Richard Ehrenborg | |
---|---|
Nationality | Swedish |
Alma mater | Massachusetts Institute of Technology |
Scientific career | |
Fields | Mathematics |
Institutions | University of Kentucky |
Thesis | Combinatorial methods in multilinear algebra (1993) |
Doctoral advisor | Gian-Carlo Rota |
Website | https://www.ms.uky.edu/~jrge/ |
Richard Ehrenborg is a Swedish mathematician working in algebraic combinatorics. [1] He is known for developing the quasisymmetric function of a poset. [2] He currently holds the Ralph E. and Norma L. Edwards Research Professorship at the University of Kentucky [3] and is the first recipient of the Royster Research Professor at University of Kentucky. [4]
Ehrenborg earned his Ph.D. from MIT in 1993 [5] under the supervision of Gian-Carlo Rota. He is a descendant of another Richard Ehrenborg , [3] (born 1655) who was a professor and Rektor of Lund University. He is also a juggler and magician. [6]
In point-set topology, the composant of a point p in a continuum A is the union of all proper subcontinua of A that contain p. If a continuum is indecomposable, then its composants are pairwise disjoint. The composants of a continuum are dense in that continuum.
In category theory, string diagrams are a way of representing morphisms in monoidal categories, or more generally 2-cells in 2-categories.
In number theory, the Stark conjectures, introduced by Stark and later expanded by Tate (1984), give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number. When K/k is an abelian extension and the order of vanishing of the L-function at s = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units. Rubin (1996) and Cristian Dumitru Popescu gave extensions of this refined conjecture to higher orders of vanishing.
André Joyal is a professor of mathematics at the Université du Québec à Montréal who works on category theory. He was a member of the School of Mathematics at the Institute for Advanced Study in 2013, where he was invited to join the Special Year on Univalent Foundations of Mathematics.
In algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different dimensions and allows one to express the Dehn–Sommerville equations in a particularly simple form. A characterization of the set of h-vectors of simplicial polytopes was conjectured by Peter McMullen and proved by Lou Billera and Carl W. Lee and Richard Stanley (g-theorem). The definition of h-vector applies to arbitrary abstract simplicial complexes. The g-conjecture stated that for simplicial spheres, all possible h-vectors occur already among the h-vectors of the boundaries of convex simplicial polytopes. It was proven in December 2018 by Karim Adiprasito.
The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era.
In mathematics, a Rota–Baxter algebra is an associative algebra, together with a particular linear map R which satisfies the Rota–Baxter identity. It appeared first in the work of the American mathematician Glen E. Baxter in the realm of probability theory. Baxter's work was further explored from different angles by Gian-Carlo Rota, Pierre Cartier, and Frederic V. Atkinson, among others. Baxter’s derivation of this identity that later bore his name emanated from some of the fundamental results of the famous probabilist Frank Spitzer in random walk theory.
In mathematics, the plactic monoid is the monoid of all words in the alphabet of positive integers modulo Knuth equivalence. Its elements can be identified with semistandard Young tableaux. It was discovered by Donald Knuth (1970), using an operation given by Craige Schensted (1961) in his study of the longest increasing subsequence of a permutation.
Richard Joseph Laver was an American mathematician, working in set theory.
In mathematics, a Barnes zeta function is a generalization of the Riemann zeta function introduced by E. W. Barnes (1901). It is further generalized by the Shintani zeta function.
In algebra and in particular in algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn a subring of the formal power series ring with a countable number of variables. This ring generalizes the ring of symmetric functions. This ring can be realized as a specific limit of the rings of quasisymmetric polynomials in n variables, as n goes to infinity. This ring serves as universal structure in which relations between quasisymmetric polynomials can be expressed in a way independent of the number n of variables.
In mathematics, the Vogel plane is a method of parameterizing simple Lie algebras by eigenvalues α, β, γ of the Casimir operator on the symmetric square of the Lie algebra, which gives a point of P2/S3, the projective plane P2 divided out by the symmetric group S3 of permutations of coordinates. It was introduced by Vogel (1999), and is related by some observations made by Deligne (1996). Landsberg & Manivel (2006) generalized Vogel's work to higher symmetric powers.
In mathematics, the nil-Coxeter algebra, introduced by Fomin & Stanley (1994), is an algebra similar to the group algebra of a Coxeter group except that the generators are nilpotent.
In the mathematical field of convex geometry, the Busemann–Petty problem, introduced by Herbert Busemann and Clinton Myers Petty, asks whether it is true that a symmetric convex body with larger central hyperplane sections has larger volume. More precisely, if K, T are symmetric convex bodies in Rn such that
In mathematics, the Goncharov conjecture is a conjecture introduced by Goncharov (1995) suggesting that the cohomology of certain motivic complexes coincides with pieces of K-groups. It extends a conjecture due to Zagier (1991).
Curtis Greene is an American mathematician, specializing in algebraic combinatorics. He is the J. McLain King Professor of Mathematics at Haverford College in Pennsylvania.
Richard M. Pollack was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus till his death. In 1986 he and Jacob E. Goodman were the founding co-editors-in-chief of the journal Discrete & Computational Geometry (Springer-Verlag).
William M. Kantor is an American mathematician who works in finite group theory and finite geometries, particularly in computational aspects of these subjects.
Henry Howland Crapo was an American-Canadian mathematician who worked in algebraic combinatorics. Over the course of his career, he held positions at several universities and research institutes in Canada and France. He is noted for his work in matroid theory and lattice theory.
Jan-Erik Ingvar Roos was a Swedish mathematician.