Jeffrey Galkowski


NSF Postdoctoral Fellow
Department of Mathematics
Stanford University




CV


Office: 384-D
E-mail: jeffrey.galkowski@stanford.edu

Papers

On non-diffractive cones. with Jared Wunsch preprint: arXiv:1807.05043

Control from an interior hyper surface. with Matthieu Léautaud preprint: arXiv:1711.03939

On the growth of eigenfunction averages: microlocalization and geometry. with Yaiza Canzani preprint: arXiv:1710.07972

Averages of Eigenfunctions Over Hypersurfaces. with Yaiza Canzani and John Toth. Communications Mathematical Physics 360 (2) 619-637 (2018). preprint: arXiv:1705.09595

Defect Measures of Eigenfunctions with Maximal L^\infty Growth. to appear in Annales de l'Institut Fourier preprint: arXiv:1704.01452

Eigenfunction Scarring and Improvements in L^\infty Bounds with John Toth. Anal. PDE. Vol. 11 (2018), No. 3, 801-812 preprint: arXiv:1703.10248

Fractal Weyl Laws and Wave Decay for General Trapping with Semyon Dyatlov. Nonlinearity. Volume 30 no. 12. preprint: arXiv # 1703.06515,

Pointwise Bounds for Steklov Eigenfunctions with John Toth. preprint: arXiv # 1611.05363. to appear in J. Geom. Anal.

The Wavenumber-explicit Analysis for the Helmholtz h-BEM: Error Estimates and Iteration Counts for the Dirichlet Problem with Eike Müller and Euan Spence. preprint: arXiv # 1608.01035.

The L^2 Behavior of Eigenfunctions Near the Glancing Set. Comm. Partial Differential Equations. 41 (2016), no. 10, 1619-1648. preprint: arXiv # 1604.01699.

Arbitrarily Small Perturbations of Dirichlet Laplacians are Quantum Unique Ergodic with Sourav Chatterjee. preprint: arXiv # 1603.00597, to appear in J. Spectr. Theory.

A Quantitative Vainberg Method for Black Box Scattering.. Comm. Math. Phys. 349 (2017), no. 2, 527-549. preprint: arXiv # 1511.05894.

The Quantum Sabine Law for Resonances in Transmission Problems. preprint: arXiv # 1511.05091.

Resonances for Thin Barriers on the Circle. Journal of Physics A. 49 (2016), 125205.

Distribution of Resonances in Scattering by Thin Barriers. preprint: arXiv # 1404.3709. To appear in Memoirs of the AMS.

Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering with Hart Smith. International Mathematics Research Notices (2015) no. 16 pp. 7473-7509.

Appendix in Sharp Norm Estimates of Layer Potentials and Operators at High Frequency (by Xiaolong Han and Melissa Tacy). Journal of Functional Analysis 269 (2015), pp. 2890-2926.

Pseudospectra of Semiclassical Boundary Value Problems. J. Inst. Math. Jussieu 14 (2015), no. 2, 405-449.

Quantum Ergodicity for a Class of Mixed Systems. J. Spectr. Theory 4 (2014), no. 1, 65-85.

Nonlinear Instability in a Semiclassical Problem. Communications in Mathematical Physics Volume 316, Issue 3 (2012), Page 705-722.

Talks and Presentations


Concentration of Eigenfunctions: Sup-norms and Averages

Analysis and PDE Seminar, UC Berkeley, January 2018
Special Seminar, Northeastern University, January 2018
Special Seminar, University of Cambridge, February 2018
Analysis Seminar, McGill University, February 2018
Analysis and PDE Seminar, Stanford University, April 2018
Mathematical Physics Seminar, UC Irvine, May 2018
Journees EDP, Obernai, France, June 2018
Around Quantum Chaos, Banff International Research Station, Banff, July 2018 Video


Fractal Weyl Laws for General Trapping and Decay on Average

Third Symposium on Scattering and Spectral Theory, UFSC, Florianopolis, Brazil, July 2017
Spectral Geometry, Graphs, and Semiclassical Analysis, Aussois, France, December 2017
Spectral Geometry Seminar, Universite de Montreal, February 2018

Defect Measures for Eigenfunctions with Maximal L^\infty Growth

Mathematical Physics and Harmonic Analysis Seminar, Texas A&M, March 2017.
PDE/Analysis Seminar, MIT, March 2017.
Analysis Seminar, Northwestern University, April 2017.

