I am a full professor and director of the UT Math Honors Program in the Department of Mathematics at the University of Tennessee, Knoxville. I graduated with honors from Guilford College in 1983, with a double major in math and English. I subsequently spent a year on a Fulbright grant in Yugoslavia, and received my MS in mathematics from the University of Kentucky in 1986. I received my Ph.D. in differential geometry at the University of Maryland, College Park, in 1989 under the direction of Karsten Grove. Subsequently, I held postdoctoral position at the Max Planck Institute for Mathematics in Bonn and Ohio State University before coming to UTK in 1992. I was a visiting researcher at the Max Planck Institute for Mathematics in the Natural Sciences in Leipzig, Germany the spring of 1999 and summer of 2001. I was a visiting researcher at the Swiss Federal Institute of Technology (ETH) in Zurich in the spring of 1999. I was undergraduate associate head in the math department from spring 2003 to summer 2005, during which time I designed the honors program I now direct. My e-mail address may be obtained through the Department of Mathematics website.
My office is in Ayres Hall 206 on The Hill, phone (865) 974-4319 or the Undergraduate Mathematics Office, Ayres 200, (865) 974-1478. This semester I’m teaching Differential Geometry (568, MWF 12:20-1:10). My office hours are tentatively MWF 1:30-2 and by appointment. If you are a math honors or prospective math honors student, or an Appalachian Scholar, and you would like to meet with me, contact Jessica in Ayres 200 (974-1478). I’m often available at other times, but be sure to call or e-mail before making the long hike up the Hill to my office when office hours are not in session. You are unlikely to find me on Tuesdays, when I tend to hide away somewhere doing research. On Wednesday afternoons in the fall I am working with the math club at Maryville High.
My research interests include Riemanian geometry, geometry of singular spaces a la A. D. Alexandrov, and uniform spaces. My work also involves topology and geometric approaches to algebraic problems, including homogeneous and symmetric spaces, geometric group theory, geometric aspects of topological groups, covering spaces of locally singular spaces. Collaborators include Valera Berestovskii (Omsk State University, Russia), Urs Lang (ETH, Zurich), and Cornelius Stallman (Augusta State). In the last several years I have given many invited lectures, including talks at the Euler Institute in St. Petersburg and Novosibirsk, Russia; CIRM in Luminy, France; Mathematics Research Institute in Oberwolfach, Germany; Max Planck Institute for Mathematics in the Natural Sciences in Leipzig, Germany; and ETH, Zurich, Switzerland.
1. Uniform universal covers of uniform spaces, to appear, Top. and its Appl.
2. Quotients of uniform spaces, Top. and its Appl. 153 (2006) 2430-2444.
3. The universal cover of the quotient of a locally defined group, with V. N. Berestovskii, Topology. Proc. 28 (2004) 1-9.
4. Embeddings of lattices in L2([0,1],Z), with V. N. Berestovskii, J. Geometry 75 (2002) 27-45.
5. Metric spaces of curvature >= k, Chapter 19, Handbook of Geometric Topology, Elsevier Science (2002).
6. Generalized lattices in topological vector spaces, with V. N. Berestovskii and V. Gichev, MPI-Leipzig preprint 49, 2001.
7. Bi-Lipschitz embeddings of metric spaces into space forms, with U. Lang, Geom. Dedicata 87 (2001) 285-307.
8. Covering group theory for compact groups, with V. N. Berestovskii, J. Pure and Appl. Algebra 161 (2001) 255-267.
9. Covering group theory for locally compact groups, with V. N. Berestovskii, Top. and its Appl. 114 (2001) 187-199.
10. Covering group theory for topological groups, with V. N. Berestovskii, to appear, Top. and its Appl. 114 (2001) 141-186.
11. Homogeneous spaces of curvature bounded below, with V. N. Berestovskii, J. Geom. Analysis 9 (1999) 203-219.
12. Geometric groups I, with V. N. Berestovskii and C. Stallman, Trans. Amer. Math. Soc. 351 (1999), no. 4, 1403--1422.
13. Geometry on groups, in Analysis on Infinite-Dimensional Lie Groups and Algebras, 15-19 September 1997, H. Heyer, et al. editors, World Scientific (1998) 368-375.
14. Spaces of Wald-Berestovskii curvature bounded below. J. Geom. Analysis. 6 (1996), no. 1, 113--134.
15. Geometrizing infinite-dimensional locally compact groups. Trans. Amer. Math. Soc. 348 (1996), no. 3, 941--962.
16. Metric pinching of locally symmetric spaces. Duke Math. J. 73 (1994), no. 1, 155--162, corr. in Duke Math. J. 75 (1994), no. 2, 527--528.
17. Metric curvature, convergence, and topological finiteness. Duke Math. J. 66 (1992), no. 1, 43--57.
18. A metric characterization of manifolds with boundary. Compositio Math. 81 (1992), no. 3, 337--354.
19. Almost Riemannian spaces. J. Differential Geom. 34 (1991), no. 2, 515--537.
Students often wonder what sort of research mathematicians do, and why they do it. Research and teaching are the two most important responsibilities of my position (the third responsibility is service to the university and community). I am a pure mathematician (as opposed to an applied mathematician), which means that I am primarily engaged in the discovery of new mathematics (theorems and instructive examples). Geometry, my field of research, has applications, for example in physics, engineering, and computer imaging, but I am generally not directly involved in finding such applications. If research in pure mathematics seems like art-for-art’s-sake, then consider the fact that pure (and even seemingly esoteric) mathematics often proves useful in surprising and unpredictable ways. The American university system, which has become by far the best system in the world, has benefited greatly from our investments in pure (or “basic”) research, and will continue to do so in the future.
