Talks (English)

Parts of this material are based upon work supported by the National Science Foundation
under Grant No. 0300398, No. 0600956, No 0901514,  and No. DMS-1160962 since 2003.

Recent materials are based upon work supported by the SFB 878, Groups, Geometry & Actions
Department of Mathematics, Westfälische Wilhelms-Universität, Münster, Germany (Since May 2016).

    Topological Insulators, Physics & Disorder    (pdf file)
        Noncommutative Geometry, Analysis, and Topological Insulators,
        Workshop, Leiden, the Netherlands, February 3-4, 2020

    Spectrum Algebraic Approach to Localization    (pdf file)
        IRMA Seminar, Strasbourg, France
        October 31, 2019

    Spectrum Approximation for Aperiodic Hamiltonians    (pdf file)
        Workshop "Random Physical Systems"
        Puerto Natales, Chile
        December 11-15, 2018

    Laplace Operator on Compact Metric Spaces    (pdf file)
        Workshop "Spectral Approaches to Fractal Geometry"
        University of Gothenburg and Chalmers University of Technology,
        September 17-19, 2018

    Periodic Approximants to Aperiodic Hamiltonians    (pdf file)
        Workshop "Group and Dynamics: Spectra and L2-invariant"
        Université de Genève, September 10-13, 2018

    Periodic Approximants to Aperiodic Hamiltonians    (pdf file)
        Conference "Systèmes Dynamiques et Systèmes Complexes",
        Celebrating J.-M. Gambaudo's 60th birthday, Université de Nice, June 13, 2018

    Persistence of Topological Invariants under Disorder    (pdf file)
        Workshop "Topological protection in messy materials"
        Georgia Institute of Technology, May 14-15, 2018

    Periodic Approximations for Energy Spectra of Aperiodic Media    (pdf file)
        Aalborg Math-Phys Seminar,
        Aalborg University, February 8, 2018

    Periodic Approximants to Aperiodic Hamiltonians    (pdf file)
        Conference "Applications of operator algebras:
        order, disorder and symmetry"
        ICMS, 15 South College Street, Edinburgh, June 26-30, 2017

    Periodic Approximants to Aperiodic Hamiltonians    (pdf file)
        Colloquium Talk, Department of Mathematics,
        Universidad Carlos III, Madrid, November 2nd, 2016

    A Toy Model for Viscosity    (pdf file)
       Joint Institute of Neutron Science,
        Oak Ridge National Laboratory, October 18th, 2016

    Periodic Approximants to Aperiodic Hamiltonians    (pdf file)
       Workshop "Between Dynamics and Spectral Theory",
        Simons Center for Geometry and Physics, June 6 – 10, 2016

    Electronic Transport in Aperiodic Solids    (pdf file)
       Solid-MATH Meeting, Aalborg, Danemark, May 26-28, 2016.

    Noncommutative Geometry of Fractals    (pdf file)
       American Mathematical Society Meeting
       Memphis TN, October 18th, 2015.

    Periodic Approximation to 1D Aperiodic Hamiltonians    (pdf file)
       International Congress of Mathematical Physics
       Santiago, Chile, July 27th, 2015.

    Modeling Liquids and Bulk Metallic Glasses    (pdf file)
       1)-Colloquium Talk, Mathematics Department
       Friedrichs-Schiller- Universität, May 19, 2015.
       2)-Workshop "Mathematics of Novel Materials",
       Institut Mittag-Leffler, Sweden, June 2, 2015
       3)-"Workshop on time-frequency analysis and aperiodic order"
       NTNU, Trondheim, June 10, 2015.

    Topics on Aperiodic Solids   
       Four Lectures :

       Lecture 1: Delone sets and the Anderson-Putnam Complex.
       Lecture 2: C*-algebras and Noncommutative Geometry Approach.
       Lecture 3: Periodic Approximants, an spectral properties, the 1D-case
       Lecture 4: Prospect and discussions.
       Mathematics Department, Texas A&M University,
       February 2-5, 2015.

    The Topology of Tiling Spaces    (pdf file)
       Colloquium Talk, Mathematics Department
       Purdue University, November 4, 2014.

