Sara Azzali

Universität Hamburg
Fachbereich Mathematik
Bundesstrasse 55
20146 Hamburg - Germany

Geomatikum, Room 318
Tel: +49-40-42838-5181
Email: sara.azzali [at]


Global analysis, index theory, spectral invariants, noncommutative geometry.


I have moved. In the winter term 2019 I am a deputy professor for geometric analysis at the University of Hamburg. This webpage will be moved.


The Baum--Connes conjecture localised at the unit element of a discrete group (with Paolo Antonini and Georges Skandalis) July 2018 arXiv:1807.05892

Spectral zeta-invariants lifted to coverings (with Sylvie Paycha)
arXiv:1603.02263, to appear on Transactions of the AMS


Two-cocycle twists and Atiyah-Patodi-Singer index theory (with Charlotte Wahl)
Mathematical Proceedings of the Cambridge Philosophical Society 167 3 (2019) 437--487 arXiv:1312.6373

Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations (with Paolo Antonini and Georges Skandalis)
Journal of Functional Analysis 270 1 (2016), 447–481, arXiv:1504.04495

Traces of holomorphic families of operators on the noncommutative torus and Hilbert modules (with Cyril Lévy, Carolina Neira-Jiménez and Sylvie Paycha)
Geometric Methods in Physics - Trends in Mathematics, pp. 3-38, Birkhäuser 2015

Flat bundles, von Neumann algebras, and K-theory with R/Z-coefficients (with Paolo Antonini and Georges Skandalis)
Journal of K-Theory 13, 2 (2014), pp. 275--303

Large time limit and local L^2 index theorems for families (with Sebastian Goette and Thomas Schick)
Journal of Noncommutative Geometry 9 (2015), no.2 pp. 621–664

Spectral flow, index, and the signature operator (with Charlotte Wahl)
Journal of Topology and Analysis 3 (2011), no. 1, pp. 37--67 link

L^2 rho form for normal coverings of fibre bundles
International Journal of Mathematics 22 (2011), no. 8, 1139--1161 link



2017-2019 Assistant (Wiss. Mitarbeiterin) Institut für Mathematik, Universität Potsdam. Temporary Positions for Principal Investigator funded by the DFG (SPP 2026 Geometry at Infinity),
2014-2017 Assistant (Wiss. Mitarbeiterin), Institut für Mathematik, Universität Potsdam
2012-2014 INdAM Fellowship in Mathematics for Experienced Researchers cofunded by Marie Curie
Hosting Institutions: Institut de Mathématiques, Paris Diderot and Dipartimento di Matematica, Roma La Sapienza
2008-2011 Post doc, Mathematisches Institut, Georg-August-Universität Göttingen
2007-2008 Post doc at LMAM , University of Metz, Equipe Géométrie noncommutative


July 2007 Ph.D. in Mathematics, La Sapienza Università di Roma. Thesis: Two spectral invariants of type Rho, advisor Paolo Piazza
March 2002 Laurea in Matematica, Università degli Studi di Parma , Thesis "Metodi geometrici per la minimizzazione dell'area", advisor Claudio Arezzo


Winter Term 2019, Hamburg

Sommer Semester 2017, Potsdam

Winter Semester 2016/2017, Potsdam

Sommer Semester 2015/2016, Potsdam

Winter Semester 2015/2016, Potsdam

Sommer Semester 2014/2015, Potsdam

Winter Semester 2014/2015, Potsdam

Sommer Semester 2014, Potsdam

2009/2010 and 2010/2011, Göttingen

  • Differential- und Integralrechnung II, teaching assistant;
  • Differential- und Integralrechnung I, teaching assistant;
  • Bio- und Geomathematik (Mathematics for Bio- and Geology), teaching assistant.
  • (link to my old teaching page)

2005/2006 and 2006/2007, Roma

  • Analisi II (Calculus II), teaching assistant for engeneers;
  • Matematica II (Course on ODE), undergraduate course for majors in Statistics;
  • Istituzioni di Matematica (Mathematics), and Matematica II (Calculus),teaching assistant for majors in Geology;
  • teaching assistant for majors in Statistics;
  • Calcolo e Biostatistica (Calculus and biostatistics), tutor.




