Alexander Grothendieck, later Alexandre Grothendieck in French was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century.
Vladimir Alexandrovich Voevodsky was a Russian-American mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. He is also known for the proof of the Milnor conjecture and motivic Bloch–Kato conjectures and for the univalent foundations of mathematics and homotopy type theory.
Samuel Eilenberg was a Polish-American mathematician who co-founded category theory and homological algebra.
Daniel Gray Quillen was an American mathematician. He is known for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.
Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry.
William Browder is an American mathematician, specializing in algebraic topology, differential topology and differential geometry. Browder was one of the pioneers with Sergei Novikov, Dennis Sullivan and C. T. C. Wall of the surgery theory method for classifying high-dimensional manifolds. He served as president of the American Mathematical Society until 1990.
Dennis Parnell Sullivan is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the Graduate Center of the City University of New York and is a distinguished professor at Stony Brook University.
John Coleman Moore was an American mathematician. The Borel−Moore homology and Eilenberg–Moore spectral sequence are named after him.
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.
Douglas Conner Ravenel is an American mathematician known for work in algebraic topology.
Charles Alexander Weibel is an American mathematician working on algebraic K-theory, algebraic geometry and homological algebra.
In mathematics, especially in algebraic geometry, the étale homotopy type is an analogue of the homotopy type of topological spaces for algebraic varieties.
Jonathan Micah Rosenberg is an American mathematician, working in algebraic topology, operator algebras, K-theory and representation theory, with applications to string theory in physics.
David Archibald Cox is a retired American mathematician, working in algebraic geometry.
Ralph Louis Cohen is an American mathematician, specializing in algebraic topology and differential topology.
In mathematics, and in particular homotopy theory, a hypercovering is a simplicial object that generalises the Čech nerve of a cover. For the Čech nerve of an open cover , one can show that if the space is compact and if every intersection of open sets in the cover is contractible, then one can contract these sets and get a simplicial set that is weakly equivalent to in a natural way. For the étale topology and other sites, these conditions fail. The idea of a hypercover is to instead of only working with -fold intersections of the sets of the given open cover , to allow the pairwise intersections of the sets in to be covered by an open cover , and to let the triple intersections of this cover to be covered by yet another open cover , and so on, iteratively. Hypercoverings have a central role in étale homotopy and other areas where homotopy theory is applied to algebraic geometry, such as motivic homotopy theory.
Marc N. Levine is an American mathematician.
Charles Waldo Rezk is an American mathematician, specializing in algebraic topology and category theory.
Aldridge Knight Bousfield, known as "Pete", was an American mathematician working in algebraic topology, known for the concept of Bousfield localization.
Dan Burghelea is a Romanian-American mathematician, academic, and researcher. He is an Emeritus Professor of Mathematics at Ohio State University.
