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Title | Home | Matthew |
Description | Repository of writings of Matthew McMillan, mathematician and philosopher, currently finishing a math PhD at |
Keywords | Matthew McMillan, Mathematics, math papers, Philosophy, writings, Leibniz, Analysis Situs, Leibniz translations |
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Matthew McMillan Leibniz Research Essays Home Contact Home Mathematics • Philosophy • Language --> I am a PhD student in mathematics at UCLA, studying under Raphaёl Rouquier, graduating in June. This year I am a visiting student at UVA, working with You Qi and writing my thesis. Math I design algebraic machinery that aims to classify the smooth-topological phenomena discovered with PDE-based manifold invariants (i.e., gauge theory) that emerged originally from quantum field theory and string theory. These phenomena were discovered using analysis, but in order to understand them we must use algebra. In one project, we hope to provide a totally new construction of Khovanov homology using Rouquier’s proposal for a tensor 2-product of 2-representations of Kac-Moody algebras. This is part of a program to build a non-trivial TQFT in dimension 4 using ‘higher representation theory’. In a second project, I am developing a theory of quantum group asymptotics for |q| ≪ 1. I hope it will |
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