Alexander Grothendieck was a 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.
In mathematics, topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
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.
Sergei Petrovich Novikov is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. In 1970, he won the Fields Medal.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act.
The Morgan Prize is an annual award given to an undergraduate student in the US, Canada, or Mexico who demonstrates superior mathematics research. The $1,200 award, endowed by Mrs. Frank Morgan of Allentown, Pennsylvania, was founded in 1995. The award is made jointly by the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. The Morgan Prize has been described as the highest honor given to an undergraduate in mathematics.
Segal's Burnside ring conjecture, or, more briefly, the Segal conjecture, is a theorem in homotopy theory, a branch of mathematics. The theorem relates the Burnside ring of a finite group G to the stable cohomotopy of the classifying space BG. The conjecture was made in the mid 1970s by Graeme Segal and proved in 1984 by Gunnar Carlsson. As of 2016, this statement is still commonly referred to as the Segal conjecture, even though it now has the status of a theorem.
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.
In mathematics, Sullivan conjecture or Sullivan's conjecture on maps from classifying spaces can refer to any of several results and conjectures prompted by homotopy theory work of Dennis Sullivan. A basic theme and motivation concerns the fixed point set in group actions of a finite group . The most elementary formulation, however, is in terms of the classifying space of such a group. Roughly speaking, it is difficult to map such a space continuously into a finite CW complex in a non-trivial manner. Such a version of the Sullivan conjecture was first proved by Haynes Miller. Specifically, in 1984, Miller proved that the function space, carrying the compact-open topology, of base point-preserving mappings from to is weakly contractible.
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools.
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.
Matthias Kreck is a German mathematician who works in the areas of Algebraic Topology and Differential topology. From 1994 to 2002 he was director of the Oberwolfach Research Institute for Mathematics and from October 2006 to September 2011 he was the director of the Hausdorff Center for Mathematics at the University of Bonn, where he is currently a professor.
Haynes Robert Miller is an American mathematician specializing in algebraic topology.
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.
Guoliang Yu is a Chinese American mathematician. After receiving his Ph.D from SUNY at Stony Brook in 1991 under the direction of Ronald G. Douglas, Yu spent time at the Mathematical Sciences Research Institute (1991–1992), the University of Colorado at Boulder (1992–2000), Vanderbilt University (2000–2012), and a variety of visiting positions. He currently holds the Powell Chair in Mathematics and was appointed University Distinguished Professor in 2018 at Texas A&M University. He is a fellow of the American Mathematical Society.
Ralph Louis Cohen is an American mathematician, specializing in algebraic topology and differential topology.
Wu-Chung Hsiang is a Taiwanese-American mathematician, specializing in topology. Hsiang served as chairman of the Department of Mathematics at Princeton University from 1982 to 1985 and was one of the most influential topologists of the second half of the 20th century.
Richard James Milgram is an American mathematician, specializing in algebraic topology. He is the son of mathematician Arthur Milgram.
Dan Burghelea is a Romanian-American mathematician, academic, and researcher. He is an Emeritus Professor of Mathematics at Ohio State University.
