01
Applied Mathematics
Geometric and matrix-based methods for nonlinear mathematical structures motivated by applications, including constructions related to relativity.
Aritra
Roy
Ph.D. candidate in Mathematics at North Dakota State University working at the intersection of applied mathematics, matrix geometry, and Riemannian geometry, with emphasis on rotation-invariant metrics, generalized Einstein and Möbius operations, pullback metrics, and geometric structures on matrix balls.
About
Mathematics shaped by geometry and structure.
Academic Profile
I am a doctoral researcher in Mathematics at North Dakota State University. I completed my master's degree in Mathematics at Jadavpur University, India, and my bachelor's degree in Mathematics at the University of Calcutta, India.
Research Perspective
My work develops mathematical frameworks for nonlinear matrix spaces by combining geometric, algebraic, and analytic ideas. I am especially interested in how symmetry, invariant structures, and matrix operations can be used to study models motivated by applied mathematics and relativity.
Research
Current research interests
My research lies broadly in applied mathematics, with a particular focus on linear algebra, matrix geometry, and Riemannian methods for nonlinear matrix spaces. I study rotation-equivariant binary operations, invariant metric tensors, pullback constructions, and curvature on matrix balls.
02
Linear Algebra Tools
Linear-algebraic methods including singular-value decompositions, matrix analysis, block structures, and matrix transformations used in the study of matrix-ball geometry.
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Matrix Geometry
Geometric structures and nonlinear operations defined on matrix domains and matrix balls.
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Riemannian Geometry
Metric tensors, geodesics, Christoffel symbols, parallel transport, and sectional curvature.
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Invariant Metrics
Rotation-invariant metric structures under transformations of the form U₁VU₂ᵀ.
06
Einstein Addition
Extensions of Einstein-type nonlinear addition from scalar and vector settings to matrices.
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Möbius Operations
Matrix analogues of Möbius addition and geometric comparisons with Einstein structures.
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Sectional Curvature
Curvature behavior of two-dimensional tangent planes at general points of the matrix ball and conditions for constant curvature.
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Metric Tensor Parametrization
Invariant-coefficient and block parametrizations of rotation-invariant Riemannian metric tensors, including positivity and singular-value compatibility conditions.
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Pullback Metrics
Pullback transformations of Riemannian metrics under rotation-equivariant maps and their relationship with isomorphisms of matrix-ball binary operations.
Research Papers & Manuscripts
Submitted and ongoing work
Current manuscripts developing the algebraic and Riemannian geometry of matrix-ball operations.
Under Review 01
A representation of Einstein Addition in Matrix Ball
Nikita Barabanov and Aritra Roy. Submitted to the Journal of Differential Geometry, June 2026; currently under review.
Under Review 02
A Parametrization of Metric Tensors Generated by Invariant Binary Operations on Matrix Balls
Aritra Roy and Nikita Barabanov. Submitted to Linear Algebra and its Applications, September 2026; currently under review.
WIP 01
Rotation-Invariant Riemannian Metrics and Isomorphisms on Matrix Balls
Classification of invariant metrics, equivariant transformations, and geometric equivalence of Einstein- and Möbius-type matrix structures.
WIP 02
Pullback Metrics and Rotation-Equivariant Binary Operations on Matrix Balls
Rotation-equivariant maps between matrix-ball operations and pullback transformations of their associated Riemannian metrics.
WIP 03
Sectional Curvature of the Matrix Einstein Metric
Sectional-curvature formulas at general points and conditions under which constant sectional curvature may or may not occur.
Teaching
Teaching mathematics through clarity and practice.
I emphasize structured problem solving, active participation, and accessible explanations of abstract concepts.
MATH 166
Calculus II
Instructor of record: Summer 2024. Teaching Assistant: Fall 2023–Spring 2025. Supported instruction in integration techniques, sequences and series, and applications of calculus.
MATH 128
Introduction to Linear Algebra
Instructor of record: Spring 2025, Fall 2025, Spring 2026, and Fall 2026. Responsible for classroom instruction, student support, assessment, and course problem solving.
MATH 129
Introduction to Linear Algebra
Instructor of record: Summer 2025.
MATH 259
Multivariable Calculus
Teaching Assistant: Spring 2025 and Spring 2026. Led independent class sessions and prepared weekly worksheets, formula guides, and active problem-solving activities.
MATH 165
Calculus I
Teaching Assistant: Spring 2021–Spring 2023 and Fall 2025. Supported student learning through class instruction, collaborative problem solving, office hours, and individualized assistance.
Curriculum Vitae
Research, teaching, and academic experience.
View or download my current academic CV, including research, manuscripts, teaching experience, conferences, and academic service.
Contact
Let’s connect.
For research discussions, postdoctoral opportunities, teaching, or collaboration, please feel free to contact me.