On the other hand, research and teaching are linked, and can strongly complement one another. Even at the level of calculus, the content of which is hardly affected by current mathematical research, I believe that my involvement in research makes a positive contribution to my teaching. I am sure that I could not be an effective calculus teacher if my mind were not engaged in mathematical problems that are as fresh and challenging for me as calculus is for my calculus students.
I enjoy teaching a wide variety of classes at all levels from calculus on up. This semester I’m teaching Math 568 (Differential Geometry). The text for my honors advanced calculus course is Honors Advanced Calculus. Prior classes I have taught at UTK include calculus (classical, reformed, hybrid, and honors, including differential equations), introduction to abstract mathematics, real analysis, honors matrix algebra, abstract algebra (regular and honors), honors advanced calculus, geometry, Lie groups/topological groups, and differential geometry. I am currently writing textbooks for a course on Lie and topological groups for advanced undergraduates and beginning graduate students and honors advanced calculus.
I am Principle Investigator of two grants directed at undergraduate education with a combined total value over $1.3 million from the National Science Foundation. The first has co-PIs Grozdena Todorova (mathematics) and Mike Berry (computer science), and is funded by the NSF-CSEMS program. It supports the Appalachian Scholars in Computer Science and Mathematics (ASCSM) program, providing provides scholarship and academic support to financially needy students from Appalachia majoring in math and/or computer science. For more details on the program, visit the ASCSM site.
The second grant is provides scholarships, summer tuition, and research and other academic support for students in the UT Math Honors program.
I am also the PI of a grant proposal from the NSF to support a summer REU (research experiences for undergraduates) summer program for three years; this proposal has been recommended for funding but final approval is pending.
Finally, I am the PI of a pending proposal to continue and expand the CSEMS program mentioned above, jointly with the departments of Chemistry, Computer Science, and Physics.
Jay Wilkins, PhD candidate.
David Phillipi, M.S., Mathematics, UTK, 2003, Ph.D. expected 2007
Tamara Bouma, M.S., Mathematics, UTK, 2001.
Cornelius Stallman, Ph.D., Mathematics, UTK, 12/96, now an Associate Professor
at Augusta State University.
Craig Spencer, M.S., Physics, University of Rochester, 12/96.
Rachel Graves, UTK, Summer 2003
Mike Jablonski, UTK, Summer 2000
Hoai Nam Tran, U. Nebraska, Summer 2000
Andromeda Yelton, Harvey Mudd, Summer 1998
Becky Cantonwine, Hanover College, Summer 1997
Aside from teaching, research, overseeing grants and directing UT Math Honors, this is what I’ve been involved in this year:
· Undergraduate Committee
· Bylaws Revision Committee
· Honors Committee
· Math Honors Advisor
· Junior Colloquium Organizer
· University Scholarship Committee
· University Honors Selection Committee
· University Honors Showcases
· Math team coach, Maryville High
In the past I have advised 300 hours (1995-1998) in the Arts and Sciences Advising Center, and advised many undergraduate math majors. I co-organized the 2000 Barrett Lectures. I have been a member of the Advisory Committee (elected), Allen Prize Committee, Graduate Committee, Math Day Committee, Search Committees (Differential Geometry and Geometric Group Theory/Algebraic geometry), Tenure/Promotion/Retention Committees, and the Undergraduate Committee. I have participated in the restructuring/strengthening of the undergraduate major, as well as curriculum planning or piloting for linear algebra for engineers, calculus, honors calculus, and differential geometry.
In service to the mathematical community I have written dozens of reviews for Mathematical Reviews, and have been a referee for the NSF and several mathematical journals, and am the “owner” of the Geometry List, which announces conferences related to differential geometry.
I have coached two Destination Imagination teams for Maryville Middle School, the second of which place third in the state competition and won the “Da Vinci” award for creativity. I have visited a number of middle and high schools and sometimes oversee (with my wife Barbara) the metric competition of the Science Olympiad at Maryville College.
Ever willing to express my opinion about anything, I occasionally write commentary (sometimes jointly with my wife) on topics ranging from roadside garbage to “year-round school” to state funding for higher education to mathematics education. For a sample, see my review (one of two) of the book “Humble Pi.” Maybe it was a coincidence, but shortly after the review appeared in the Notices of the American Mathematical Society, the book went on sale at an 80% discount.
I live at 606 Cardinal Street in Maryville with my beautiful and highly intelligent wife Barbara, our two beautiful and highly intelligent daughters Lena (4/27/87) and Chelsea (10/17/88). Our beautiful German Shepherd Greta died last year at the ripe old age of 13. We’re located right off the Maryville Greenway, just across the footbridge over Pistol Creek near mile marker 3. Barbara is the computer science professor at Maryville College. Lena is a sophomore digital arts major at Viterbo University in Wisconsin and Chelsea is a senior at Maryville High. Chelsea intends to come to UT next year to study math and music.
In addition to doing mathematics, my other interests include outdoor activities, especially trout fishing, hiking, roller-blading and bicycling.
