The intention of this workshop was to explore the fundamental role of Dirac operators, in particular their index theory and their spectral theory, in a variety of areas of Mathematics, including topology, Riemannian, Lorentzian and symplectic geometry, foliations, and representation theory. The goal was to promote this central role of Dirac operators and to employ it in order to foster the interaction between mathematicians in different areas. The meeting promoted new collaborations amongst people working in different fields, but with a common theme and angle of attack.


Christian Bär (Potsdam), Paolo Piazza (Roma), Thomas Schick (Göttingen), Hang Wang (Eastern China normal university, Shanghai)


Programme and abstracts as PDF. You can download the presentation slides of each talk by clicking on its title.

Time Speaker Title
09h00-09h40 Werner Müller Universität Bonn Heat asymptotics and Weyl law for locally symmetric manifolds of finite volume
09h55-10h35 Nelia Charalambous University of Cyprus The Lᵖ spectrum of the Dirac operator
10h45 Coffee ☕
11h15-11h55 Peter Hochs Radboud University Equivariant analytic torsion for proper actions
13h00 Lunch break 🍕
16h15 Coffee ☕
17h00-17h40 Alexander Strohmaier University of Leeds The η-invariant on curved spacetimes
18h00-18h40 Michał Wrochna Cergy Paris Université Dynamical residues of spectral ζ-functions
09h00-09h40 Simone Cecchini Universität Göttingen Metric inequalities with positive scalar curvature
09h55-10h35 Mehran Seyedhosseini Universität Potsdam Relative L²-ρ-invariants and the moduli space of positive scalar curvature metrics on manifolds with boundary
10h45 Coffee ☕
11h15-11h55 Jonathan Glöckle Universität Regensburg Enlargeability obstruction for spacetimes with both big bang and big crunch
12h10-12h50 Thorsten Hertl Universität Göttingen Positive scalar curvature from a concordance viewpoint
13h00 Lunch break 🍕
16h15 Coffee ☕
17h00-17h40 Boris Botvinnik University of Oregon Spinᶜ -manifolds, psc-metrics and manifolds with fibered singularities
18h00-18h40 Georg Frenck Universität Augsburg Spaces of positive scalar curvature metrics on totally nonspin manifolds
09h00-09h40 Georges Skandalis Université Paris Cité The Godbillon-Vey invariant in KK-theory with real coefficients
09h55-10h35 Vito Felice Zenobi Sapienza Università di Roma Interior Kasparov products for ρ-classes on Riemannian foliated bundles
10h45 Coffee ☕
11h15-11h55 Omar Mohsen Paris-Saclay Université An introduction to maximally hypoelliptic differential operators
12h10-12h50 Clément Cren Université Paris-Est - Créteil Transversal index for transversally Rockland operators on filtered manifolds
13h00 Lunch 🍕 and free afternoon
09h00-09h40 Valerio Proietti East China Normal University, Shanghai Classification via index theory on the mapping torus
09h55-10h35 Frédéric Rochon Université du Québec à Montréal L²-cohomology of quasi-fibered boundary metrics
10h45 Coffee ☕
11h15-11h55 Bernd Ammann Universität Regensburg Self-adjoint codimension 2 boundary conditions for Dirac operators
13h00 Lunch break 🍕
16h15 Coffee ☕
17h00-17h40 Francesco Bei Sapienza Università di Roma On weakly Kähler hyperbolic manifolds and geometric applications
18h00-18h40 Shu Shen Sorbonne Université Coherent sheaves, superconnection, and the Riemann-Roch-Grothendieck formula
20h00 Social dinner at Taverna Pane e Vino 🍷
09h00-09h40 Ursula Ludwig Universität Münster Bismut-Zhang theorem for singular spaces
09h55-10h35 Xiaonan Ma Université Cité Differential K-theory and localization formula for eta invariants
10h45 Coffee ☕
11h15-11h55 Yanli Song Washington University St. Louis Higher APS index theorem for proper Lie group action
12h10-12h50 Sebastian Goette Universität Freiburg Extra twisted connected sums and their ν-invariants
13h00 Lunch 🍕 and end of conference


