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Dr. Siegfried Beckus


(I have moved to the Technion in Haifa, Israel. However, I will keep this website updated.)


Bild1
Office:

Technion Campus, Amado Building
Office 700

E-Mail:

e_mail

Addresse:

Technion Haifa,

Department of Mathematics

Technion Campus, Amado Building
Office 700

32000 Haifa
Israel

Research interests

  • spectral theory of Schrödinger operators with aperiodic ordered potentials
  • dynamical Systems
  • Delone sets
  • graph limits and graphings
  • aperiodic tilings
  • fields of C*-algebras (especially C*-algebras induced by groupoids)

Publications & Preprints

Delone dynamical systems and spectral convergence
(with Felix Pogorzelski), arXiv:1711.07644

Spectral Continuity for Aperiodic Quantum Systems I. General Theory
(with Jean Bellissard, Giuseppe de Nittis), arxiv.org/abs/1709.00975

Shnol-type theorem for the Agmon ground state
(with Yehuda Pinchover), arXiv:1706.04869

On the spectrum of operator families on discrete groups over minimal dynamical Systems
(with Daniel Lenz, Marko Lindner, Christian Seifert), to appear in: Mathematische Zeitschrift

Continuity of the spectrum of a field of self-adjoint operators
(with Jean Bellissard), Annales Henri Poincare, Volume 17, Issue 12 (2016), Page 3425-3442

Note on spectra of non-selfadjoint operators over dynamical system
(with Daniel Lenz, Marko Lindner, Christian Seifert), to appear in: Proc. Edinburgh Math. Soc.

Spectrum of Lebesgue measure zero for Jacobi operators of quasicrystals
(with Felix Pogorzelski), Mathematical Physics, Analysis and Geometry, Volume 16, Issue 3 (2013), Page 289-308


PhD thesis

Spectral approximation of aperiodic Schrödinger operators


Diploma thesis

Generalized Bloch Theory for Quasicrystals


CV (pdf)

Current position

Since October 2016
Post-Doc, Israel Institute of Technology (Technion), Haifa, Department of Mathematics

March 2012 - September 2016
research assistant (Ph.D. student in mathematics), Friedrich-Schiller-Universität Jena

Education

March 2012 - September 2016
PhD in mathematics, Friedrich-Schiller-Universität Jena

February 2014 - April 2014
Research Collaborator at Georgia Institute of Technology, Atlanta, USA

September 2009 - December 2009
Exchange Semester at the faculty of science, University of Joensuu

October 2006 - February 2012
Diploma studies in mathematics with minor subject physics, Friedrich-Schiller-Universität Jena

Research funding

March 2014 - April 2014
Student Internship (J1), Georgia Institute of Technology

July 2015
Scholarship of the DAAD, Program to participate at congresses, XVII International Congress on Mathematical Physics, Santiago de Chile

Funding
March 2013 - September 2016
Funding for the PhD Seminar by the graduate school of Jena, "Förderung von interdisziplinären Arbeitsgruppen und Nachwuchsnetzwerken"

Talks

November 16, 2017, Spectral theory seminar, Pontificia Universidad Catolica de Chile, Santiago, Chile, "Shnol type Theorem for the Agmon ground state"

November 15, 2017, Mathematical physics seminar, Pontificia Universidad Catolica de Chile, Santiago, Chile, "Spectral approximation of Schrödinger operators"

November 1, 2017, Analysis seminar, Hebrew Universit, Jerusalem, Israel, "When do the spectra of self-adjoint operators converge?"

