Maciej Zworski

Maciej Zworski is a Polish mathematician noted for contributions to microlocal analysis, semiclassical analysis, and the theory of partial differential equations. He has held academic positions in North America and Europe and has influenced research in spectral theory, scattering, and inverse problems. Zworski's work connects methods from Fourier analysis, differential geometry, and mathematical physics and is widely cited in the literature on resonances and propagation of singularities.

Early life and education

Zworski was born in Poland and received early schooling in Kraków, where institutions such as the Jagiellonian University and the University of Warsaw shaped the mathematical community. He completed undergraduate and graduate studies at the Jagiellonian University before undertaking doctoral work that engaged with analytic techniques developed by researchers associated with Massachusetts Institute of Technology, Stanford University, and the University of California, Berkeley. His doctoral studies were supervised by Richard Melrose, a leading figure in microlocal analysis and the calculus of pseudodifferential operators, and occurred in an era influenced by developments at the Institute for Advanced Study and collaborations linked to the Courant Institute of Mathematical Sciences.

Academic career

Zworski held postdoctoral and faculty positions that connected him to centers such as the University of California, Berkeley, the University of Chicago, and the University of British Columbia. He joined faculty ranks where he taught courses on Fourier integral operators and scattering theory, contributing to programs at the American Mathematical Society meetings and workshops at the Mathematical Sciences Research Institute. Zworski's appointments included involvement with graduate programs associated with the University of Toronto and exchanges with researchers at the Max Planck Institute for Mathematics and the École Polytechnique. He has supervised doctoral students who pursued research in spectral theory, influenced by seminars at the International Congress of Mathematicians and collaborations at the Fields Institute.

Research contributions

Zworski's research centers on microlocal analysis, semiclassical analysis, and applications to linear and nonlinear partial differential equations. He developed techniques for studying resonances in scattering theory that build on methods from Lax–Phillips scattering theory, the WKB approximation, and the complex scaling approach associated with work at the Royal Society and the National Academy of Sciences. His analysis of resonances and scattering poles has been applied in contexts linked to the Helmholtz equation, the Schrödinger equation, and models inspired by general relativity and quantum chaos studies related to the Bohigas–Giannoni–Schmit conjecture. Zworski has advanced understanding of propagation of singularities through contributions that integrate the calculus of pseudodifferential operators, Fourier integral operators, and the microlocal framework pioneered by Lars Hörmander and Jean Leray.

His work on semiclassical resolvent estimates, resonance free regions, and Weyl laws connects to spectral asymptotics studied in relation to the Atiyah–Singer Index Theorem and trace formulae reminiscent of Selberg trace formula techniques. Zworski's research has impacted inverse spectral problems, control theory for wave equations, and analysis of damped wave phenomena with links to studies at the Courant Institute of Mathematical Sciences and the Steklov Institute of Mathematics. Collaborations and citations tie his results to those by Semyon Dyatlov, Johannes Sjöstrand, Luca Tartar, Carlos Kenig, and Peter Sarnak.

Awards and honors

Zworski's contributions have been recognized by appointments and invitations to prominent venues such as plenary and invited lectures at the International Congress of Mathematicians and speaker roles at meetings of the European Mathematical Society and the American Mathematical Society. He received research fellowships and grants from organizations including the National Science Foundation and national funding agencies connected to the Polish Academy of Sciences. Zworski has been elected or appointed to visiting positions at institutes like the Mathematical Sciences Research Institute, the Institute for Advanced Study, and the Max Planck Institute for Mathematics, reflecting international recognition of his work.

Selected publications

- Zworski, M., "Distribution of poles for scattering on the real line", a work connecting resonance theory to complex scaling and contributions by Boris Pavlov and Vladimir Buslaev; widely cited in scattering literature. - Zworski, M., "Semiclassical analysis", a monograph that synthesizes methods linking the WKB approximation, microlocal techniques of Lars Hörmander, and spectral asymptotics studied in the context of the Atiyah–Singer Index Theorem. - Zworski, M., papers with Semyon Dyatlov on resonance gaps and fractal Weyl laws, integrating ideas from dynamics associated with the Anosov flow literature and quantum chaos research connected to Michael Berry and Eugene Bogomolny. - Zworski, M., joint works with Johannes Sjöstrand and Maciej Zworski collaborators on resonance expansions, complex scaling, and trace formulae comparable to techniques used by Atle Selberg and Don Zagier. - Selected articles on control and stabilization for the wave equation and spectral estimates linked to contributions by Lars Hörmander, Carlos Kenig, and Gunther Uhlmann.

Category:Polish mathematicians Category:Mathematical analysts Category:20th-century mathematicians Category:21st-century mathematicians