CURRICULUM VITÆ. Biographical Data

Transcription

1 CURRICULUM VITÆ Biographical Data Name: Benjamin W. McKay Born: July 29, 1970 Citizenship: Canadian Birthplace: Toronto, Canada U.S. Visa type: J-1 (exempt from 2 year rule) Education: B.Sc. University of Toronto, 1993 M.Sc. University of Toronto, 1994 (Advisor: Richard W. Sharpe) PhD. Duke University, 1999 (Advisor: Robert L. Bryant) Awards: J.S. McLean Scholarship, University of Toronto, $4500/annum C. L. Burton Scholarship, University of Toronto, 1992 $250 and 1993 $500 NSERC Undergraduate Research Awards, 1992 $4500 and 1993 $4500 Arts & Sciences Faculty Scholar, University of Toronto, Ontario Graduate Scholarship, $7906 NSERC Postgraduate Scholarship A, $31200 Departmental Award, University of Toronto, $2500 Tuition Scholarship, Duke University, Fall 1994 Spring 1999 $13630/annum Graduate Fellowship, Duke University, Fall 1994 Spring 1999 $5100/annum Departmental Fellowship, Duke University, Fall 1996 $5700 Departmental Fellowship, Duke University, Spring 1998 $5700 Alfred P. Sloan Foundation Fellowship, $15000 Experience Computer programmer in arctic geological exploration, Covello, Bryan and Associates, Yellowknife, Canada Researcher, Department of Electrical Engineering, Dalhousie University, Halifax, Canada Member, School of Mathematics, Institute for Advanced Study, Princeton, USA Postdoctoral Fellow, Max-Planck-Institut für Mathematik, Bonn, Germany Instructor, University of Utah, Salt Lake City, USA Scott Assistant Professor, University of Utah, Salt Lake City, USA present. Assistant Professor, University of South Florida, Saint Petersburg, USA. 1

2 2 Teaching Experience Course Institution Semester Reform Precalculus Duke University Spring 1996 Traditional Calculus Duke University Spring 1997 Reform Calculus Duke University Fall 1997 PDE for Engineers University of Utah Fall 2000 Applied Complex Variables University of Utah Spring 2001 Complex Analysis University of Utah Summer 2001 Business Calculus University of Utah Fall 2001 Applied Complex Variables University of Utah Spring 2002 Complex Analysis University of Utah Spring 2002 PDE for Engineers University of Utah Spring 2002 Business Precalculus University of Utah Fall 2002 Business Calculus University of Utah Spring 2003 Doctoral thesis Duality and integrable systems of pseudoholomorphic curves I make the only discovery known of geometric structure living on moduli spaces of pseudoholomorphic curves, refining the well known topological structure. I apply Cartan s equivalence method to first order elliptic differential equations for 2 functions of 2 variables: generalized Cauchy Riemann equations. I write down infinite dimensional families of integrable systems of such equations. I show that 4 dimensional moduli spaces of solutions to such equations bear a natural dual generalized Cauchy Riemann equation, generalizing dual curves in the projective plane. I show that this dual equation is not an almost complex structure generalized Cauchy Riemann equations are a more robust category than almost complex structures for symplectic topology. I also provide an explicit description in differential invariants of Gromov s pseudoconvexity and of plurisubharmonicity, and prove the existence of Bishop disks. Papers in Pure Mathematics (1) Dual curves and pseudoholomorphic curves, to appear in Selecta Mathematica, math.dg/ I show that the analysis due to McDuff and others of the local behaviour of pseudoholomorphic curves in symplectic manifolds extends to the case of generalized Cauchy Riemann equations. This enables intersection theory arguments for regularity, as in the theory of almost complex manifolds. I also prove the existence of pseudoholomorphic lines in tame tori, first discovered by Victor Bangert on tame almost complex tori. (2) Analogues of complex geometry, submitted to Communications in Analysis and Geometry, math.dg/ I prove that any differential equations which behave locally like Cauchy Riemann equations of complex

3 3 submanifolds must either be Cauchy Riemann equations, or must be equations of pseudoholomorphic curves there are no pseudoholomorphic theories in higher dimension, even allowing far more general PDEs than almost complex structures. (The only exceptions are on 4-manifolds, where one finds the equations discussed in my thesis.) The surprise, totally unexpected by comparison with almost complex manifolds, is that there are lots of such equations for pseudoholomorphic hypersurfaces, at least microlocally (no obstruction to all orders in perturbation theory) but not locally. Geometric and topological arguments (using Chern classes, holomorphic contact geometry, and my own theory of great circle fibrations of spheres) show finally that these hypersurface theories don t exist. As an application, I classify Legendre fibrations with compact fibers on complex contact manifolds. (3) The topological Blaschke conjecture I: great circle fibrations of spheres, submitted to American Journal of Mathematics, math.dg/ I prove the topological Blaschke conjecture for Blaschke manifolds modelled on complex projective spaces, using only elementary mathematics (calculus of differential forms). Motivated by symplectic topology, I take any great circle fibration of a sphere, and construct a diffeomorphism with the Hopf fibration. This diffeomorphism is expressed explicitly algebraically in terms of local differential invariants of the great circle fibration. This improves on C. T. Yang s difficult surgery method proving this result in sufficiently high dimensions, and H. Sato s nonrigorous K-theory argument that a PL-homeomorphism should exist. Further, I sketch how to approach great sphere fibrations of spheres, to prove the full topological Blaschke conjecture. Biomedical Engineering Papers (1) (with Devashish Shrivastava and Robert Roemer), Derivation of two dimensional conduction shape factors: part A solving the Poisson equation, submitted for publication to SIAM Journal of Applied Mathematics, October (2) (with W.P.S. McKay and P.H. Gregson), Transfer-function analysis in anesthesia research, Canadian Journal of Anaesthesia September 1999, vol. 46, #9, pp An introduction to the use of transfer-function methods for digitized biological signals, written for the working anaesthesiology researcher: common pitfalls, and examples of successful applications. (3) (with W.P.S. McKay, P.H. Gregson, and J. Militzer), Sternal acceleration ballistocardiography and arterial pressure wave analysis to determine