    Periodic Approximant to 1D Aperiodic Hamiltonian    (pdf file)
       1)- Institut of Science and Technology, Klosterneuburg, Austria
       Aug. 27, 2014, First Version    (pdf file)
       2)- ESI workshop "Topological Phases of Condensed Matter"
       Erwin Schrödinger Institute, Vienna, September 9, 2014.
       3)- Conference "Inverse Problems and Spectral Theory"
       Texas A&M University, Oct 17-19, 2014.

    A Noncommutative Geometry Approach to
        topological invariants in Solid State Physics    (pdf file)

       Three Lectures :
       Lecture 1: C*-algebras,
       Lecture 2: K-Theory,
       Lecture 3: Dirac Operator,
       ESI workshop "Topological Phases of Condensed Matter"
       Erwin Schrödinger Institute, Vienna, August 4-8, 2014.

    Computational Noncommutative Geometry    (pdf file)
       Conference "Noncommutative Geometry Festival"
       In honor of Henri Moscovici 70th birthday.

       Texas A&M University, Mathematics, April 30th-May 3rd, 2014

    The Transverse Geometry of Tiling Spaces   (pdf file)
       Colloquium, Vanderbilt University, Mathematics, April 3rd, 2014

    The Topology of Tiling Spaces   (pdf file)
       Colloquium, Seoul National University, Mathematics, March 20, 2014
       Quantum Hall Effect
       Four Lectures, Seoul National University, Mathematics, March 17-18-19-21, 2014.

    Bloch Theory for 1-D FLC Aperiodic Media   (pdf file)
       Lecture given at WCAOS , UC Davis, October 26th, 2013.

    Noncommutative Metric Spaces and Dynamical Systems
       Three Lectures delivered at SISSA, Italy, June 17-20, 2013

       Lecture 1: Spectral Triples and Spectral Metric Spaces
       Lecture 2: Compact metric spaces as spectral metric space
       Lecture 3: Z-action and Spectral triples on the crossed product algebra

    Wannier Transform and Bloch Theory for Aperiodic Repetitive FLC Tilings
       Four Lecture delivered at the workshop "Dynamical Methods in Spectral Theory of Quasicrystals"
       U.C. Irvine, May 15-19, 2013

       Lecture 1: The Toolbox
       Lecture 2: The Anderson-Putnam complex
       Lecture 3: The Wannier transform
       Lecture 4: Bloch Hamiltonians

    Topological Invariants in Disordered Systems
       Distinguished Lecture Series in Applied and Computational Analysis
       UC Santa Barbara, Dept of Mathematics, May 5-15,2013
       & at the workshop "Random Matrices, Quantum Hall Effect, Group Theory",
      DYGEST Corfou Meeting, May 28-31, 2013

       Lecture 1: Electrons in Aperiodic Media (pdf file)
       Lecture 2: Computational Noncommutative Geometry (pdf file)
       Lecture 3: The Integer Quantum Hall Effect (pdf file)
       Lecture 4: Higher Topological Invariants: topological insulators (pdf file)

    Computational Noncommutative Geometry, the work of Emil Prodan (pdf file)
       Trails in Quantum Mechanics and Surrounding
       INFN, Frascati National Lab, January 29-February 2, 2013

    Modeling Liquid Metals & Bulk Metallic Glasses (pdf file)
       1)-Yeshiva University, College of Women, Physics,
       New-Yok City, December 4th, 2012
       2)-Joint Institute for Neutron Science, Oak Ridge, January 18th, 2013

    1)-Transverse Geometry of Tiling Spaces (pdf file)
       University of Connecticut, November 29th, 2012

      2)- Cantorization and Reconnection Cohomology (Temporary Draft)
       University of Connecticut, November 30th, 2012

    Hull and Tiling Space in Aperiodic Solids (pdf file)
       Joint Institute for Neutron Science, Oak Ridge, October 4th, 2012

    On the Noncommutative Geometry of Aperiodic Solids
INDAM Meeting Noncommutative Geometry, Index Theory and Applications ,
        Cortona, Italy, June 11-15 2012.
  Four lectures: (June 11,12,13,14, 2012)
         1)- Gap Labeling Theorems (pdf file)

         2)-The Hull (pdf file)

         3)-Cohomology (pdf file)

         4)-Transverse Geometry (pdf file)

    Atomic Motion in Aperiodic Solids ( pdf file )
       Polygone Scientifique, Maison des Magistères, Grenoble
        Theoretical Physics Colloquium, June 1st, 2012
    Aperiodic Solids and their Noncommutative Geometry
The University of Chicago, Graduate School of Mathematics
        Four lectures: (Apr 17, 19, 24, 26, 2012)
         1)- Aperiodic Solids: a review
         2)- The Hull
         3)-  The C*-algebra and its K-Theory
         4)- The Gap Labeling Theorem

    TheTransverse Geometry of Tiling Spaces  (pdf file)
CRM - University of Ottawa Distinguished Lecture Series
        Department of Mathematics,
        University of Ottawa, Ontario, Canada, April 13 2012

    Laplaceans on compact metric spaces (pdf file)
Talk at the Institut Henri Poincaré, Mar 12 2012

    Theory of Aperiodic Solids: from 1980 to present (pdf file)
The 2012 WPI-AIMR Annual Workshop,
        Cutting-edge Functional Materials for Green Innovation

         Tohoku University, Sendai, Japan, Feb 20-23, 2012

    Dissipative Dynamics for Electrons in Semiconductors    (pdf file)
        Workshop, "Correlations and Interactions for Random Quantum Systems"
        Mathematisches Forschungsinstitut Oberwolfach, October 24, 2011
        Workshop "Quantum Mechanics: From Foundations to Quantum Information Science"
        Zentrum für interdisciplinäre Forschung, Bielefeld, March 6, 2012

    Atomic Motion and Transverse Geometry of Tiling Spaces     (pdf file)
        Colloquium talk, Department of Mathematics,
        University of Victoria, October 6, 2011
        - Workshop "Mathematical approach to emerging topics in material sciences 2012"
        WPI-AIMR, Tohoku University, Sendai, Japan, Feb 18-19, 2012
        - Talk at the Gakushuin University, Tokyo, Japan, Feb 25, 2012
        - Talk at LPTMS, U. Paris-Sud, Orsay, France, Mar 13, 2012

    Wannier Transform for Aperiodic Solids  (pdf file)
Conference "Modern Trends in PDE's, Geometric Analysis and 
        Mathematical Physics"  .

  University of Cergy-Pontoise September 5-6, 2011.

    Mathematical Aspects of Electronic Transport in Aperiodic Solids ,
International Congress on Industrial and Applied Mathematics (ICIAM 2011),
        July 21, 2011 in Vancouver, Canada.

    Riemannian Geometry on Compact Metric Spaces  (pdf file)
Workshop "Wave and Quantum Fields",
        Technion, Physics, Haifa, Israel, June 26-30
, 2011

    Riemannian Geometry on Metric Cantor Sets  (pdf file)
Math Department, Tsinghua University, Beijing, June 1st, 2011
-Math Department,Fudan University, Shanghai, June 15, 2011

    Transverse Geometry for Tiling Spaces  (pdf file)
Mini-course, delivered at SISSA, Trieste, Italy
"Trails in a Non Commutative Land"
May 18-20, 2011
        SISSA, International School for Advanced Studies

    Wannier Transform for Aperiodic Solids  (pdf file)
Mathematical Physics Seminar, School of Math., Georgia Tech
        March 16th, 2011.

