mathematics Graduate Curriculum: Multimodal Learning, RUME, February 2024
Diamond Fractal & the Moduli Space of Fractals, Fractal Analysis & 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, Fractal Analysis & Mathematical Physics Seminar, UCR, 2023
Six Operations on Topos and Infinity-Categorical Adjunction Theorem for Topoi, Fractal Analysis Seminar, UCR, 2023
Moduli Space of Fractals and Modular Flow of Zeta Functions: a Comprehensive Review, Fractal Analysis Seminar, UCR, 2023
Six Operations on Diamond Topos, JMM 2023 AMS Special Session: Langlands Program
Coniveau Spectral Sequence, Fractal Analysis & Mathematical Physics Seminar, UCR, 2023
MathArt Deconstruction, Active Inference Institute https://www.youtube.com/watch?
K-Theory of Schemes, Fractal Analysis & 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 Analysis Seminar, UCR, 2022
Geometric Langlands and Geometric Stake Equivalence: A Comprehensive Review, Fractal Analysis Seminar, UCR, 2022
Modular Curves at Infinite Level and Perfectoid Modular Curves, Fractal Analysis Seminar, UCR, 2022
Condensed Sets: a Comprehensive Review, Fractal Analysis & Mathematical Physics Seminar, UCR, 2022
Perfectoid Spaces: a Comprehensive Review, Fractal Analysis & Mathematical Physics Seminar, UCR, 2021
M-Theory and F-Theory: a Review, Fractal Analysis & Mathematical Physics Seminar, UCR
Motivic Homtopy Theory: a Review, Fractal Analysis & Mathematical Physics Seminar, UCR
Geometric Langlands and Mirror Symmetry: a Comprehensive Review, Fractal Analysis & Mathematical Physics Seminar, UCR, 2021
Infinity Categories and Factorization Homology: a Comprehensive Review, Fractal Analysis & 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