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.
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Famous quotes containing the word work:
“The best work of artists in any age is the work of innocence liberated by technical knowledge. The laboratory experiments that led to the theory of pure color equipped the impressionists to paint nature as if it had only just been created.”
—Nancy Hale (b. 1908)
“when I work I am pure as an angel
tiger and clear is my eye and hot
my brain and silent all the whining
grunting piglets of the appetites.”
—Marge Piercy (b. 1936)
“Writing a book I have found to be like building a house. A man forms a plan, and collects materials. He thinks he has enough to raise a large and stately edifice; but after he has arranged, compacted and polished, his work turns out to be a very small performance. The authour however like the builder, knows how much labour his work has cost him; and therefore estimates it at a higher rate than other people think it deserves,”
—James Boswell (1740–1795)