Publications and Preprints

Most recent first:

• Quantum Flux and Quantum Ergodicity for Cross Sections, with J. Toth, submitted.
• Small-Scale Mass Estimates for Neumann Eigenfunctions: Piecewise Smooth Planar Domains, with J. Toth, submitted.
• Control Estimates for 0-th Order Pseudodifferential Operators, with J. Wang and R. P.T. Wang, Int. Math. Res. Not. IMRN, to appear.
• Energy Distribution for Dirichlet Eigenfunctions on Right Triangles, with D. Pezzi, submitted.
• Non-concentration and restriction bounds for Neumann eigenfunctions of piecewise $C^{\infty}$ bounded planar domains, with J. Toth, (this paper has been divided into two parts and expanded in this paper.)
• Conformal Perturbations and Local Smoothing with D. Muckerman, submitted.
• Local smoothing for the Schrodinger equation on a multi-warped product manifold with inflection-transmission trapping with D. Nowak, Proc. Amer. Math. Soc., Vol. 150 (2022), no. 1, 213–229. 
  
• Asymptotic Boundary Observability for the Schrodinger Equation on Simplices with S. Carpenter, submitted.
• Asymptotic Boundary Observability For The Wave Equation On Simplices with Z. Lu, submitted.
• Neumann Data Mass on Perturbed Triangles with J. Xi, submitted.
• Asymptotic Boundary Observability for the Wave Equation on One Side of a Planar Triangle with E. Stafford, Ann. Henri Poincare, Vol. 20 (2019), no. 9, 2987–3006.
  
• A one point non-concentration estimate for Laplace eigenfunctions on polygons, (this paper has been superseded by the much stronger results in this paper.)
• Localized Energy for Wave Equations with Degenerate Trapping with R. Booth, J. Metcalfe, and J. Perry Math. Res. Lett., Vol. 26 (2019), no. 4, 991–1025.
• Equidistribution of Neumann data mass on simplices and a simple inverse problem Math. Res. Lett., Vol. 26 (2019), no. 2, 421–445.
• Equidistribution of Neumann data mass on triangles Proc. Amer. Math. Soc. Vol. 145 (2017), no. 12, 5247–5255.
  
• Imperfect geometric control and overdamping for the damped wave equation with N. Burq Comm. Math. Phys. Vol.  336 (2015), Issue 1, 101–130.
• A Non-concentration Estimate for Partially Rectangular Billiards Comm. Partial Differential Equations Vol. 40 (2015), no. 4, 629–651.
• Unique Continuation for Quasimodes on Surfaces of Revolution: Rotationally invariant Neighbourhoods Ann. Inst. Fourier (Grenoble) Vol. 65 (2015), no. 4, 1617–1645.
• High-frequency resolvent estimates on asymptotically Euclidean warped products Comm. Partial Differential Equations, Vol. 43 (2018), no. 9, 1306–1362.
  
• Exterior mass estimates and $L^2$ restriction bounds for Neumann data along hyper surfaces with A. Hassell and J. Toth Int. Math. Res. Not. IMRN Vol. 2015 (2015), 1638–1665.
• Sharp local smoothing for warped product manifolds with smooth inflection transmission with J. Metcalfe Indiana Univ. Math. J. Vol. 63 (2014), no. 4, 969–992.
• From resolvent estimates to damped waves with E. Schenck, A. Vasy, and J. Wunsch  J. Anal. Math. Vol. 122 (2014), Issue 1, pp 143-162
• Quantum Ergodic Restriction for Cauchy Data: Interior QUE and Restricted QUE with J. Toth and S. Zelditch Math. Res. Lett. Vol. 20 (2013), no. 3, 1–11.
  
• Nonlinear Bound States on Weakly Homogeneous Spaces with J. Marzuola, J. Metcalfe, and M. Taylor Comm. Partial Differential Equations, Vol. 39 (2014), no. 1, 34–97.
  
• Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping  Comm. Math. Phys. Vol. 324 (2013), no. 3, 657–693.
• Local Smoothing for the Schrodinger Equation with a Prescribed Loss with J. Wunsch Amer. J. Math. Vol. 135 (2013), no. 6, 1601–1632.
• Nonlinear Quasimodes near Elliptic Periodic Geodesics with P. Albin, J. Marzuola, and L. Thomann Phys. D  Vol. 241 (2012), no. 4, 409–425.
• Random Walk on Surfaces with Hyperbolic Cusps with C. Guillarmou and L. Michel Ann. Henri Poincare Vol. 12 (2011), no. 4, 743–775.
• Strichartz Estimates for the Water-wave problem with Surface Tension with V.M. Hur and G. Staffilani Comm. Partial Differential Equations Vol. 35 (2010), no. 12, 2195–2252.
• Existence and Stability of Solitons for the Nonlinear Schrodinger Equation on Hyperbolic Space with J. Marzuola Nonlinearity Vol. 23 (2010), no. 1, 89–106.
• Corrigendum to Semiclassical non-concentration near hyperbolic orbits [J. Funct. Anal. 246 (2) (2007) 145–195], Journal of Functional Analysis Vol. 258 (2010), no. 3, 1060–1065.
• Local Smoothing Effects for the Water-wave Problem with Surface Tension with V.M. Hur and G. Staffilani C. R. Math. Acad. Sci. Paris Vol. 347 (2009), no. 3-4, 159–162.
• Quantum Monodromy and Non-concentration Near a Closed Semi-hyperbolic Orbit Trans. Amer. Math. Soc. Vol. 363 (2011), no. 7, 3373–3438.
• Isomorphisms between Algebras of Semiclassical Pseudodifferential Operators Proc. Amer. Math. Soc. Vol. 139 (2011), no. 2, 499–510.
• Applications of Cutoff Resolvent Estimates to the Wave Equation Math. Res. Lett. Vol. 16 (2009), no. 4, 577–590.
• Cutoff Resolvent Estimates and the Semilinear Schrodinger Equation Proc. Amer. Math. Soc. Vol. 136 (2008), no. 10, 3513–3520.
• The Colin de Verdiere Graph Parameter for Threshold Graphs with Felix Goldberg unpublished
• Dispersive Estimates for Manifolds with one Trapped Orbit Comm. Partial Differential Equations Vol. 33, (2008) no. 7, 1147–1174.
• Semiclassical Non-concentration near Hyperbolic Orbits, Journal of Functional Analysis Vol. 246 (2007), no. 2, 145–195.
• Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps, Canadian Journal of Mathematics, Vol. 59 (2007), no. 2, 311–331.
• On Correlations of CM-Type Maass Waveforms under the Horocyclic Flow, with Dennis Hejhal Journal of Physics A, Mathematical and General, Vol. 36 (2003), no. 12, 3467–3486.
• The Critical Group of a Threshold Graph, with Victor Reiner Linear Algebra and its Applications, Vol. 349 (2002), 233–244.

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