  • Jan 2018, Kasparov theory with real coefficients and secondary invariants, Séminaire d’Algèbres d’Opérateurs IMJ-PRG Université Paris Diderot
  • Oct 2017, Flat bundles, R/Z K-theory and rho invariants “Forschungsseminar Differentialgeometrie” Mathematisches Institut, Universität Freiburg, Germany
  • Mar 2017, The class of a flat vector bundle and a noncommutative generalisation, Séminaire Physique mathématique Institut Camille Jourdan, Université Lyon 1, France
  • Mar 2017, Introduction to index theory Séminaire de Mathématiques accessibles, Université Jean Monnet, Saint-Étienne, France
  • Dec 2015, Spectral invariants eta and rho of Dirac operators, Forschungsseminar Analysis Universität Duisburg-Essen
  • Jul 2015, Flat bundles and K-theory with R/Z-coefficients, Universität Regensburg
  • Feb 2015, Large time limit and L2-index theorems for families, Seminar “Geometrische Analysis und Spektraltheorie”, Humboldt Universität zu Berlin
  • Apr 2014, Invariants Rho et l’espace de métriques a' courbure scalaire strictement positive, Institut de Mathématiques, Université P. Sabatier, Toulouse
  • Nov 2013, The invariant rho in geometry, Institut für Mathematik, Universität Potsdam
  • Nov 2013, Flat bundles, von Neumann algebras and K-theory with R/Z-coefficients, Seminär Topologie, Mathematisches Institut, Georg-August-Universität Göttingen
  • Apr 2013, Invariants eta et rho d’opérateurs de Dirac et courbure scalaire strictement positive, Séminaire de Physique Mathématique, ICJ, Université Lyon 1
  • Feb 2013, L2-eta forms, Séminaire Algèbre et Géométrie, Laboratoire de Mathématiques et applications, Metz
  • Nov 2012, Eta invariants and positive scalar curvature, Séminaire Géométrie, Algèbre, Algèbres d’opérateurs, Université de Clermont-Ferrand
  • Feb 2012, Invariants eta et courbure scalaire positive, Séminarie Géométrie Dynamique Lille 1
  • Mar 2011, The signature operator and the L2-local index theorem, Séminaire d'Algèbres d'Opérateurs, IMJ Paris 7


  • July 2018, Discrete group actions and a weak form of the Baum–Connes conjecture, Workshop “Non-commutative Geometry, Index Theory and Mathematical Physics”, MFO Oberwolfach
  • June 2018, The “free and proper part” of K-theory, Conference “Secondary and delocalized index invariants 2018”, Copenhagen, Denmark
  • Aug 2017, Flat bundles, R Z-K-theory and rho invariants Conference “Topology Ecuador 2017”, San Cristobal, Ecuador
  • Aug 2017, Rho invariants Summer school “Geometric, algebraic and topological methods in quantum field theory”, Villa de Leyva, Colombia
  • May 2017, Secondary invariants for two-cocycle twists, Meeting “Index Theory and Singular Structures”, Toulouse France
  • Feb 2017, KK-theory with R-coefficients and discrete group actions on C*-algebras, Workshop Noncommutative Geometry and Applications, ICTP Trieste, Italy
  • Oct 2016, Discrete group actions on C*-algebras and rho classes of unitary representations, Meeting Noncommutative index theory, Warsaw, Poland
  • Sept 2015, Relative spectral invariants and operator algebraic point of view Minisymposium “Symplectic Structures in Geometric Analysis” bei der Jahrestagung der deutschen Matimatiker-Vereinigung, Hamburg
  • Jul 2015, Spectral invariants eta and rho of Dirac operators Summer school “Geometric, algebraic and topological methods in quantum field theory” Villa de Leyva (Colombia)
  • Jun 2015, Bivariant K-theory with coefficients and rho classes of unitary representations, Conference «Noncommutative methods in Topology and Geometry», Université Claude Bernard Lyon 1 (France)
  • Feb 2015, Eta and rho invariants for projectively invariant operators, Workshop “Geometric and Singular Analysis”, Universität Potsdam
  • Secondary invariants for two-cocycle twists, Workshop “Methods of Noncommutative Geometry in Analysis and Topology”, Hannover
  • July 2014, Two-cocycle twists and Atiyah–Patodi–Singer index theory, « Operator Algebras and Applications to Quantum Physics », First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Bilbao, Spain
  • June 2014, Spectral invariants for two-cocycle twists, Conférence GREFI–GENCO « Noncommutative Geometry and Applications to Physics », Mondragone - Roma, Italy
  • June 2014, Conference « Noncommutative Analysis, Operator Theory and Applications », Politecnico di Milano
  • Dec 2012, R/Z K-theory and the relative eta invariant, Meeting GREFI–GENCO « Noncommutative Geometry and Applications to Physics », Politecnico di Milano, Italy
  • Dec 2011, Invariant eta tordue par un 2-cocycle du groupe et courbure scalaire positive, Rencontre GDR Géométrie noncommutative, MAPMO, Orleans
  • Dec 2010, Teoria dell' indice e invarianti secondari: risultati sull'operatore di segnatura, Seminario degli ex-studenti dell' Università di Parma, Italy
  • Nov 2010, Flusso spettrale, indice e applicazioni a foliazioni misurate, Progressi Recenti in Geometria Reale e Complessa, Levico Terme, TN, Italy
  • Jul 2010, Large time limit and L^2 local index theorem, MFO Oberwolfach
  • Jun 2010, Spectral flow, index and applications to measured foliations, Meeting YMT, Hausdorff centre, Bonn +poster presented

Talks in research training groups: