Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
David Bryant Mumford is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science. He is currently a University Professor Emeritus in the Division of Applied Mathematics at Brown University.
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.
Sir Vaughan Frederick Randal Jones was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990.
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
Nicholas Michael Katz is an American mathematician, working in arithmetic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. He is currently a professor of Mathematics at Princeton University and an editor of the journal Annals of Mathematics.
John K. S. McKay was a British-Canadian mathematician and academic who worked at Concordia University, known for his discovery of monstrous moonshine, his joint construction of some sporadic simple groups, for the McKay conjecture in representation theory, and for the McKay correspondence relating certain finite groups to Lie groups.
Hyman Bass is an American mathematician, known for work in algebra and in mathematics education. From 1959 to 1998 he was Professor in the Mathematics Department at Columbia University. He is currently the Samuel Eilenberg Distinguished University Professor of Mathematics and Professor of Mathematics Education at the University of Michigan.
Dorian Morris Goldfeld is an American mathematician working in analytic number theory and automorphic forms at Columbia University.
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and D. H. Smith.
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
John Robert Stallings Jr. was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.
Norman Linstead Biggs is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.
Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.
Nolan Russell Wallach is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the 2-volume treatise Real Reductive Groups.
I. Martin "Marty" Isaacs is a group theorist and representation theorist and professor emeritus of mathematics at the University of Wisconsin–Madison. He currently lives in Berkeley, California and is an occasional participant on MathOverflow.
Aleksei Nikolaevich Parshin was a Russian mathematician, specializing in arithmetic geometry. He is most well-known for his role in the proof of the Mordell conjecture.
Sergei Aleksandrovich Stepanov is a Russian mathematician, specializing in number theory. He is known for his 1969 proof using elementary methods of the Riemann hypothesis for zeta-functions of hyperelliptic curves over finite fields, first proved by André Weil in 1940–1941 using sophisticated, deep methods in algebraic geometry.
The Colloquium Lecture of the American Mathematical Society is a special annual session of lectures.
