Nicholas M. Ercolani

Professor

Department Head (2001-2008)

Ph.D. (1980), University of California, Berkeley

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Interests

• Nonlinear Analysis
• Applied Partial Differential Equations
• Integrable Systems Theory
• Random Matrix Theory

Current Teaching

Currently on Sabbatical

Graduate Students

• Adrian Espinola-Rocha PhD 2006 Applied Mathematics
• Yixia Lu PhD 2005 Applied Mathematics
• Virgil Pierce PhD 2004 Mathematics
• Guadalupe Lozano PhD 2004 Mathematics
• Maria Agrotis PhD 2002 Mathematics
• Stephen Shipman PhD 1997 Mathematics
• Matthew Russell 1997 Mathematics
• Barbara Shipman PhD 1995 Mathematics
• Annalisa Calini PhD 1994 Applied Mathematics
• Stephanie Singer PhD (NYU) 1993 Mathematics
• Constance Schober PhD 1992 Applied Mathematics
• Otis Wright, III PhD (Princeton) 1991 Applied & Computational Mathematics
• Heinz Roitner PhD 1991 Applied Mathematics

Selected Publications

• “A Variational Theory for Point Defects in Patterns”, N.M. Ercolani and S. Venkataramani Journal of Nonlinear Science 19, 267-300 (2009).
• “A Quick Deerivation of the Loop Equations for Random Matrices”, N.M. Ercolani and Kenneth T.-R. McLaughlin, in Prorobability, Geometry and Integrable Systems, MSRI vol. 55, 185-198, Cambridge University Press (2008).
• “Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices”, N.M. Ercolani, Kenneth T.-R. McLaughlin and V.U. Pierce Commun. Math. Physics 278, 31-81 (2008).
• “A Bi-Hamiltonian Structure for the Integrable, Discrete Non-Linear Schrodinger Equation”, N.M. Ercolani and G. Lozano, Physica D 218, 105-121 (2006).
• “The Dirichlet-to-Neumann Map, Viscosity Solutions to Eikonal Equations, and the Self-Dual Equations of Pattern Formation”, N.M. Ercolani and M. Taylor, Physica D 196, 205-223 (2004).
• “The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy”, N.M. Ercolani, Shan Jin, C. David Levermore and Warren Mcevoy, Jr., International Mathematics Research Notices (2003), no. 14, 2529-2564 (2003).
• “Global Description of Patterns Far from Onset: A Case Study”, N.M. Ercolani, R. Indik, A.C. Newell, and T. Passot, Physica D 184,127-140 (2003).
• “Asymptotics of the Partition Function for Random Matrices via Riemann-Hilbert Techniques, and Applications to Graphical Enumeration”, N.M. Ercolani and Kenneth T.-R. McLaughlin, International Mathematics Research Notices (2003), no. 14, 755-820.
• “Asymptotics and Integrable Structures for Biorthogonal Polynomials Associated to a Random Two-Matrix Model”, N.M. Ercolani and Kenneth T.-R. McLaughlin, Physica D 152-153,232-268 (2001).
• “Complete Integrability of the Reduced Maxwell-Bloch Equations with Permanent Dipole”, M. Agrotis, N.M. Ercolani, S.A. Glasgow, and J.V. Moloney, Physica D 138, 134-162 (2000).
• “The Geometry of the Phase Diffusion Equation”, N.M. Ercolani, R. Indik, A.C. Newell, and T. Passot, J. Nonlinear Sci. 10, 223-274 (2000).
• “Density of Heat Curves in Moduli Space”, A. Bobenko, N.M. Ercolani, H. Knörrer and E. TrubowitzPanoramas of Mathematics 34 19-27 (1995).
• “Finite Genus Solutions to the Ablowitz-Ladik Equations”, P.D. Miller, N.M. Ercolani, I.M. Krichever and C.D. Levermore, Commun. in Pure and Appld. Math. 48 1369-1440 (1995).
• “Hyperelliptic Curves that Generate Constant Mean Curvature Tori in R³”, N.M. Ercolani, H. Knörrer and E. Trubowitz, Progress in Mathematics 115, 81-114 (1993).
• “The Geometry of the Full Toda Lattice”, N.M. Ercolani, H. Flaschka and S. Singer, Progress in Mathematics 115, 181-226 (1993).
• “Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems”, w/ R.E. Caflisch, T.Y. Hou and Y. Landis, Commun. in Pure and Appld. Math. 46, 453-499 (1993).
• “Geometry of the Modulational Instability III: Homoclinic Orbits for the Periodic Sine-Gordon Equation”, N.M. Ercolani, G. Forest and D. McLaughlin, Physica D 43, 349-384 (1990).
• “Geometry of KdV(4): Abel Sums, Jacobi Variety, and Theta Function in Scattering Case”, N.M. Ercolani and H. McKean, Inventiones Math., 99, 483-544 (1990).
• “Monopoles and Baker Functions”, N.M. Ercolani and A. Sinha, Commun. Math. Physics, 125 385-416 (1989).
• “The Geometry of the Hill Equation and of the Neumann System”, N.M. Ercolani and H. Flaschka, Phil. Trans. Royal Soc. London A, 315 405-422 (1985).
• “The Geometry of Real Sine-Gordon Wavetrains”, N.M. Ercolani and G. Forest, Commun. Math. Physics, 99 1-49 (1985).

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E-mail: ercolani@math.arizona.edu
This page was last updated on: March 22, 2009