October 3, 2017, Workshop "Spectral Structures and Topological Methods in Mathematical Quasicrystals", Oberwolfach, Germany, "Spectral Stability of Schrödinger operators in the Hausdorff metric"

August 11, 2017, C*-algebra seminar, University of Oslo, Norway, "Spectral approximation via an approach from C*-algebras"

July 31, 2017, Conference "Analysis and Geometry on Graphs and Manifolds", Universität Potsdam, Germany, "Shnol type Theorem for the Agmon ground state"

July 27, 2017, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, "The space of Delone dynamical systems and its applications"

July 18, 2017, RWTH Aachen, Germany, "Shnol type Theorem for the Agmon ground state"

May 28, 2017, Conference "Israel Mathematical Union 2017", Acre, Israel, "The space of Delone dynamical systems and related objects"

May 15, 2017, PhD Seminar, Friedrich-Schiller-Universität Jena, Germany, "Unique ergodicity of Delone dynamical systems"

May 11, 2017, Oberseminar, Friedrich-Schiller-Universität Jena, Germany, "The space of Delone dynamical systems and related objects"

May 9, 2017, GRK Seminar, Friedrich-Schiller-Universität Jena, Germany, "Shnol type Theorem for the Agmon ground state"

March 1, 2017, Seminar, Aalborg University, Denmark, "Spectral Approximation of Schrödinger Operators"

January 24, 2017, Workshop on Mathematical Physics, Weizmann Institute of Science, "Spectral Approximation of Schrödinger Operators", Poster presentation

January 11, 2017, ​PDE and Applied Mathematics Seminar, Israel Institute of Technology, "Spectral Approximation of Schrödinger Operators"

Dezember 15, 2016, Seminar "Groups, Dynamics and related Topics", Israel Institute of Technology, "Existence of periodic elements: a topological point of view"

September 5, 2016, Seminar, Aalborg University, Denmark, "Continuous variation of the spectra: A characterization and a tool"

July 26, 2016, Seminar in Siegmundsburg, "Continuous variation of the spectra: A characterization and a tool"

July 5, 2016, Seminar, Universität Bielefeld, "Hölder-continuous behavior of the spectra associated with self-adjoint operators"

June 15, 2016, Thematic School "Transversal Aspects of Tilings", Oleron, France, "Continuity of the spectra associated with Schrödinger operators"

April 26, 2016, Universität Potsdam, Seminar, "Continuous variation of the spectra: A characterization and a tool"

February 19, 2016, Annual Meeting GRK 1523 "Quantum and Gravitational Fields", "Schrödinger operators associated with dynamical systems"

January 28, 2016, Workshop on Spectral Geometry, Universität-Potsdam, "Operators over dynamical systems: The dependence of the spectrum with respect to the underlying geometry"

January 27, 2016, Oberseminar "Analysis, Geometrie & Dynamik", Friedrich-Schiller-Universität Jena, "Spectral Approximation of Schrödinger Operators: Continuous Behavior of the Spectra"

January 12, 2016, Norwegian University of Science and Technology, Trondheim"Spectral Approximation of Schrödinger Operators: Continuous Behavior of the Spectra"

November 11, 2015 Ph.D. seminar in Jena, "Continuous behavior of the spectrum: Application to Schrödinger operators"

November 2, 2015 Ph.D. seminar in Jena, "Continuous behavior of the spectrun of fields of operators"

September 29, 2015, Workshop on Spectral Properties of Quasicrystals via Analysis, Dynamics and Geometric Measure Theory, Casa Matemática Oaxaca - Banff International Research Station, Oaxaca, Mexiko, "Spectral Approximation of Schrödinger Operators: Continuity of the Spectrum"

July 28, 2015, XVIIIth International Congress on Mathematical Physics, Santiago de Chile, "Spectral Study of Schrödinger Operators with Aperiodic Ordered Potentials", Poster presentation

July 25, 2015, Young Researcher Symposium, Pontificia Universidad Catolica de Chile, Santiago de Chile, "Spectral Study of Schrödinger Operators with Aperiodic Ordered Potential in One-dimensional Systems"

June 09, 2015, Norwegian University of Science and Technology, Trondheim, Workshop on time-frequency analysis and aperiodic order"An Approximation Theorem for the Spectrum of Schrödinger Operators Related with Quasicrystals", Talk

Mai 07, 2015, Technische Universität Chemnitz, PhD Seminar, "Schrödinger operators on Quasicrystals"

April 15, 2015, Technion -Israel Institute of Technology, Seminar: Groups, Dynamics and Related Topics, "The role of Gähler-Anderson-Putnam Graphs in the view of Schrödinger operators"

January 05, 2015, The University of Leicester, England, Workshop on Aperiodic Order, "Gähler-Anderson-Putnam graphs of 1-dimensional systems"

October 27, 2014, Ph.D. seminar in Jena, "Spectral Approximation of bounded Operators"

July 23, 2014, Seminar in Siegmundsburg, "Periodic approximation of 1-dimensional Schrödinger operators."

