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D. Gepner, V. Snaith, On the motivic spectra representing algebraic cobordism and algebraic K-theory, Doc. Math., 14:359–396 (electronic), 2009, pdf

Snaith’s self-description of research is as follows:

My research interests include algebraic K-theory, algebraic topology, algebraic geometry, number theory and representation theory of groups. These subjects are all closely linked together and I am inclined to use the techniques from one to solve problems in another. For example, the idea of cohomology runs through all these topics, even though cohomology and homology were first developed in the context of algebraic topology. Here is another example: stable homotopy theory is a part of algebraic topology but back in 1985/6 I used it to find a canonical, explicit form of an existence result in representation theory called Brauer’s Induction Theorem. My formula, called Explicit Brauer Induction, solved a problem posed by Brauer when he discovered his famous result in 1946.

Similarly algebraic K-theory, as developed by Quillen in 1973, is a powerful topological mathematical gadget for studying algebraic geometry which in turn is used in many of the recent advances in number theory such as Wiles’s proof of Fermat’s Last Theorem. Incidentally the application of algebraic geometry to number theory is called arithmetic-algebraic geometry.