CURRICULUM VITAE

RAZVAN GELCA,

Born February 28, 1967,
Timisoara, Romania
US and Romanian Citizen

EDUCATION

High school diploma, C.D. Loga High School, Timisoara, Romania, 1985
Coach for Mathematical Olympiads: Titu Andreescu

Diploma of Merit in Mathematics, awarded by the Romanian
Ministry of Education for the highest GPA in the country, University of Timisoara, Romania, 1989
Mentor: Gheorghe Eckstein

MS, University of Bucharest, Romania,1990
Dissertation: Invariant subspaces for subdecomposable operators
Advisor: Florian-Horia Vasilescu

PhD, University of Iowa, 1997
Dissertation: Problems in topology and operator theory
Co-advisors: Charles Frohman, Raúl Curto

APPOINTMENTS

Researcher, Institute of Mathematics of the Romanian Academy 1990-
Assistant Professor, University of Michigan, 1997-2000
Assistant Professor, Texas Tech University, 2000-2006
Associate Professor, Texas Tech University, 2006-present.

SHORT TERM APPOINTMENTS

Coach of the US International Mathematical Olympiad Team, Mathematical Olympiad Summer Program, 1997, 1998, 2000, 2002, 2006, 2007, 2008, 2009.
Visiting Professor, Universite de Nantes, May 1999.
Coach of the International Mathematical Olympiad Team of India, Homi Bhabha Center of Science Education, Mumbai, India, 2004, 2005.
Instructor, Awesome Math, Dallas, 2009.

ACADEMIC HONORS/AWARDS/GRANTS

First Prize, Balkan Mathematical Olympiad, (Sofia, Bulgaria), 1985.
Gold Medal, International Mathematical Olympiad, (Helsinki, Finland), 1985.
First Prize, Romanian National Mathematical Competition for Universities "Traian Lalescu", 1986.
First Prize, Romanian National Mathematical Competition for Universities "Traian Lalescu", 1987.
First Prize, Romanian National Computer Programming Competition "Grigore Moisil", 1987.
Romanian National Fellowship, 1987, 1988.
Award for best performance on the qualifying examinations, Department of Mathematics, University of Iowa, 1992.
Outstanding Teaching Award, University of Iowa, 1997.
D.C. Spriestersbach Dissertation Prize for best dissertation in Mathematical and Physical Sciences and Engineering, University of Iowa, 1998.
Rackham Summer Grant, University of Michigan, 1999.
Research Enhancement Fund, Texas Tech University, 2000 and 2001.
NSF grant for the study of the quantization of the moduli space of flat SU(2)-connections on a surface, 2006-2009.
NSF grant for organizing The Topology and Geometry of Physics Conference, 2008.

PAPERS

1. Quantum mechanics and non-abelian theta functions for the gauge group SU(2), with Alejandro Uribe, submitted for publication.
2. Some results about the Kauffman bracket skein module of the twist knot exterior, with Fumikazu Nagasato, J. Knot Theory Ramif., 8(2006), 1095-1106.
3. El polinomio de Jones y la mecanica cuantica, Aportaciones Math. Comun, 36, Soc. Mat. Mexicana, Mexico, 2006, 85--99.
5. On the holomorphic point of view in the theory of quantum knot invariants, J. Geom. Phys., 56(2006), 2163-2176.
5. The computation of the noncommutative A-ideal for the figure eight knot, with Jeremy Sain, J. Knot Theory Ramif. 6(2004), Vol. 16, 1-24.
6. The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same, with Alejandro Uribe, Communications in Mathematical Physics, 233(2003), 493-512.
7. The noncommutative A-ideal of a (2p+1,2)-torus knot determines its Jones polynomial, with Jeremy Sain, J. Knot Theor. Ramif, 2(2003), Vol. 12, 187-201.
8. Noncommutative trigonometry and the A-polynomial of the trefoil knot, Mathematical Proceedings of the Cambridge Philosophical Society, 1(2002).
9. On the relation between the A-polynomial and the Jones polynomial, Proceedings Amer. Math. Soc., 4(2001), Vol 130, 1235-1241.
10. The A-polynomial from the noncommutative viewpoint, with Charles Frohman and Walter Lofaro, Transactions Amer. Math. Soc., 354(2001), 735-747.
11. Skein modules and the noncommutative torus, with Charles Frohman, Transactions Amer. Math. Soc., 352(2000), 4877-4888.
12. On the formula for the quantum invariant of three manifolds with boundary, Bulletin Math. Soc. Sc. Math. Roumanie, 43(91) 2(2000).
13. On the groupoid of transformations of rigid structures, with Louis Funar, Journal of Math. Sci. Univ. Tokyo, 4(1999), Vol 6, 599-646.
14. Topological SL(2,C) quantum field theory with corners, J. Knot Theor. Ramif., 7(1998), 893-906.
15. Topological quantum field theory with corners based on the Kauffman bracket, Comment. Math. Helv., 72(1997), 216-243.
16. The quantum invariant of the regular neighborhood of a link, Topology and its Applications 81(1997), 147-157.
17. Topological Hilbert Nullstellensatz for Bergman spaces, Integral Equations and Operator Theory, 28(1997), 191-195.
18. Rings with topologies induced by spaces of functions, Houston Journal of Mathematics, Vol. 21, no.2(1995), 395-406.
19. Compact perturbations of Fredholm n-tuples, Proceedings Amer. Math. Soc. 122(1994), 195-199.
20. Compact perturbations of Fredholm n-tuples, II, Integral Equations and Operator Theory 19(1994), 360-363.
21. A short proof of a result on polynomials, Amer. Math. Monthly 100(1993), 936-937.