   (i) J. Bellissard: Riemannian Geometry of Compact Metric Spaces
(ii) G. De Nittis: Wannier Transform for Quasicrystals  (pdf file)
"Challenge in Aperiodic Media" and workshop "ANR SubTile"
       Institut Camille Jordan, Lyon, Feb. 28-Mars 4, 2011

    1D-Quantum Systems (1980-1993), a review  (pdf file)
workshop "Dynamics of Trace Maps and Applications to Spectral Theory"
        Mathematisches Forschungsinstitut Oberwolfach
        January 17-21, 2011

    Wannier Transform for Aperiodic Solids  (pdf file)
Workshop "Random Schrödinger Operators"
        Centre Interfaculataire Bernoulli
          EPFL, Lausanne, June 3rd, 2010
Workshop "The Mathematics of Aperiodic Order"
        KIAS, Seoul, Korea September 27, 2010

    Riemannian Geometry on Metric Cantor Sets  (pdf file)
Dept. of Mathematics,  UC-Irvine, May 13, 2010
Workshop "Quantum Dynamics", in honor of Pierre Duclos,
        CIRM, Luminy, Marseille, France, November 23-25, 2010

   Riemannian Geomerty of Compact Metric Spaces (pdf file)
      Dept. of Mathematics,  Northwestern University Evanston, IL,
29 2010  

   A Mathematical Model for Mott Variable Range Hopping Conductivity (pdf file)
      Conference "Quantum Probability and Related Topics"
       Pontificia Universidad Católica de Chile,
       Facultad de Matemáticas, Santiago
, Chile, 26 November 2009  

   Topological Aspects in the Theory of Aperiodic Solids andTiling Spaces (pdf file)
        - Research Horizon: graduate seminar -
Georgia Institute of Technology, School of Mathematics
, 11 November 2009  

    The Topology of Tiling Spaces (pdf file)
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       Michigan State University, East Lansing, MI, 16 October 2009  

The Gap Labeling Theorem then and now  (pdf file)
      Montana State University, Department of Mathematics, 29 April 2009  

    Riemannian Geometry on Metric Cantor Sets  (pdf file)
      Institut Camille Jordan, 
Université Claude Bernard - Lyon I , France, 20 June 2008
       Fakultät für Mathematik , Universität Bielefeld , July 4, 2008

    The theory of Aperiodic Solids: 4 Lectures
          0)- Colloquium Talk: The Noncommutative Geometry of Aperiodic Solids
          1)- Lecture I:    Construction of the Noncommutative Brillouin Zone
          2)- Lecture II:  Coherent and Dissipative transport
          3)- Lecture III: The Riemannian Geometry of Atomic Surfaces
      SISSA, Trieste, Italy, 26-30 May 2008  

    Quantum Computing: what is it ?     Power Point file   
       School of Mathematics, Georgia Institute of Technology, Thursday March 6, 2008

    The Topology of Tiling Spaces     pdf.file     
       (i) Friedrich-Alexander-Universität Erlangen-Nürnberg,
       Mathematisches Institut, June 26th, 2007
      (ii) Fakultät für Mathematik Universität Bielefeld, June 28th, 2007
      (iii)  DMA-Ecole Normale Supérieure, Paris, July 4th, 2007
      (iv) Born-Hilbert Seminar, Universität Göttingen, July 9th, 2007
        (v) Meccanica (a conference in honor of Sandro Graffi), Bologna, Italy, August 30th, 2008

    Analysis and Probability in Quantum Physics
      Pan-American Advanced Studies Institute, 2006 (PASI)
      Pontificia Universidad Católica de Chile, Santiago de Chile,
      24 July-4 August, 2006
     Transport Theory in Dissipative Quantum Systems (135 pages)
                                                 pdf.file (.7Mb)       psfile (2.9Mb)

    Max Born Symposium in Theoretical Physics, Wroclaw June 26-28, 2006
       "Mathematical Problems in Nonrelativistic Quantum Dynamics"
       Topics in Quantum Transport Theory  (pdf)  (ps)

Festival Colin de Verdière Grenoble Mai 29-June 2  2006
      Bloch Electrons in a Magnetic Field  (pdf)

    Three Lectures on the Quantum Hall Effect  (pdf)
Vanderbilt University, Department of Mathematics, Dec 2-3 2005

      Three Lectures on the Theory of Aperiodic Solids
Gill Foundation, Distinguished Lecture Series
UCLA, Department of Mathematics, May 3-6, 2005
          Lecture I:     Structural Aspects and Noncommutative Geometry  (pdf)
          Lecture II:   Coherent and Dissipative Transport  (pdf)
          Lecture III:  The Integer Quantum Hall Effect   (pdf)

