CURRICULUM VITAE

• Born: 19 October 1965 in Petersburg, Virginia, USA
• Sex: Male
• Nationality: USA
• Marital Status: Never married (no children)
• Languages (ability): American English (native), French (good)

Work Address:

Home Address:

• High School Diploma, Highland Park High School, Highland Park, Illinois, USA, May 1983
• B.S. Physics, Massachusetts Institute of Technology, June 1987
• B.S. Mathematics, Massachusetts Institute of Technology, June 1987
• M.S. Physics, University of California, Berkeley, May 1989
• Ph.D. Physics, University of California, Berkeley, December 1994

• Honorable Mention, National Merit Scholarship, spring semester 1982
• Sigma Pi Sigma, MIT, spring semester 1986
• Phi Beta Kappa, MIT, spring semester 1987
• Honorable Mention, National Science Foundation Fellowship, spring semester 1987
• UC Regents Fellowship, fall semester 1987, spring semester 1988
• Faculty Assistant Teaching Award, Department of Physics, UC Berkeley, spring semester 1989
• American Association of Physics Teachers, spring semester 1989
• Department of Education Graduate Research Fellowship, spring semester 1994
• Reviewer, Mathematical Reviews, July 1998-present

• Private Tutor, first- and second-year calculus, Mathematics Department, University of New Mexico, Albuquerque, New Mexico, USA, summer semesters 1984 and 1985
• Graduate Student Instructor, Department of Physics, UC Berkeley, fall and spring semesters 1987-8 (half-time), 1988-9, 1989-90, 1990-1, summer semesters 1989 (half-time), 1990 (half-time), fall semester 1994

• Graduate Student Research Assistant, Theoretical Physics Group, Lawrence Berkeley Laboratory, Berkeley, California, USA, 1 June 1991-31 December 1994
• Chercheur Associé, Centre de Physique Théorique, Centre National de la Recherche Scientifique, Marseille, France, 1 January-30 September 1995
• Postdoctoral Associate, Department of Physics, University of Miami, Coral Gables, Florida, USA, 15 October 1995-31 August 1997
• Postdoctoral Scholar, School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin, Ireland, 1 September 1997-present

1. Low Dimensional Applications of Quantum Field Theory, Institut d'Études Scientifiques Cargèse, Cargèse, France, 11-29 July 1995

PUBLICATIONS:

1. Edmund Bertschinger and Paul N. Watts, "Galaxy Formation with Cosmic Strings and Massive Neutrinos", Astrophys. J. 328 (1988) 23
2. Peter Schupp, Paul Watts and Bruno Zumino, "The 2-Dimensional Quantum Euclidean Algebra", Lett. Math. Phys. 24 (1992) 141, hep-th/9206024
3. Peter Schupp, Paul Watts and Bruno Zumino, "Differential Geometry on Linear Quantum Groups", Lett. Math. Phys. 25 (1992) 139, hep-th/9206029
4. Peter Schupp, Paul Watts and Bruno Zumino, "Bicovariant Quantum Algebras and Quantum Lie Algebras", Commun. Math. Phys. 157 (1993) 305, hep-th/9210150
5. Paul Watts, "Toward a q-Deformed Standard Model", J. Geom. Phys. 24 (1997) 61, hep-th/9603143
6. Paul Watts, "Ward Identities and Anomalies in Pure W₄ Gravity", Nucl. Phys. B545 (1999) 677, hep-th/9809078
7. Paul Watts, "Noncommutative String Theory, the R-Matrix, and Hopf Algebras", Phys. Lett. B474 (2000) 295, hep-th/9911026

CONFERENCE PROCEEDINGS

1. Peter Schupp, Paul Watts and Bruno Zumino, "Cartan Calculus on Quantum Lie Algebras", Adv. Appl. Clifford Alg. (Proc. Supp.) 4 (S1) (1994) 125, hep-th/9312073
2. Paul Watts, "Generalized Wess-Zumino Consistency Conditions for Pure W₃ Gravity Anomalies", in: Compte-Rendus, W-Algebras: Extended Conformal Symmetries, R. Grimm, V. Ovsienko, eds. CPT-95/P.3268 (1995) 68, hep-th/9509044
3. Paul Watts, "Classical W₃ Supergravity", Conference Presentations at http://hepwww.rl.ac.uk/SUSY98/