BOOKS

1. Putnam and Beyond, with Titu Andreescu, Springer, 2007.
2. Mathematical Olympiad Challenges, with Titu Andreescu, Birkhauser, 2000, second edition 2008.

TALKS DELIVERED AT MEETINGS

1. Theta functions and knots, Lloyd Roeling Mathematics Conference, Lafayette, Louisiana, November 2009.
2. The reduced Kauffman bracket skein algebra of the torus has a unique irreducible representation, 1037th Sectional Meeting of the AMS, Baton Rouge, Louisiana, March 2008.
3. The quantum group quantization of the moduli space of flat SU(2)-connections on a surface determines the Reshetikhin-Turaev representation of the mapping class group, First Joint Meeting of the American Mathematical Society and the Polish Mathematical Society, Warsaw, Poland, August 2007.
4. The quantum group quantization of the moduli space of flat SU(2)-connections on a surface determines the Reshetikhin-Turaev representation of the mapping class group, "A second time around the volume conjecture" conference, Baton Rouge, Louisiana, June 2007.
5. The computation of the basis of the Hilbert space of a certain quantum system, National Meeting of the American Mathematical Society, San Antonio, January 2006.
6. El polinomio de Jones y la mecanica cuantica, Congreso Nacional de la Sociedad Matematica Mexicana, Mexico City, October 2005.
7. On the holomorphic point of view in the teory of quantum knot invariants, 1002nd Sectional Meeting of the AMS, Pittsburgh, Pennsylvania, November 2004.
8. Towards the computation of the noncommutative A-polynomial of twist knots, 1000th Sectional Meeting of the AMS, Albuquerque, New Mexico, October 2004.
9. On the quantization of the moduli space of flat SU(2)-connections on the torus, 6th Joint meeting of the AMS and the SMM, Houston, May 2004.
10. The computation of the matrix of the quantum group quantization of the moduli space of flat SU(2)-connections on the torus, Spring Topology and Dynamical Systems Conference, Lubbock, March 2003.
11. The computation of the noncommutative generalization of the A-polynomial for the figure-eight knot, National Meeting of the AMS, Baltimore, January 2003.
12. On the quantization of the flat SU(2)-connections on the torus, International Conference on Geometric Topology, Xi'an, China, August 2002.
13. The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on the torus are the same, 974th Sectional Meeting of the AMS, Ann Arbor, Michigan, March 2002.
14. Skein modules and the Berezin quantization of the moduli space of flat SU(2)-connections on the torus, 972nd Sectional Meeting of the AMS, Irvine, California, November 2001.
15. The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial, 969th Sectional Meeting of the AMS, Columbus, Ohio, September 2001.
16. Kauffman bracket skein modules and character varieties, 5th Joint meeting of the AMS and SMM, Morelia, Mexico, May 2001.
17. Kauffman bracket skein modules and character varieties, Texas Geometry and Topology Conference, February 2001.
18. On the noncommutative version of the A-polynomial, 954-th Sectional AMS Meeting, Lafayette, Louisiana, April 2000.
19. On the relation between the A-polynomial and the Jones polynomial, AMS National Meeting, Washington, January 2000.
20. Noncommutative trigonometry and the A-polynomial, 949-th Sectional AMS Meeting, Charlotte, North Carolina, October 1999.
21. Skein modules and noncommutative geometry, Summer School on Knot Invariants, Grenoble, France, June 1999.
22. Skein modules and the noncommutative torus, Knots in Hellas, Delphi, Greece, August 1998.
23. Kauffman bracket skein modules and the noncommutative torus, 932-nd Sectional AMS Meeting, Manhattan, Kansas, March 1998.
24. On the quantum invariant of torus knots, 920-th Sectional AMS Meeting, College Park, Maryland, April 1997.
25. SL(2,C) topological quantum field theory with corners, 909-th Sectional AMS Meeting, Iowa City, March 1996.
26. Topological quantum field theory with corners, Thirteenth annual workshop on geometric topology, Colorado Springs, June 1996.
27. Topological quantum field theory with corners based on the Jones-Wenzl idempotents, Great Plains Operator Theory Symposium, Phoenix, May 1996.
28. Topological quantum field theory with corners via the Jones-Wenzl idempotents, Sixteenth International Operator Theory Conference, Timisoara, Romania, July 1996.
29. Topological SL(2,C) invariants for 3-manifolds with boundary, Minisemester in Knot Theory, Warsaw, Poland, July 1995.
30. On a conjecture of R. G. Douglas and V. Paulsen, South-Eastern Analysis Meeting, Atlanta, March 1995.
31. On a conjecture of R. G. Douglas and V. Paulsen, Great Plains Operator Theory Symposium, Cincinnati, May 1995.
32. Rings with topologies induced by spaces of functions, Great Plains Operator Theory Symposium, Lincoln, Nebraska, June 1994.
33. Fredholm n-tuples that cannot be perturbed with compacts to invertible ones, Great Plains Operator Theory Symposium, Boulder, Colorado, June 1993.
34. Fredholm n-tuples that cannot be perturbed with compacts to invertible ones, Amer. Math. Soc. Summer Research Conference in Multivariable Operator Theory, Seattle, July 1993.