    Dissipative Transport and Kubo's Formula in Aperiodic Solids  (pdf)
Program on Open Quantum Systems
Erwin Schrödinger Institute, Wien, Feb. 1st, 2005

      Various Mathematical Aspects of Tiling Spaces  (pdf)
School of Mathematics, Georgia Tech, Jan. 24th, 2005

    Kubo's Formula for Quantum Transport  (pdf)
Mathematics and Physics of Disordered Systems
Mathematisches Forschungsinstitut Oberwolfach, May2-7, 2004

    Two Lectures on "Quantum Computing"
        "I: Introduction. Qubits, Quantum circuits (pdf) "
                                      (PowerPoint version 0.4MB)
        "II: Algorithms, Error-correcting codes, Physical Realizations (pdf)"
                                      (PowerPoint version 0.7MB)

Georgia Institute of Technology,
School of Mathematics, Atlanta, GA, October 15 & 29,  2003

    Coherent and Dissipative Transport in Aperiodic Media   (pdf)
        "The Noncommutative Geometry of Aperiodic Solids"
        "Entropy and Information: a physicist point of view" (PowerPoint Presentation 1.7 MB
Florida State University, Gainesville, FL, October 1-3,  2003

    Kinetic Models for Electronic Transport in Aperiodic Solids  (pdf)
Université Scientifique et Technique de Lille (USTL), France, June 24,  2003

    Linear Response Theory & Kubo's Formula for Electronic Transport  (pdf)
University of California Irvine, CA, May 29,  2003

    Tilings, Aperiodic Media and their Noncommutative Geometry  (pdf)
Duke University, February 28,  2003,
Vanderbilt University, Nashville TN, May 12-13, Shanks Lectures.

    Random Matrix theory and the 2D Anderson Model  (pdf)
-Rutgers, December 15, 2002: "88th Statistical Mechanics Conference" Rutgers University,
    Celebrating E. Lieb's 70th birthday.
-Pasadena, February 17-18, 2003: "Western Seminar" Caltech, Mathematics,
- Como "Quantum Chaos: Theory and Applications", Villa Olmo, Como, June 17-22, 2003,
Celebrating G. Casati's 60th birthday. 

     I.H.E.S., Bures s/Yvette, France,  April 3, 2002    The Noncommutative Geometry of Aperiodic Solids   (pdf)
           "Rencontres de géométrie non-commutative" en l'honneur d'Alain Connes,

     38th Winter School of Theoretical Physics, 6-15 February 2002, Lądek Zdrój, Poland
           "Dynamical Semigroups: Dissipation, Chaos, Quanta"
           Coherent and Dissipative Transport in Aperiodic Solids: Part A   (pdf)
           Coherent and Dissipative Transport in Aperiodic Solids: Part B   (pdf)

     Georgia Institute of Technology, School of Physics, September 3-6, 2001
           The Strange Properties of Quasicrystals

     UC Berkeley, Departement of Mathematics, NJ,  August 23, 2001
           The Gap Labelling Theorem for Tilings   (pdf)

     Princeton, NJ,  December 12, 2000   Coherent and Dissipative Transport in Aperiodic Media   (pdf)

     MSRI, Berkeley, CA, October 17, 2000   Noncommutative Fermi surfaces  (pdf)
     MSRI, Berkeley, CA,  September 26, 2000
           Gap Labelling Theorem for Aperiodic Solids  (pdf)
     De Rham Colloquium, Lausanne, Switzerland, March 15, 2000
           Noncommutative Geometry of Aperiodic Solids  (pdf)
     Mathematical and Physical aspects of the (fractional) Quantum Hall Effect,
            Adelaide, Australia, August 16-20, 1999, 
           The Noncommutative Geometry of the Integer Quantum Hall Effect.   (pdf)
     Clausthal, Germany, November 2-6, 1998
           Kinetic Models for Quantum Transport: anomalous transport   (pdf)