| Professor Mladen Bestvina, on the photo with his wife Cynthia, is associate editor of the Annals of Mathematics since 2006, one of the most prestigious mathematical journals in the world. He completed his studies of mathematics at the University of Zagreb before he moved to the USA. Professor Bestvina is distinguished professor of mathematics at the University of Utah. He is a member of the editorial board of Glasnik Matematički, a Croatian math journal. |
Mladen Bestvina is a three-time medalist at the International Mathematical Olympiad (two silver medals in 1976 and 1978 and a bronze medal in 1977). He received a B. Sc. in 1982 from the University of Zagreb. He obtained a PhD in Mathematics in 1984 at the University of Tennessee under the direction of John Walsh. Bestvina had been a faculty member at UCLA, and joined the faculty in the Department of Mathematics at the University of Utah in 1993. He was appointed a Distinguished Professor at the University of Utah in 2004. Bestvina received the Alfred P. Sloan Fellowship in 1988-89 and a Presidential Young Investigator Award in 1988-91.
Bestvina served as an Editorial Board member for the Transactions of the American Mathematical Society. He is currently an associate editor of the Annals of Mathematics and an Editorial Board member for Geometric and Functional Analysis, the Journal of Topology and Analysis, Groups, Geometry and Dynamics, Michigan Mathematical Journal, Rocky Mountain Journal of Mathematics, and Glasnik Matematicki.
A 1988 monograph of Bestvina gave an abstract topological characterization of universal Menger compacta in all dimensions; previously only the cases of dimension 0 and 1 were well understood. John Walsh wrote in a review of Bestvina's monograph:This work, which formed the author's Ph.D. thesis at the University of Tennessee, represents a monumental step forward, having moved the status of the topological structure of higher-dimensional Menger compacta from one of ``close to total ignorance" to one of ``complete understanding".
In a 1992 paper Bestvina and Feighn obtained a Combination Theorem for word-hyperbolic groups. The theorem provides a set of sufficient conditions for amalgamated free products and HNN extensions of word-hyperbolic groups to again be word-hyperbolic. The Bestvina-Feighn Combination Theorem became a standard tool in geometric group theory and has had many applications and generalizations .
Bestvina and Feighn also gave the first published treatment of Rips' theory of stable group actions on R-trees In particular their paper gives a proof of the Morgan-Shalen conjecture that a finitely generated group G admits a free isometric action on an R-tree if and only if G is a free product of surface groups, free groups and free abelian groups.
A 1992 paper of Bestvina and Handel introduced the notion of a train track map for representing elements of Out(Fn). In the same paper they introduced the notion of a relative train track and applied train track methods to solve the Scott conjecture which says that for every automorphism α of a finitely generated free group Fn the fixed subgroup of α is free of rank at most n. Since then train tracks became a standard tool in the study of algebraic, geometric and dynamical properties of automorphisms of free groups and of subgroups of Out(Fn). Examples of applications of train tracks include: a theorem of Brinkmann proving that for an automorphism α of Fn the mapping torus group of α is word-hyperbolic if and only if α has no periodic conjugacy classes; a theorem of Bridson and Groves that for every automorphism α of Fn the mapping torus group of α satisfies a quadratic isoperimetric inequality; a proof of algorithmic solvability of the conjugacy problem for free-by-cyclic groups; and others.
Bestvina, Feighn and Handel later proved that the group Out(Fn) satisfies the Tits alternative,settling a long-standing open problem.
In a 1997 paper Bestvina and Brady developed a version of discrete Morse theory for cubical complexes and applied it to study homological finiteness properties of subgroups of right-angled Artin groups. In particular, they constructed an example of a group which provides a counter-example to either the Whitehead asphericity conjecture or to the Eilenberg−Ganea conjecture, thus showing that at least one of these conjectures must be false. Brady subsequently used their Morse theory technique to construct the first example of a finitely presented subgroup of a word-hyperbolic group that is not itself word-hyperbolic.Source Wikipedia
Mladen Bestvina: Distinguished Professor at the University of UTAH
Congratulations to Mladen Bestvina, who was named one of five new Distinguished Professors at the University of Utah in 2004.
Mladen joined our faculty in 1993 after an associate professorship at UCLA and visiting positions
at MSRI, IHES, IAS in Princeton and Berkeley. Mladen completed his Ph.D. at the University of Tennessee under the direction of J.Walsh. He is a leading authority in geometric topology and geometric
group theory. Maladen is editor of eight mathematics journals, has organized numerous special semesters and conferences in geometric group theory and topology and has directed eleven Ph.D. students, seven at Utah. Mladen is a terrific lecturer who received the department’s Faculty Undergraduate Teaching Award in 2006.
Mladen views algebraic problems geometrically by studying actions of infinite groups on topological spaces. He has made many fundamental contributions to the field of geometric group theory. Among them are Bestvina-Brady Morse theory for studying the finiteness properties of groups, the Bestvina-Handel algorithm for studying dynamical properties of homotopy equivalences of graphs or surfaces, and the Bestvina normal form for Artin groups.
Professor Bestvina was born near the city of Osijek, on the NW part of Croatia. He has published a paper in Mathematica communications, a professional journal issued by the Math Society of the Osijek University, where he serves as a member of the editorial board. See Mladen Bestvina: PL Morse Theory. The paper is based on his lecture delivered in 2008 at the Fourth Croatian Mathematical Congress 2008 in Osijek, where professor Bestvina was a member of the scientific committee.
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