SEMINAR TALKS

1. Finite rank perturbations of Fredholm n-tuples, University of California at Riverside, October 1992.
2. Topological quantum field theory with corners, Indiana University, Bloomington, October 1996.
3. Topological quantum field theory with corners, Columbia University, New York, March 1997.
4. Topological quantum field theory with corners, University of Michigan, Ann Arbor, February 1997.
5. Skein modules and the noncommutative torus, George Washington University, Washington, September 1998 (Colloquium talk).
6. Skein modules and the noncommutative torus, Northeastern University, Boston, March 1999.
7. Skein modules and noncommutative geometry, Universite de Nantes, May 1999.
8. The A-polynomial from the noncommutative viewpoint, University of Texas at Austin, November 1999.
9. The A-polynomial from the noncommutative viewpoint, George Washington University, Washington, January 2000.
10. The A-polynomial from the noncommutative viewpoint, Michigan State University, East Lansing, January 2000.
11. Skein modules and noncommutative geometry, SUNY at Buffalo, February 2000 (Colloquium talk).
12. Skein modules and noncommutative geometry, Texas Tech University, Lubbock, February 2000 (Colloquium talk).
13. Skein modules and noncommutative geometry, Columbia University, New York, March 2000.
14. The A-polynomial from the noncommutative viewpoint, Universidad Nacional Autonoma de Mexico, Mexico City, May 2001.
15. On the quantization of the moduli space of flat SU(2)-connections on a surface, University of Texas at Dallas, October 2001.
16. The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on a torus are the same, University of Notre Dame, March 2002.
17. The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on a torus are the same, University of South Alabama, Mobile, November 2002 (Colloquium talk).
18. The Weyl quantization and the quantum group quantization of the moduli space of flat SU(2)-connections on a torus are the same, University of Wisconsin, Madison, November 2002.
19. Knots and quantum physics, The Boeing Company, Seattle, March 2003.
20. Recursive relations for colored Jones polynomials, Indiana University, Bloomington, November 2003.
21. Recursive relations for colored Jones polynomials, University of Texas at Dallas, January 2004 (Colloquium talk).
22. On the quantization of the moduli space of flat SU(2)-connections on the torus, Tata Institute for Fundamental Research, Mumbai, India, June 2004 (Colloquium talk).
23. Some geometric aspects of quantum topology, Georgia Tech University, Atlanta, November 2004.
24. Computing the basis of a vector space arising in quantum physics , Indiana University, Bloomington, April 2005.
25. The Jones polynomial and quantum mechanics, Boise State University, Boise, November 2006 (Colloquium talk).
26. Teoria espectral y la cuantizacion del espacio de moduli de conexiones planas en una superficie, CINVESTAV, Mexico City, March 2007.
27. Sobre la relacion entre la cuantizacion del espacio de moduli de conexiones planas de su(2) en una superficie y el functor modular, CINVESTAV, Mexico City, September 2007.
28. Nudos y mecanica cuantica, Universidad Nacional Autonoma del Estado de Mexico, Toluca, Mexico, September 2007.
29. On knots and linear operators, University of Texas at San Antonio, April 2008.
30. Theta functions and knots, Yale University, November 2009.

