Amitesh Datta's user avatar
Amitesh Datta's user avatar
Amitesh Datta's user avatar
Amitesh Datta
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About

Homepage: https://amiteshdatta.wixsite.com/amitesh-datta

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 non-isotopic 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 K-theory, Differential Geometry, Algebraic Number Theory, Riemannian Geometry, Lie Groups and Lie Algebras, Spectral Sequences, Morse Theory + Homology, Symplectic + Contact Geometry, Algebraic K-theory, 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

K-theory by Atiyah

Lie Groups by Bump

Cohomology Operations by Steenrod + Epstein

Riemannian Geometry by do Carmo

Morse Theory by Milnor

Lectures on the h-corbodism theorem by Milnor

The local structure of algebraic K-theory by Dundas, Goodwillie + McCarthy

Symplectic Geometry by da Silva

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