Work
Borcherds is best known for his work connecting the theory of finite groups with other areas in mathematics. In particular he invented the notion of vertex algebras, which Igor Frenkel, James Lepowsky and Arne Meurman used to construct an infinite-dimensional graded algebra acted on by the monster group. Borcherds then used this, and methods from string theory, to prove the monstrous moonshine conjecture by Conway and Norton, relating the monster group to the coefficients of the q-expansion of the j-invariant. The result was not only a great increase in understanding of the monster group, a very large finite simple group whose structure was previously not well understood, but tied the monster to various aspects of mathematics and mathematical physics. In recent years, Borcherds has been attempting to construct quantum field theory in a mathematically rigorous manner.
Read more about this topic: Richard Borcherds
Famous quotes containing the word work:
“If therefore my work is negative, irreligious, atheistic, let it be remembered that atheism—at least in the sense of this work—is the secret of religion itself; that religion itself, not indeed on the surface, but fundamentally, not in intention or according to its own supposition, but in its heart, in its essence, believes in nothing else than the truth and divinity of human nature.”
—Ludwig Feuerbach (1804–1872)
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—“Seumas” “O’Sullivan” (1879–1958)