Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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SMI course "Conformal geometry, Cartan connection and locally conformally Kaehler structures"

created by calamai on 26 Sep 2017
modified on 25 May 2018

13 may 2018 - 19 may 2018

Palazzone di Cortona

The workshop consists of a ten-hours course delivered by Paul Gauduchon, plus around ten seminars on current research in differential geometry.

The event is supported by: Dipartimento di Matematica e Informatica "Ulisse Dini", Firenze; Scuola Matematica Interuniversitaria; SIR2014 AnHyC "Analytic aspects in complex and hypercomplex geometry" (code RBSI14DYEB), GNSAGA-INdAM.

The participants interested in presenting a poster should get in contact with David Petrecca, see below.

Posters should be prepared and brought in hard copy in format up to A1 in portrait (594 x 841 mm) or A2 in landscape (420 x 594 mm).

We suggest some possible poster styles: http://www.latextemplates.com/cat/conference-posters

for further information contact David Petrecca: petrecca at math.uni-hannover.de

Directions: On Sunday, May 13th, Il Palazzone will be open from 14:00 to 19:30 to welcome the participants. Latecomers will need to find accommodation at their own expense.

Further travel information (including taxi and driving directions) here

Program of the course:

1) General theory of Weyl structures. Weyl's fundamental theorem of conformal geometry. Existence and uniqueness of Gauduchon gauges.

2) Conformal invariant differential operators and universal Bochner formulae.

3) Construction of the conformal Cartan connection as a linear connection on the vector bundle of Einstein $2$-jets of sections of the scaling line bundle.

4) Construction of the Cartan connection (continuation) and applications: Kuiper and Liouville theorems.

5) Spinor interpretation of the Cartan connection.

Organizers: Daniele Angella, Simone Calamai, Graziano Gentili, Alexandra Otiman, David Petrecca, Nicoletta Tardini.

Participants (27).

Timetable.

Courses:
14 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 1 Cortona
14 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 2 Cortona
15 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 3 Cortona
15 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 4 Cortona
16 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 5 Cortona
16 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 6 Cortona
17 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 7 Cortona
17 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 8 Cortona
18 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 9 Cortona
18 May 2018: P. Gauduchon: Conformal geometry, Cartan connection and locally conformally Kaehler structures, 10 Cortona

Seminars:
14 May 2018: M. Pilca: Conformal Kaehler Metrics Cortona
14 May 2018: L. Li: On the strict convexity of the Mabuchi functional Cortona
14 May 2018: C. Yao: A cohomogeneity-one hypersymplectic flow and some related convergence results Cortona
15 May 2018: F. Madani: $S^1$-Yamabe invariant on $3$-manifolds Cortona
16 May 2018: E. Legendre: Contact toric manifolds of arbitrary codimension and Levi-Kaehler reduction Cortona
17 May 2018: N. Istrati: Toric locally conformally Kaehler manifolds Cortona
17 May 2018: S. Calamai: A characterization of Projectively Flat manifolds Cortona
18 May 2018: S. Huang: Epsilon-regularity of four dimensional gradient shrinking Ricci solitons Cortona

Speakers: Simone Calamai, Paul Gauduchon , Shaosai Huang, Nicolina Istrati, Eveline Legendre, Long Li, Farid Madani, Mihaela Pilca, Chengjian Yao.


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