Nicholas M. Ercolani

Professor and Department Head

Ph.D., University of California, Berkeley

Interests

• Nonlinear Analysis
• Variational and Hamiltonian Partial Differential Equations
• Integrable Systems
• Random Matrix Theory

Teaching

• Introduction to Statistics and Biostatistics

Recent PhD Students

• Guadalupe Lozano
• Virgil Pierce
• Maria Agrotis
• Stephen Shipman
• Barbara Shipman
• Annalisa Calini
• Stephanie Singer (NYU)
• Yixia Lu
• Otis Wright (Princeton)

Selected Publications and Papers

• “The Dirichlet-to-Neumann Map, Viscosity Solutions to Eikonal Equations, and the Self-Dual Equations of Pattern Formation”, w/ M. Taylor, Physica D 196, 205-223 (2004).
• “The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy”, w/ 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”, w/ 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”, w/ 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”, w/ Kenneth T.-R. McLaughlin, Physica D 152-153,232-268 (2001).
• “Complete Integrability of the Reduced Maxwell-Bloch Equations with Permanent Dipole”, w/ M. Agrotis, S.A. Glasgow, and J.V. Moloney, Physica D 138, 134-162 (2000).
• “The Geometry of the Phase Diffusion Equation”, w/ R. Indik, A.C. Newell, and T. Passot, J. Nonlinear Sci. 10, 223-274 (2000).
• “The Behaviour of the Weyl Function in the Zero-Dispersion KdV Limit”, w/ D. Levermore and T. Zhang, Commun. Math. Physics 183 119-143 (1997).
• “Geometry of Singularities for the Steady Boussinesq Equations”, w/ R.E. Caflisch and G. Steele, Selecta Mathematica (New Series) 2 1-46 (1996).
• “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).