Hi, I'm Daniel! I love to think about math ∪ computer science ∪ physics.
In my academic career, I conducted research in quantum algebra, a beautiful field that explores
and draws connections between representation theory, low-dimensional topology, combinatorics, non-commutative
algebra/geometry, and quantum field theory.
I'm also very interested in learning algorithms! I like to study these in part to understand the differences
between classical and quantum computation.
Feel free to contact me at daniel.copeland@gmail.com.
I completed my PhD in mathematics in 2020 at UC San Diego, under the supervison of Hans Wenzl.
The main result is a classification of ribbon categories with certain tensor product rules.
Take a look here:
Classification of ribbon categories with the fusion rules of SO(N)
Defense presentation
Also, check out the thesis errata. [coming one day...]
10.23.2021 On the semisimplicity of braid group representations in braided tensor categories
AMS special session, virtual.
2.26.2021 Oracle Comparison and Simulation, David Meyer's discrete physics meeting, UCSD.
1.11.2018 Quantum query complexity of symmetric problems, AMS special session at JMM, San Diego CA.
11.4.2017 Classification of ribbon categories with SO(N) fusion rules, AMS Fall Western Sectional Meeting, Riverside CA.
6.3.2017 Endomorphism algebras in tensor categories of Lie type, NSF West Coast Lie Theory Workshop, San Diego CA.
11.14.2016 Improve your learning with a quantum computer!, Food for thought seminar, UCSD.
1. Classification of pivotal tensor categories with fusion rules related to SO(4), with Cain Edie-Michell. Journal of Algebra, volume 619, April 1 2023.
2. Quantum query complexity of symmetric oracle problems, with Jamie Pommersheim. Quantum, volume 6, p. 403, 2021.
3. Single-query quantum algorithms for symmetric problems, with Orest Bucicovschi, David Meyer, and Jamie Pommersheim. Quantum Information and Computation, volume 16, p. 19-38, 2016.
The Multivariable Alexander Polynomial and Thurston Norm Eötvös Loránd Tudományegyetem, M.Sc. thesis, 2014.
Advisor: András Stipsicz.
Quantum State Discrimination and Concept Learning. Reed College B.A. thesis, 2011.
Advisor: Jamie Pommersheim.
A nice tetrahedron.
Some notes on TQFTs, string net models, topological quantum computation:
Overview,
Turaev-Viro as a 3-2-1 TQFT,
Toric code as an instance of Turaev-Viro