Homepage: https://amiteshdatta.wixsite.com/amiteshdatta
My seminar talk "Does the Jones polynomial detect the unknot?": https://www.youtube.com/watch?v=cN_Kh2mfRW0
A Princeton YouTube video where a student talks about the impact of my teaching: https://www.youtube.com/watch?v=qJbvJnKYjz0
New Papers!
https://arxiv.org/abs/2303.05281 (The complete classification of isotopy classes of degree three symplectic curves in $\mathbb{CP}^2$ with a novel algebraic theory of braid monodromy (independent of Gromov's theory of pseudoholomorphic curves))
https://arxiv.org/abs/2204.13660 (A concrete and novel connection between number theory and topology: The failure of classical knot polynomials (Alexander/Jones) to distinguish nonisotopic links of braid index $3$ is measured by class numbers of quadratic number fields)
https://arxiv.org/abs/2209.10826 (A new theory to precisely characterize the entries of Burau matrices of $4$braids, which yields a strong generic faithfulness result for the Burau representation of $B_4$ (a longstanding question posed in the 1930s))
Princeton Math Faculty Page: https://web.math.princeton.edu/~amiteshd
Contact: [email protected]
I generally answer questions in these areas:
General Topology, Finite Group Theory, Ring theory, Galois theory, Measure Theory, Functional Analysis, Complex Analysis, Fourier Analysis, Algebraic Geometry, Algebraic Topology, Topological Ktheory, Differential Geometry, Algebraic Number Theory, Riemannian Geometry, Lie Groups and Lie Algebras, Spectral Sequences, Morse Theory + Homology, Symplectic + Contact Geometry, Algebraic Ktheory, Topological Quantum Field Theory
I have read substantial parts of the following books and recommend them (the list is not exhaustive):
Principles of Mathematical Analysis by Rudin
Topology: A First Course by Munkres
Algebra: A Graduate Course by Isaacs
Real and Complex Analysis by Rudin
Linear Algebra Done Right by Axler
An Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby
Elements of Algebraic Topology by Munkres
Finite Group Theory by Isaacs
Topics in Algebra by Herstein
Algebraic Number Fields by Janusz
Introduction to Commutative Algebra by Atiyah + Macdonald
Algebraic Geometry: A First Course by Harris
Algebraic Geometry by Hartshorne
Algebraic Geometry and Arithmetic Curves by Liu
Classical Fourier Analysis by Grafakos
Finite Dimensional Vector Spaces by Halmos
Problems in Algebraic Number Theory by Esmonde + Murty
Analysis on Manifolds by Munkres
Noncommutative Rings by Herstein
Ktheory by Atiyah
Lie Groups by Bump
Cohomology Operations by Steenrod + Epstein
Riemannian Geometry by do Carmo
Morse Theory by Milnor
Lectures on the hcorbodism theorem by Milnor
The local structure of algebraic Ktheory by Dundas, Goodwillie + McCarthy
Symplectic Geometry by da Silva

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