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Colin Conrad Adams (born October 13, 1956) is a mathematician primarily working in the areas of hyperbolic 3-manifolds and
knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...
. His book, ''The Knot Book'', has been praised for its accessible approach to advanced topics in
knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...
. He is currently
Francis Christopher Oakley Francis Christopher Oakley (born 1931) is the former Edward Dorr Griffin Professor of the History of ideas at Williams College, President Emeritus of Williams College and President Emeritus of the American Council of Learned Societies, New York. He ...
Third Century Professor of Mathematics at Williams College, where he has been since 1985. He writes "Mathematically Bent", a column of math for the '' Mathematical Intelligencer''. His nephew is popular American singer Still Woozy.


Academic career

Adams received a B.Sc. from MIT in 1978 and a Ph.D. in
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
from the University of Wisconsin–Madison in 1983. His dissertation was entitled "Hyperbolic Structures on Link Complements" and supervised by James Cannon. In 2012 he became a fellow of the American Mathematical Society.List of Fellows of the American Mathematical Society
retrieved 2012-11-03.


Work

Among his earliest contributions is his theorem that the
Gieseking manifold In mathematics, the Gieseking manifold is a cusped hyperbolic 3-manifold of finite volume. It is non-orientable and has the smallest volume among non-compact hyperbolic manifolds, having volume approximately V \approx 1.0149416. It was discovere ...
is the unique cusped hyperbolic 3-manifold of smallest volume. The proof utilizes
horoball In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic ''n''-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and its point o ...
-packing arguments. Adams is known for his clever use of such arguments utilizing horoball patterns and his work would be used in the later proof by Chun Cao and G. Robert Meyerhoff that the smallest cusped orientable hyperbolic 3-manifolds are precisely the figure-eight knot complement and its sibling manifold. Adams has investigated and defined a variety of geometric invariants of hyperbolic links and hyperbolic 3-manifolds in general. He developed techniques for working with volumes of special classes of hyperbolic links. He proved augmented alternating links, which he defined, were hyperbolic. In addition, he has defined almost alternating and toroidally alternating links. He has often collaborated and published this research with students from SMALL, an undergraduate summer research program at Williams.


Books

* C. Adams, ''The Tiling Book: An Introduction to the Mathematical Theory of Tilings.'' American Mathematical Society, Providence, RI, 2022. * C. Adams, ''The Knot Book: An elementary introduction to the mathematical theory of knots.'' Revised reprint of the 1994 original. American Mathematical Society, Providence, RI, 2004. xiv+307 pp.  (Take care in reading this book. There are two different first editions, one of which has a lot of mistakes noted by R. Riley. Corrections were then incorporated in a so-called "second printing" of the first edition -- a classic example of back-dating corrective mathematical work. --Ken Perko) * C. Adams, J. Hass, A. Thompson, ''How to Ace Calculus: The Streetwise Guide.'' W. H. Freeman and Company, 1998. * C. Adams, J. Hass, A. Thompson, ''How to Ace the Rest of Calculus: The Streetwise Guide.'' W. H. Freeman and Company, 2001. * C. Adams, ''Why Knot?: An Introduction to the Mathematical Theory of Knots.'' Key College, 2004. * C. Adams, R. Franzosa, "Introduction to Topology: Pure and Applied." Prentice Hall, 2007. * C. Adams, "Riot at the Calc Exam and Other Mathematically Bent Stories." American Mathematical Society, 2009. * C. Adams,"Zombies & Calculus." Princeton University Press, 2014. * C. Adams, J. Rogawski, "Calculus." W. H. Freeman, 2015.


Selected publications

* C. Adams, ''Thrice-punctured spheres in hyperbolic $3$-manifolds.'' Trans. Am. Math. Soc. 287 (1985), no. 2, 645—656. * C. Adams, ''Augmented alternating link complements are hyperbolic.'' Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984), 115—130, London Math. Soc. Lecture Note Ser., 112, Cambridge Univ. Press, Cambridge, 1986. * C. Adams, ''The noncompact hyperbolic $3$-manifold of minimal volume.'' Proc. Am. Math. Soc. 100 (1987), no. 4, 601—606. * C. Adams and A. Reid, ''Systoles of hyperbolic $3$-manifolds.'' Math. Proc. Camb. Philos. Soc. 128 (2000), no. 1, 103—110. * C. Adams; A. Colestock; J. Fowler; W. Gillam; E. Katerman. ''Cusp size bounds from singular surfaces in hyperbolic 3-manifolds.'' Trans. Am. Math. Soc. 358 (2006), no. 2, 727—741 * C. Adams; O. Capovilla-Searle, J. Freeman, D. Irvine, S. Petti, D.Vitek, A. Weber, S. Zhang. ''Bounds on Ubercrossing and Petal Number for Knots.'' Journal of Knot Theory and its Ramifications, vol. 24, no. 2 (2015) 1550012 (16 pages).


References


Math Prof. Wins Distinguished Teaching Award


External links


Faculty page
at Williams
Mathematical genealogy




{{DEFAULTSORT:Adams, Colin 1956 births Living people 20th-century American mathematicians 21st-century American mathematicians Topologists University of Wisconsin–Madison College of Letters and Science alumni Massachusetts Institute of Technology School of Science alumni Williams College faculty Fellows of the American Mathematical Society