Biography:Tim Cochran

Short description: American mathematician

Tim Cochran
Tim Cochran at Multnomah Falls in 2012
Born	(1955-04-07)April 7, 1955
Died	December 16, 2014(2014-12-16) (aged 59)
Nationality	United States
Alma mater	University of California
Known for	Cochran–Orr–Teichner (solvable) filtration
Scientific career
Fields	Mathematics
Institutions	Rice University
Doctoral advisor	Robion Kirby
Doctoral students	Shelly Harvey

Thomas "Tim" Daniel Cochran (April 7, 1955 – December 16, 2014) was a professor of mathematics at Rice University specializing in topology, especially low-dimensional topology, the theory of knots and links and associated algebra.

Education and career

Cochran in 1986

Tim Cochran was a valedictorian for the Severna Park High School Class of 1973. Later, he was an undergraduate at the Massachusetts Institute of Technology, and received his Ph.D. from the University of California, Berkeley in 1982 (Embedding 4-manifolds in S⁵). He then returned to MIT as a C.L.E. Moore Postdoctoral Instructor from 1982 to 1984. He was an NSF postdoctoral fellow from 1985 to 1987. Following brief appointments at Berkeley and Northwestern University, he started at Rice University as an associate professor in 1990. He became a full professor at Rice University in 1998. He died unexpectedly, aged 59, on December 16, 2014, while on a year-long sabbatical leave supported by a fellowship from the Simons Foundation.

Research contributions

With his coauthors Kent Orr and Peter Teichner, Cochran defined the solvable filtration of the knot concordance group, whose lower levels encapsulate many classical knot concordance invariants.

Cochran was also responsible for naming the slam-dunk move for surgery diagrams in low-dimensional topology.

Awards and honors

While at Rice, he was named an Outstanding Faculty Associate (1992–93), and received the Faculty Teaching and Mentoring Award from the Rice Graduate Student Association (2014)

He was named a fellow of the American Mathematical Society in 2014, for contributions to low-dimensional topology, specifically knot and link concordance, and for mentoring numerous junior mathematicians.

Selected publications

• Cochran, T. (1984). "Four-manifolds which embed in [math]\displaystyle{ \mathbb{R}^6 }[/math] but not in [math]\displaystyle{ \mathbb{R}^5 }[/math] and Seifert manifolds for fibered knots". Inventiones Mathematicae 77: 173–184. doi:10.1007/BF01389141. 
• Cochran, Tim D. (1985). "Geometric invariants of link cobordism". Commentarii Mathematici Helvetici 60: 291–311. doi:10.1007/BF02567416. 
• Cochran, Tim D. (1990). "Derivatives of links: Massey products and Milnor's concordance invariants". Memoirs of the American Mathematical Society 84 (427). doi:10.1090/memo/0427. 
• Cochran, Tim D.; Orr, Kent E. (1993). "Not all links are concordant to boundary links". Annals of Mathematics 138 (3): 519–554. doi:10.2307/2946555. http://projecteuclid.org/euclid.bams/1183555721. 
• Cochran, Tim D.; Orr, Kent E. (2003). "Knot Concordance, Whitney Towers and [math]\displaystyle{ L^2 }[/math]-signatures". Annals of Mathematics 157 (2): 433–519. doi:10.4007/annals.2003.157.433. 
• Cochran, Tim D.; Orr, Kent E. (2004). "Structure in the Classical Knot Concordance Group". Commentarii Mathematici Helvetici 79 (1): 105–123. doi:10.1007/s00014-001-0793-6. 
• Cochran, Tim D. (2004). "Noncommutative Knot Theory". Algebraic and Geometric Topology 4: 347–398. doi:10.2140/agt.2004.4.347. 
• Cochran, Tim D. (2007). "Knot Concordance and von Neumann [math]\displaystyle{ \rho }[/math]-invariants". Duke Mathematical Journal 137 (2): 337–379. doi:10.1215/S0012-7094-07-13723-2. 
• Cochran, Tim D. (2008). "Homology and Derived Series of Groups II: Dwyer's Theorem". Geometry and Topology 12 (1): 199–232. doi:10.2140/gt.2008.12.199. 
• Cochran, Tim D. (2009). "Knot concordance and Higher-order Blanchfield duality". Geometry and Topology 13 (3): 1419–1482. doi:10.2140/gt.2009.13.1419. 
• Cochran, Tim D. (2011). "Primary decomposition and the fractal nature of knot concordance". Mathematische Annalen 351 (2): 443–508. doi:10.1007/s00208-010-0604-5. 
• Cochran, Tim D.; Davis, Christopher William (2015). "Counterexamples to Kauffman's conjectures on slice knots". Advances in Mathematics 274: 263–284. doi:10.1016/j.aim.2014.12.006. 

External links

• Tim Cochran's home page.