COMMITTEES

Undergraduate Committee, Texas Tech University, 2006-2008.
PhD Dissertation Committee of Jeff Sink, University of Michigan 1999, and of Kendrick Smith, University of Michigan 2000, Todd Kennaugh, Texas Tech University, 2009.
Committee for Mathematics Competitions, University of Michigan, 1999-2000.

CONFERENCES ORGANIZED

Organizer of the 8th Annual Red Raider Symposium - The Topology and Geometry of Physics Conference, October 2008.

Co-organizer of Texas Geometry and Topology Conference, Spring 2002, Spring 2005, Spring 2008.

Session organizer at the AMS sectional meeting 8-10 April 2005.

Session organizer at the AMS sectional meeting 22-23 April 2006.

ACTIVITIES RELATED TO MATHEMATICS COMPETITIONS

Deputy Leader of the US International Mathematical Olympiad Team, Madrid, Spain, 2008.

Assistant Editor of Mathematics Magazine, 2002-2007.

Member of the USA Mathematical Olympiad Advisory Panel, 2007-present.

Coordinator of the grading, 40th International Mathematical Olympiad, Bucharest, Romania, 1999, and of the 42nd International Mathematical Olympiad, Washington, USA, 2001.

Advisor for the coordination of grading, 44th International Mathematical Olympiad, Tokyo, Japan, 2003.

Coach of University of Michigan Putnam Team, 1998-1999. In 1998 the Michigan Team placed 14th among over 200 teams. In 1999 the Michigan Team was one of the 5 winners of the Putnam Competition, placing 4th. One of my students, Dapeng Zhu placed 16th.

Coach of the Texas Tech University Putnam Team, 2000-present. In 2000 one of the students, Jeremy Sain, placed 86th in the nation, and in 2001 he placed 78th in the nation.

Grader of the USA Mathematical Olympiad, 1997-2005, 2007-2009.

September 1992-May 1995, coach of Jay Chung, a student at West High School (Iowa City, IA). Jay obtained a bronze medal at the International Mathematical Olympiad, Toronto, Canada, July 1995.

Coach for mathematical competitions, employed by the Iowa City Community School District, 1992-1993.

Associate Editor for Revista Matematica din Timisoara (Timisoara Mathematics Review), 1985-1989.

Talks on mathematical Olympiads presented at

COURSES TAUGHT

Precalculus, Calculus I, Calculus II, Multivariable Calculus, Advanced Calculus, Introduction to Differential Equations, Geometry for Teachers, Linear Algebra, Math for Business Students, Problem Solving, Introduction to Topology, Number Theory for Teachers, Introduction to Mathematical Reasoning, Real Analysis, Low Dimensional Topology.

HOBBIES

landscape photography (I love the Southwest), tourism (as long as I organize everything myself), music (classical, ethnic), skiing (no bumps), renaissance painting, indo-european languages, cooking.