PREPRINTS

1. Chryssomalis Chryssomalakos, Peter Schupp and Paul Watts, "The Role of the Canonical Element in the Algebra of Differential Operators AxU", LBL-33274, UCB-PTH-92/42 and hep-th/9310100
2. Peter Schupp, Paul Watts and Bruno Zumino, "Cartan Calculus for Hopf Algebras and Quantum Groups", NSF-ITP-93-75, LBL-34215, UCB-PTH-93/20 and hep-th/9306022
3. Peter Schupp and Paul Watts, "Universal and General Cartan Calculus on Hopf Algebras", LBL-33655, UCB-PTH-93/36 and hep-th/9402134
4. Paul Watts, "Differential Geometry on Hopf Algebras and Quantum Groups" (Ph.D. thesis), LBL-36537, UCB-PTH-94/35 and hep-th/9412153
5. Paul Watts, "Killing Form on Quasitriangular Hopf Algebras and Quantum Lie Algebras", CPT-95/P.3201 and q-alg/9505027
6. Paul Watts, "Derivatives and the Role of the Drinfel'd Twist in Noncommutative String Theory", DIAS-STP-00-03 and hep-th/0003234 (submitted to Lett. Math. Phys.)

IN PREPARATION

1. Paul Watts, "U(N) Gauge Theory in the Randall-Sundrum Model" (working title)
   

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   RESEARCH INTERESTS

   My research interests lie mainly in the field of theoretical particle physics and mathematical physics, in particular those type of problems which may be attacked using differential geometry, topology, group theory, and algebraic methods.
   
   My postgraduate research concentrated primarily on quantum groups (QGs) and Hopf algebras (HAs) and their possible physical applications, specifically the formulation of a field theory with a deformed gauge symmetry. My collaborators and I extensively studied the differential geometric properties of the QGs GL_q(N) and SL_q(N), successfully introducing a Cartan calculus on each and also made significant progress in doing the same for arbitrary bicovariant quantum Lie algebras and HAs. As a postdoctoral researcher, I continued to work in this area, and found a form for the Killing metric of a quantum Lie algebra, showing for the case of SU_q(N) that this deformed metric has many of the same properties as the undeformed version. I then used this metric to construct a deformed Standard Model (SM) which possessed many of the properties of the usual SM, and contained other interesting features as well, such as a single coupling constant and a prediction for the Weinberg angle.
   
   The latter presented a general way to consider noncommutative Yang-Mills theories, an area which is currently the subject of much work: It has recently been demonstrated that an open string theory with Dp-branes on a space with constant nonzero Neveu-Schwarz 2-form B_ij may be thought of as having a noncommutative geometric structure, and that when gauge fields on the branes are introduced, the resulting action is simply that of a Yang-Mills theory, albeit with a noncommutative multiplication and deformed gauge fields. I have shown that this multiplication may be expressed in the language of a quasitriangular HA, where the R-matrix (which depends only on the deformation parameter θ^ij, related to B and the open string metric) provides the transition from the usual commutative space to the noncommutative one. Then, I generalised this result, demonstrating that the multiplication and derivatives in the noncommuting theory were in fact related to a Drinfel'd twist. This suggests there may be an overall HA structure to the theory, and I plan on pursuing this possibility.
   
   Furthermore, the recent work of D. Kreimer and A. Connes has shown that there is an underlying HA structure to the process of renormalization. The renormalization map which they introduce to accomplish this is very general; however, I feel that it may be possible to find explicit forms for this map for particular field theories, e.g. for an SU(2) gauge theory, the R-matrix for SU(2) may play a role in determining this map.
   
   I have also examined the anomalies appearing in the context of pure W₃ gravity, comparing those arising from an effective conformal field theory with a W₃ gauge symmetry and those obtained via the BRS algebra arising from an embedding of sl(2) into sl(3). I have found that the two seemingly different sets of anomalies are in fact particular cases of a more general set satisfying an extended version of the Wess-Zumino consistency conditions. I have used the same approach to find the Ward identities and general forms for the anomalies in pure W₄ gravity from a purely algebraic standpoint. I would like to extend these ideas to pure W_N supergravity as well; I have done some preliminary work in this direction for N=3.
   
   Another subject which I am currently working on is the appearence of a U(N) gauge theory in the Randall-Sundrum (RS) scenario. I have modified the original RS analysis to include 2N instead of only 2 3-branes placed evenly around S¹; then, by a similar orbifolding procedure, one gets two boundaries, each with N coincident 3-branes, and thus a U(N) gauge theory. This also has the result of putting an explicit N dependence into the four-dimensional gravitational constant, and thus gives an indication as to how this particular coupling constant will scale in a large-N approximation.