About

The intention of this workshop is 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 is 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 will promote new collaborations amongst people working in different fields, but with a common theme and angle of attack.

Organizers

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

Location

Il Palazzone, Cortona, Italy

palazzone

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 will take 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.

Programme

Programme and abstracts as PDF.

Time           Speaker Title
MONDAY
9h00-9h40 Werner Müller Universität Bonn Heat asymptotics and Weyl law for locally symmetric manifolds of finite volume
9h55-10h35 Léo Bénard Universität Göttingen Ruelle ζ-functions and Reidemeister-Turaev torsion on unit tangent bundles of hyperbolic surfaces
10h50 Coffee ☕
11h15-11h55 Peter Hochs Radboud University Equivariant analytic torsion for proper actions
12h10-12h50 Nelia Charalambous University of Cyprus The Lᵖ spectrum of the Dirac operator
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
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TUESDAY
9h00-9h40 Simone Cecchini Universität Göttingen Metric inequalities with positive scalar curvature
9h55-10h35 Mehran Seyedhosseini Universität Potsdam Relative L²-ρ-invariants and the moduli space of positive scalar curvature metrics on manifolds with boundary
10h50 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
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WEDNESDAY
9h00-9h40 Georges Skandalis Université Paris Cité The Godbillon-Vey invariant in KK-theory with real coefficients
9h55-10h35 Vito Felice Zenobi Sapienza Università di Roma Interior Kasparov products for ρ-classes on Riemannian foliated bundles
10h50 Coffee ☕
11h15-11h55 Valerio Proietti East China Normal University, Shanghai Classification via index theory on the mapping torus
12h10-12h50 Clément Cren Université Paris-Est - Créteil Transversal index for transversally Rockland operators on filtered manifolds
13h00 Lunch and free afternoon
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THURSDAY
9h00-9h40 Pierre Albin University of Illinois at Urbana-Champaign Witless Dirac operators on stratified spaces
9h55-10h35 Frédéric Rochon Université du Québec à Montréal L²-cohomology of quasi-fibered boundary metrics
10h50 Coffee ☕
11h15-11h55 Bernd Ammann Universität Regensburg Self-adjoint codimension 2 boundary conditions for Dirac operators
12h10-12h50 Omar Mohsen Paris-Saclay Université An introduction to maximally hypoelliptic differential 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 🍷
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FRIDAY
9h00-9h40 Ursula Ludwig Universität Münster Bismut-Zhang theorem for singular spaces
9h55-10h35 Xiaonan Ma Université Cité Differential K-theory and localization formula for eta invariants
10h50 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

Sponsors

Participants

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

Contact

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