June 02, 2014, Friedrich-Alexander Universität Erlangen-Nürnberg, AG Mathematische Physik, "Gähler-Anderson-Putnam graphs of 1-dimensional Delone sets of finite local complexity"


April 04, 2014, UAB Birmingham,  USA, Probability and Math Physics Seminar
"Gähler-Anderson-Putnam graphs of 1-dimensional Delone sets of finite local complexity", Abstract

January 14, 2014, TUHH Hamburg, "Wannier transformation for Schrödinger operators with aperiodic potential.", Abstract

October 2, 2013, Ph.D. Symposium in Chemnitz within the Fall school Dirichlet forms, operator theory and mathematical physics
: "One-dimensional Schrödinger operators with aperiodic potential: The Fibonacci sequence"

July 16, 2013, Seminar in Siegmundsburg, "Quasicrystals and the Floquet-Bloch theory"


May 2, 2013 Ph.D. seminar in Jena,
"Quasicrystals and the Floquet-Bloch theory"

December 13, 2012,
Workshop on Dirichlet forms, operator theory and mathematical physics, "
Lebesgue measure zero spectrum for Jacobi matrices of quasicrystals"

September 20, 2012,
DMV Tagung at University of Saarbrücken, "Generalized Bloch Theory for Quasicrystals"

Organized Scientific meetings

Ph.D. Symposium in Chemnitz within the Fall school Dirichlet forms, operator theory and mathematical physics, Wednesday October 2nd 2013
(organized by Siegfried Beckus, Marcel Hansmann, Felix Pogorzelski and Marcel Schmidt)

Ph.D. Seminar, Friedrich-Schiller-Universität Jena, SS 2013, WS 2013/2014, SS 2014, WS 2014/2015
(organized by Siegfried Beckus and Therese Mieth)

(Co-) Supervision

Daniel Sell, "Topological Groupoids and Matuis Spatial Realization Theorem" , Master thesis 2015

Franziska Sieron, "Die Balanciertheitseigenschaft primitiver Substitutionen" , Bachelor thesis 2014

Teaching

WS 2017
Minicourse on "The connection of the K-theory with the Gap-labeling theorem of Schrödinger operators" (abstract, notes)
 
SS 2016 Ph.D. seminar (with Therese Mieth)  
Tutorial Ordinary Differential Equations  
WS 2015/16
Ph.D. seminar (with Therese Mieth)
Kolloquium "Mathematik ... und dann?" (with Markus Lange, Therese Mieth)
SS 2015
Ph.D. seminar (with Therese Mieth)
Tutorial Functional Anslysis I for mathematicians

WS 2014/15



Ph.D. seminar (with Therese Mieth)
Tutorial Analysis III for mathematicians
Kolloquium "Mathematik ... und dann?" (with Marlis Bärthel, Therese Mieth)
SS 2014 Ph.D. seminar (with Therese Mieth)
Tutorial Analysis II for mathematicians
WS 2013/14 Ph.D. seminar (with Therese Mieth)
Tutorial Analysis I for mathematicians
Ph.D. Symposium in Chemnitz
  Kolloquium "Mathematik ... und dann?" (with Therese Mieth)
 SS 2013  Ph.D. seminar (with Therese Mieth)
Tutorial Analysis II for mathematicians
WS 2012/13 Tutorial Analysis I  for mathematicians
SS 2012 Tutorial Ordinary Differential Equations
WS 2011/12

Tutorial Analysis III  for mathematicians and physicists

SS 2011

Tutorial Linear Algebra and analytic Geometry II for teacher

WS 2010/11

Tutorial Linear Algebra and analytic Geometry I for teacher