group picture

  1. Bernd Ammann, Regensburg
  2. Iakovos Androulidakis, Athens
  3. Paolo Antonini, Universitá del Salento
  4. Sara Azzali, Universitá di Bari
  5. Christian Bär, Potsdam
  6. Francesco Bei, Roma Sapienza
  7. Boris Botvinnik, Univ. of Oregon
  8. Maxim Braverman, Northeastern
  9. Simone Cecchini, Göttingen
  10. Alessandro Contini, Hannover
  11. Nelia Charalambous, Cyprus
  12. Clément Cren, Créteil
  13. Anda Degeratu, Stuttgart
  14. Georg Frenck, Augsburg
  15. Penelope Gehring, Potsdam
  16. Jonathan Glöckle, Regensburg
  17. Sebastian Goette, Freiburg
  18. Nadine Große, Freiburg
  19. Thorsten Hertl, Göttingen
  20. Peter Hochs, Nijmegen
  21. Rubens Longhi, Potsdam
  22. Ursula Ludwig, Münster
  23. Xiaonan Ma, Paris 7
  24. Agnese Mantione, Münster
  25. Omar Mohsen, Paris Orsay
  26. Werner Müller, Bonn
  27. Hessel Bouke Posthuma, Amsterdam
  28. Paolo Piazza, Roma Sapienza
  29. Valerio Proietti, Shanghai
  30. Massimiliano Puglisi, Roma Sapienza
  31. Frédéric Rochon, Montréal
  32. Thomas Schick, Göttingen
  33. Mehran Seyedhosseini, Potsdam
  34. Shu Shen, Sorbonne
  35. Georges Skandalis, Paris 7
  36. Yanli Song, Missouri
  37. Alexander Strohmaier, Leeds
  38. Xiang Tang, Missouri
  39. Boris Vertman, Oldenburg
  40. Michał Wrochna, Cergy Paris
  41. Vito Zenobi, Sapienza


Il Palazzone, Cortona, Italy


Cortona is a small town in southern Tuscany, dating back to Etruscan times, situated on a hill 20 km north of the Lake Trasimeno. The meeting took place in the "Palazzone", a 16th century castle 2 km outside of Cortona in a typical Tuscan landscape of olive and wine gardens. The Palazzone is owned by the Scuola Normale Superiore di Pisa which lets it to the Instituto Nazionale di Alta Matematica for several meetings every year. In the early summer, this is the perfect stimulating environment to concentrate on mathematics in general and on the role of Dirac operators in particular.

How to reach Cortona

Il Palazzone is located outside the massive ancient town walls of Cortona and can be reached by a pleasant walk from the center of Cortona (about 1.5 km: you walk from Piazzale Garibaldi on Via Gino Severini; along the way you will find several tourist signs directing you to Il Palazzone).

By train: There are two railway stations, Terontola-Cortona (10 km to center) and Camucia-Cortona (5 km to center), on the track from Florence to Rome (one hour from Florence and two hours from Rome, Siena, or Pisa). Both stations are connected to Cortona by an infrequent bus and by taxi. The train schedules can be obtained from the official timetable of Trenitalia or, alternatively, at the German Rail company DB which also covers non-Italian stations.

If in doubt, Camucia-Cortona is recommended. When looking for trains from Florence or Rome, keep in mind that they might start at different stations: Roma Tiburtina or Roma Termini, Firenze SMN or Firenze Campo di Marte.

By car: Arriving on Autostrada del Sole (State Highway A1) take the exit "Valdichiana". Upon exiting the highway, take the Siena-Perugia State Road towards Perugia. Exit at "Cortona via Strada Statale 71" (State Road 71) and follow the signs all the way to Cortona.

By plane: The closest airport is Florence but for inter-continental flights it is Rome. Pisa can be another option. From the airport continue by train.



If you have any inquiries please contact Paolo Piazza (piazza@mat.uniroma1.it).