** 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
1990-2000

Assistant Professor, University of
Michigan, 1997-2000 (post-doctoral position with Ruth Lawrence as mentor)

Assistant Professor, Texas Tech University, 2000-2006

Associate Professor, Texas Tech University, 2006-2015

Professor, Texas Tech University, 2015-present.

SHORT TERM APPOINTMENTS

Coach of the US International Mathematical Olympiad Team,
Mathematical Olympiad Summer Program,
1997, 1998, 2000, 2002, 2006-2017.

Visiting Professor, Université de Nantes, May 1999.

Coach of the International
Mathematical Olympiad Team of Brazil, Colégio Etapa, Saõ Paulo, Brazil, 2011, 2013.

Coach of the International Mathematical Olympiad Team of India, Homi
Bhabha Center of Science Education, Mumbai, India, 2004, 2005.

Instructor, Awesome Math, Dallas, 2009, 2010, 2012.

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.

Grant from the National Science Foundation for the study of the
quantization of the moduli space of flat SU(2)-connections
on a surface, 2006-2009.

Grant from the National Science Foundation for organizing The Topology
and Geometry of Physics Conference, 2008.

PAPERS

BOOKS

- 1. Putnam and Beyond, with Titu Andreescu, Springer, 2007, second edition 2017.
- 2. Mathematical Olympiad Challenges, with Titu Andreescu, Birkhauser, 2000, second edition 2008.
- 3. Theta Functions and Knots, World Scientific, 2014.

TALKS DELIVERED AT MEETINGS

- 1.Weyl quantization and Chern-Simons theory , 1131st Sectional Meeting of the AMS, Denton, TX, September 2017.
- 2.Theta functions and knots, Conferencias Samuel Gitler, Mexico City, Mexico, October 2016.
- 3. Theta functions and knots, Conference on Knot Theory and Its Applications to Physics and Quantum Computing, Dallas, TX, January 2015.
- 4. Weyl quantization versus quantum group quantization of moduli spaces of flat connections on a surface, SMS Spring Conference on Quantization of Moduli Spaces, Geneva, Switzerland, April 2014.
- 5. Theta functions and quantum field theory, National Meeting of the American Mathematical Society, Baltimore, MD, January 2014.
- 6. Classical theta functions in a quantum group perspective, 1080th Sectional Meeting of the American Mathematical Society, Washington, DC, March 2012.
- 7. Obtaining the Witten-Reshetikhin-Turaev invariants from quantum mechanical considerations, 50 Years of Topology, Geometry and Physics at Cinvestav, Mexico City, November 2011.
- 8. Representations of the Kauffman bracket skein algebra of the punctured torus, Knots in Washington XXXII, Washington, DC, May 2011.
- 9. La teorėa Chern-Simons desde el punto de vista de la mecānica cuāntica, Congreso Nacional de la Sociedad Matemātica Mexicana, Tuxtla-Gutierrez, November 2010 (plenary talk).
- 10. Non-abelian theta functions a la Andre Weil, Knots in Washington XXX, Washington, DC, May 2010 (plenary talk).
- 11. The theory of classical theta functions from a topological perspective, 1060th Sectional Meeting of the American Mathematical Society, Newark, May 2010.
- 12. From classical theta functions to topological quantum field theory, 8th Joint Meeting of the American Mathematical Society and the Sociedad Matematica Mexicana, Berkeley, June 2010.
- 13. Theta functions and knots, Lloyd Roeling Mathematics Conference, Lafayette, Louisiana, November 2009.
- 14. 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.
- 15. 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.
- 16. 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.
- 17. 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.
- 18. El polinomio de Jones y la mecanica cuantica, Congreso Nacional de la Sociedad Matematica Mexicana, Mexico City, October 2005.
- 19. On the holomorphic point of view in the teory of quantum knot invariants, 1002nd Sectional Meeting of the AMS, Pittsburgh, Pennsylvania, November 2004.
- 20. Towards the computation of the noncommutative A-polynomial of twist knots, 1000th Sectional Meeting of the AMS, Albuquerque, New Mexico, October 2004.
- 21. 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.
- 22. 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.
- 23. The computation of the noncommutative generalization of the A-polynomial for the figure-eight knot, National Meeting of the AMS, Baltimore, January 2003.
- 24. On the quantization of the flat SU(2)-connections on the torus, International Conference on Geometric Topology, Xi'an, China, August 2002.
- 25. 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.
- 26. 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.
- 27. 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.
- 28. Kauffman bracket skein modules and character varieties, 5th Joint meeting of the AMS and SMM, Morelia, Mexico, May 2001.
- 29. Kauffman bracket skein modules and character varieties, Texas Geometry and Topology Conference, February 2001 (plenary talk).
- 30. On the noncommutative version of the A-polynomial, 954-th Sectional AMS Meeting, Lafayette, Louisiana, April 2000.
- 31. On the relation between the A-polynomial and the Jones polynomial, AMS National Meeting, Washington, January 2000.
- 32. Noncommutative trigonometry and the A-polynomial, 949-th Sectional AMS Meeting, Charlotte, North Carolina, October 1999.
- 33. Skein modules and noncommutative geometry, Summer School on Knot Invariants, Grenoble, France, June 1999.
- 34. Skein modules and the noncommutative torus, Knots in Hellas, Delphi, Greece, August 1998.
- 35. Kauffman bracket skein modules and the noncommutative torus, 932-nd Sectional AMS Meeting, Manhattan, Kansas, March 1998.
- 36. On the quantum invariant of torus knots, 920-th Sectional AMS Meeting, College Park, Maryland, April 1997.
- 37. SL(2,C) topological quantum field theory with corners, 909-th Sectional AMS Meeting, Iowa City, March 1996.
- 38. Topological quantum field theory with corners, Thirteenth annual workshop on geometric topology, Colorado Springs, June 1996.
- 39. Topological quantum field theory with corners based on the Jones-Wenzl idempotents, Great Plains Operator Theory Symposium, Phoenix, May 1996.
- 40. Topological quantum field theory with corners via the Jones-Wenzl idempotents, Sixteenth International Operator Theory Conference, Timisoara, Romania, July 1996.
- 41. Topological SL(2,C) invariants for 3-manifolds with boundary, Minisemester in Knot Theory, Warsaw, Poland, July 1995.
- 42. On a conjecture of R. G. Douglas and V. Paulsen, South-Eastern Analysis Meeting, Atlanta, March 1995.
- 43. On a conjecture of R. G. Douglas and V. Paulsen, Great Plains Operator Theory Symposium, Cincinnati, May 1995.
- 44. Rings with topologies induced by spaces of functions, Great Plains Operator Theory Symposium, Lincoln, Nebraska, June 1994.
- 45. Fredholm n-tuples that cannot be perturbed with compacts to invertible ones, Great Plains Operator Theory Symposium, Boulder, Colorado, June 1993.
- 46. 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 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, New Haven, November 2009 (Colloquium talk).
- 31. Theta functions and knots, University of Nevada at Reno, February 2010 (Colloquium talk).
- 32. Theta functions and knots, Vassar College, October 2013 (Colloquium talk).
- 33. Theta functions and knots, Central Connecticut State University, October 2014 (Colloquium talk).
- 34.Theta functions and knots, University of Michigan, November 2014 (Colloquium talk).
- 35.Theta functions and knots, Universidade Federal de Fortaleza, Brazil, May 2015.
- 36.Chern-Simons theory and Weyl quantizations, Dartmouth College, September 2015 (Colloquium talk).
- 37. Chern-Simons theory and Weyl quantization, University of Texas at Dallas, October 2015.
- 38. Theta functions and knots University of Texas at Dallas, April 2016 (Colloquium talk).

COMMITTEES

Graduate Committee 2014-present.

Undergraduate Committee, Texas Tech University, 2006-2008, 2010-2011.

Hiring Committee, Texas Tech University, 2010-2015.

PhD Dissertation Committees of:

- Jeff Sink, University of Michigan 1999
- Kendrick Smith, University of Michigan 2000
- Todd Kennaugh, Texas Tech University, 2009
- Jea-Pil Cho, Texas Tech University, 2012 (PhD advisor)
- Nadeeka De Silva, Texas Tech University, 2012
- Elias Gonzalez, Texas Tech University, 2016
- Hongwei Wang, Texas Tech University, 2017 (PhD advisor)

MS Dissertation Committee of:

- Jea-Pil Cho, Texas Tech University, 2010 (committee chair),
- Hongwei Wang, Texas Tech University, 2015 (committee chair).
- Lale Asik, Texas Tech University, 2016.

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.

Session organizer at the Sectional Meeting of the American Mathematical Society, April 11-13, 2014.

Co-organizer of 93rd Texas MAA Sectional Meeting, April 11-12, 2013.

Co-organizer of Texas Geometry and Topology Conference, Spring 2002, Spring 2005, Spring 2008, Spring 2011, Spring 2014.

Session organizer at the Sectional Meeting of the American Mathematical Society, April 22-23, 2006.

Session organizer at the Sectional Meeting of the American Mathematical Society, 8-10 April 2005.

Co-organizer of the Spring Topology and Dynamical Systems Conference, March 2003.

ACTIVITIES RELATED TO MATHEMATICS COMPETITIONS

Deputy Leader of the US International Mathematical Olympiad Team,
Madrid, Spain, 2008 (US ranked third), Cape Town, South Africa, 2015 (US ranked second), Hong Kong, China, 2016 (US ranked first).

Leader of the US Team taking part in the Romanian Masters in Mathematics,
Bucharest, Romania, 2011 (US ranked first), 2012 (US ranked third), 2013 (US ranked first), 2015 (US ranked second), 2016 (US ranked first), 2017 (US ranked sixth).

Member of the USA Mathematical Olympiad Subcommittee
of the MAA, 2013-present.

Member of the USA Mathematical Olympiad Advisory Panel, 1997-present. As such I propose problems for the USA Mathematical Olympiad.

Coordinator of the grading, 40th International Mathematical
Olympiad, Bucharest, Romania, 1999, 42nd International
Mathematical Olympiad, Washington, USA, 2001, 58th International Mathematical Olympiad, Rio de Janeiro, Brazil, 2017.

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, 2013-2017.

Writer of the problems for the Konhauser Problem Fest, 2010, 2014.

Coach of Jay Chung, a student at West High School, Iowa City, 1992-1995. 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.

Editor of universo.math, 2014-present

Assistant Editor of Mathematics Magazine, 2002-2007.

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

Talks on mathematical Olympiads presented at

- University of Michigan, Ann Arbor, February 1998,
- Northeastern University, Boston, March 1999,
- Ft. Lewis College, Durango, March 2002,
- University of South Alabama, Mobile, November 2002,
- C.D. Loga High School, Timisoara, December 2002,
- Texas Tech University Summer Math Academy, June 2006, June 2011,
- Texas Tech University Research Experience for Undergraduates, June 2007,
- Universidad Autonoma del Estado de Mexico, Toluca, September 2007,
- Mathematical Olympiad Training Program of the Estado de Mexico, September 2007,
- Dallas Metroplex Math Circle, November 2007, March 2009, January 2010, November 2010, November 2014,
- University of Texas at San Antonio, April 2008,
- Yale University, November 2009,
- Sistema Elite high school, Rio de Janeiro, Brazil, July 2011,
- Etapa high school, São Paulo, Brazil, June 2013,
- Vassar College, October 2013,
- Central Connecticut State University, October 2014,
- Ari de Sa high school, Fortaleza, Brazil, May 2015,

COURSES TAUGHT

HOBBIES

landscape photography (I love the Southwest),
tourism (as long as I organize everything myself),
music (classical: instrumental and opera, ethnic: blues, latin,
Romanian, etc), skiing (no bumps), snorkeling,
kayaking, hiking, history of painting,
indo-european languages, cooking, carpentry, gardening.