Benjamin Eichinger

Senior Scientist at TU Wien, Vienna, Austria

News

I was selected as the recepient of the 2026 SIAM Gábor Szegő Prize.

Contact Information

Institute of Analysis and Scientific Computing, TU Wien
1040 Wien
Austria

E-Mail: benjamin (dot) eichinger (at) tuwien (dot) ac (dot) at

Employment

• 2026-:    Senior Scientist, TU Wien, Austria
• 2024-2026: Lecturer, Lancaster University, Lancaster, UK
• 2021-2024: Postdoctoral Fellow, TU Wien, Austria
• 2020:     Postdoctoral Fellow, Johannes Kepler University, Linz, Austria
• 2019:     Postdoctoral Fellow, Rice University, Houston, USA
• 2018:     Postdoctoral Fellow, Lund University, Lund, Sweden
• 2017:     Postdoctoral Fellow, Johannes Kepler University, Linz, Austria

Degrees

• Habilitation Mathematics, TU Wien, Austria, 2025
• Ph.D. Mathematics, Johannes Kepler University, Linz, Austria, 2017
• M.Sc. Mathematics, Johannes Kepler University, Linz, Austria, 2014
• B.Sc. Mathematics, Johannes Kepler University, Linz, Austria, 2012

Research Interests

• Spectral Theory
• Orthogonal Polynomials
• Universality phenomena for Orthogonal Polynomials and Random Matrices
• Continuum and discrete Schrödinger operators
• Canonical Systems
• Integrable Systems
• Functional Models
• Extremal Problems of Chebyshev type

Selected publications

• Chebyshev polynomials on a Jordan arc, with B. Buchecker and O. Rubin and A. Wennman, (submitted). [arXiv]

  We prove Szegő–Widom asymptotics for the Chebyshev polynomials of an analytic Jordan arc, resolving a problem that has remained open since Widom's 1969 work.

• Necessary and sufficient conditions for universality limits, with M. Lukic and H. Woracek, to appear in Invent. Math.(to appear). [arXiv]

  We derive the first necessary and sufficient conditions for universality limits for fixed measures. Our results cover prominent universality classes such as bulk universality, hard-edge universality, and universality for measures with Fisher–Hartwig singularities.

• An approach to universality using Weyl m-functions, with M. Lukic and B. Simanek, Ann. of Math. (2). [article]

  We prove the first pointwise, purely local sufficient condition for bulk universality limits. To do so, we introduce a new framework for studying scaling limits of orthogonal polynomials via canonical systems.

• Stahl-Totik regularity for continuum Schrödinger operators, with M. Lukic, Anal. PDE. [article]

  We develop a theory of Stahl–Totik regularity for unbounded operators. Using the Martin compactification, we identify a constant associated with the spectrum of the operator that plays the role of a renormalized Robin constant for unbounded spectra.

• KdV hierarchy via Abelian coverings and operator identities, with T. VandenBoom and P. Yuditskii, Trans. Amer. Math. Soc. Ser. B. [article]

  We develop a method that extends the classical study of algebro-geometric solutions of the KdV equation to non-compact Riemann surfaces. We use this theory to prove that solutions of the KdV equation with reflectionless initial data satisfying a finite gap length condition are almost periodic in time. This confirms, for a large class of initial data, a conjecture of Deift that almost periodic initial data yield solutions that are almost periodic in time. The conjecture was later disproved in full generality by Chapouto, Killip, and Vişan in Duke Math. J.

I am an editor of Advances in Approximation Theory

More information can be found on my Curiculum Vitae.

Scientific Outreach

• A public lecture (in german) about Kac's famous question Can one hear the shape of a drum at TU Wien TUFORMATH
• An article about my recent work on universality limits (in german)