About
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.
Organizers
Christian Bär (Potsdam), Paolo Piazza (Roma), Thomas Schick (Göttingen), Hang Wang (Eastern China normal university, Shanghai)
Programme
Programme and abstracts as PDF. You can download the presentation slides of each talk by clicking on its title.
| Time | Speaker | Title |
|---|---|---|
| MONDAY | ||
| 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 |
| 〰️〰️〰️ | ||
| TUESDAY | ||
| 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 |
| 〰️〰️〰️ | ||
| WEDNESDAY | ||
| 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 | |
| 〰️〰️〰️ | ||
| THURSDAY | ||
| 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 🍷 | |
| 〰️〰️〰️ | ||
| FRIDAY | ||
| 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 |
Participants
- Bernd Ammann, Regensburg
- Iakovos Androulidakis, Athens
- Paolo Antonini, Universitá del Salento
- Sara Azzali, Universitá di Bari
- Christian Bär, Potsdam
- Francesco Bei, Roma Sapienza
- Boris Botvinnik, Univ. of Oregon
- Maxim Braverman, Northeastern
- Simone Cecchini, Göttingen
- Alessandro Contini, Hannover
- Nelia Charalambous, Cyprus
- Clément Cren, Créteil
- Anda Degeratu, Stuttgart
- Georg Frenck, Augsburg
- Penelope Gehring, Potsdam
- Jonathan Glöckle, Regensburg
- Sebastian Goette, Freiburg
- Nadine Große, Freiburg
- Thorsten Hertl, Göttingen
- Peter Hochs, Nijmegen
- Rubens Longhi, Potsdam
- Ursula Ludwig, Münster
- Xiaonan Ma, Paris 7
- Agnese Mantione, Münster
- Omar Mohsen, Paris Orsay
- Werner Müller, Bonn
- Hessel Bouke Posthuma, Amsterdam
- Paolo Piazza, Roma Sapienza
- Valerio Proietti, Shanghai
- Massimiliano Puglisi, Roma Sapienza
- Frédéric Rochon, Montréal
- Thomas Schick, Göttingen
- Mehran Seyedhosseini, Potsdam
- Shu Shen, Sorbonne
- Georges Skandalis, Paris 7
- Yanli Song, Missouri
- Alexander Strohmaier, Leeds
- Xiang Tang, Missouri
- Boris Vertman, Oldenburg
- Michał Wrochna, Cergy Paris
- Vito Zenobi, Sapienza
Location
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.
Sponsors
Contact
If you have any inquiries please contact Paolo Piazza (piazza@mat.uniroma1.it).