4 4 stroke volume, Clinical and Investigative Medicine volume 22, number 1, February, We propose a novel procedure for measuring the flow of blood moving through the heart, using measurements of body motion from an accelerometer attached to the patient. The method is not invasive, and compares well (R = 0.79) with (invasive) pulmonary artery thermodilution. (4) (with W.P.S. McKay, P.H. Gregson, and T. Blanchet), Resting muscle sounds in anaesthetised patients, Canadian Journal of Anaesthesia 45 (1998), no. 5, part II:A26. (5) (with W.P.S. McKay, P.H. Gregson, and T. Blanchet), Muscle sounds in anaesthetized patients, The Canadian Journal of Physiology and Pharmacology This article presents over 10 years of experimental work and statistical analysis on very weak physiologic signals. We prove that resting muscle generates sound, while paralyzed muscle does not. This contradicts previous understanding of muscle sound generation. Patients in better physical condition have louder resting muscle sounds. (6) (with W.P.S. McKay, M. Erjavec, P.H. Gregson, T. Blanchet and G. Kember), Muscle sounds in anaesthetized patients, (abstract) Canadian Journal of Anaesthesia 43 (1996), no. 5, part II:A10-A. (7) (with W.P.S. McKay and P.H. Gregson), Sternal accelerometer ballistocardiography and arterial pressure wave analysis to determine stroke volume, (abstract) Canadian Journal of Anaesthesia 41 (1994), no. 5, part II:A45A. (8) (with W.P.S. McKay and P.H. Gregson), Direct accelerometer ballistocardiography for the detection of coronary artery disease, (abstract) Clinical and Investigative Medicine 15 (1992), no. 4:A9. Books (in progress) (1) Partial Differential Equations for Engineers, (Draft version available on my web page.) Maple programming, Fourier series and transforms, Bessel series, the heat, wave, Laplace and rigid beam equations, Green s functions, perturbation theory. (2) (with K.Becker, M. Becker, A. Bertram and P. Green), Proceedings of the 2004 AMS-IMS-SIAM Conference on String Geometry.

5 5 Invited talks (1) Dual curves and pseudoholomorphic curves, Seminar in Formal Geometry & Mathematical Physics, Utah State University, September 11, Organizer: Ian Anderson. (2) Pseudoholomorphic twistor theory on 4-manifolds, Developments and Applications in Differential Geometry, AMS Conference, Northeastern University, October 5-6, Organizers: Chuu-Lian Terng & Xiaobo Liu. (3) The Blaschke conjecture, Colloquium, Utah State University, October 17, Organizer: Mark Fels. (4) Biological signals: listening to people without cutting them open, Colloquium, University of Florida, January 27, Organizer: David Groisser. (5) The Blaschke conjecture, Geometry & Mathematical Physics Seminar, University of Florida, January 28, Organizer: Richard Crew. (6) The Blaschke conjecture, Geometry Seminar, University of Texas Austin, February 13, Organizer: Daniel Allcock. (7) Biological signals: listening to people without cutting them open, College of Arts & Sciences Colloquium, University of South Florida, February 18, Organizer: George Yanev. (8) Biological signals: listening to people without cutting them open, Colloquium, Fordham University, February 26, Organizer: Robert Lewis. Organizing of Conferences Co-organizer (with Katrin Becker, Melanie Becker, Aaron Bertram and Paul Green), Joint AMS IMS SIAM Conference on String Geometry, Snowbird Resort, Utah, June 5 11, Seminars Founder and organizer, Differential Geometry Seminar, University of Utah. Founder and organizer (joint with Katrin Becker), QFT/String Geometry Seminar, University of Utah. * $2000 seminar grant, University of Utah Mathematics Department * $2600 seminar grant, University of Utah Astrophysics Institute * $2000 seminar grant, University of Utah Physics Department Lists of speakers with abstracts: mckay/diffgeomseminar.html mckay/qftseminar.html

6 6 Other professional activities Copyeditor for Marcel Berger s A Panoramic View of Riemannian Geometry. Mathematics Department University of Utah 155 South 1400 East Salt Lake City, UT Tel: Fax: After August 5, 2003: Mathematics Department University of South Florida th Avenue South Saint Petersburg, Florida 33701, USA Tel: Fax: Last updated Friday, April 18, Current location