Pointwise Bounds for Steklov Eigenfunctions

Spectral and Scattering Theory Seminar, Purdue University, December 2016.
Analysis Seminar, University of North Carolina, Chapel Hill, January 2017.
Bay Area Microlocal Analysis Seminar, UC Berkeley, February 2017.
Spectral Geometry Seminar, Universite de Montreal, March 2017
Analysis Seminar, University of Laval, April 2017.

The L^2 Behavior of Eigenfunctions Near the Glancing Set

Analysis Seminar, University of Rochester, October 2016.

Arbitrarily Small Perturbations of Laplacians are Quantum Unique Ergodic

Student Harmonic Analysis and Differential Equations Seminar, UC Berkeley, April 2016.
Probabilistic Methods in Spectral Geometry and PDE, CRM Montreal, August 2016

Resonance Free Regions and Average Smoothing Times

Partial Differential Equations/ Analysis Seminar, UC Berkeley, December 2015.
Partial Differential Equations/ Analysis Seminar, McGill University, September 2016.

A Quantum Sabine Law for Resonances in Transmission Problems

Spectral and Scattering Theory Seminar, Purdue University, October 2015.
Bay area Microlocal Analysis Seminar, Stanford, February 2016.
Evolution Equations on Singular Spaces, CIRM Luminy, April 2016 Video.
Dirichlet to Neumann Maps: Spectral Theory, Inverse Problems and Applications, Oaxaca Research Station, June 2016. Video.

Distribution of Resonances for Scattering by Thin Barriers

Mathematics Colloquium, University of Reading, July 2015.
Geometric Scattering Theory and Applications, Banff International Research Station, November 2014 Video.
PDE Seminar, Brown University, October 2014.
PDE/Analysis Seminar, MIT, October 2014.
Seminaire Geometrie et Analyse, University of Nice, June 2014.
Bay area Microlocal Analysis Seminar, Stanford, May 2014.
Partial Differential Equations Mini School, University of North Carolina: Chapel Hill, April 2014.
Student Harmonic Analysis and Differential Equations Seminar, UC Berkeley, October 2013.

Pseudospectra for Semiclassical Boundary Value Problems

Student Harmonic Analysis and Differential Equations Seminar, UC Berkeley, February 2013.

Quantum Ergodicity for a Class of Mixed Systems

Student Harmonic Analysis and Differential Equations Seminar, UC Berkeley, October 2012.

Nonlinear Instability in a Semiclassical Problem

Partial Differential Equations/ Analysis Seminar, UC Berkeley, August 2012.
Analysis, Dynamics, and Applications Seminar, University of Arizona, February 2012
Student Harmonic Analysis and Differential Equations Seminar, UC Berkeley, November 2011.


Other Research

Distribution of Resonances in Scattering by Thin Bariers. Ph. D. dissertation (May 2015), written under the supervision of Maciej Zworski.

Synthesis of Size-Controlled and Shaped Copper Nanoparticles by Derrick Mott, Jeffrey Galkowski, Lingnan Wan, Jin Luo, and Chuan-Jian Zhong. Langmuir. Volume 23, No. 10 (2007), Page 5740-5745.


Expository Work

Poincare Recurrence


Teaching

Stanford

Fall 2017: Math 175 - Elementary Functional Analysis
Fall 2017: Math 272 - Topics in Partial Differential Equations

McGill

Fall 2016: Math 564

Stanford

Winter 2016: Minicourse on Vasy's Method

UC Berkeley

Spring 2014: GSI Math 1B

Fall 2013: GSI Math 16A

Spring 2013: GSI Math 16B

Fall 2012: GSI Math 55

Spring 2011: GSI Math 53

Fall 2010: GSI Math 1A