Workshop on
"Geometry of vector distributions,  differential   equations, and variational problems"

SISSA, Trieste, Italy, 13--15 December 2006

organized by  Andrei Agrachev and  Igor Zelenko

co-sponsored  by  CEI (Central European  Initiative)

and   CTS (Control Training Site)


The aim of the workshop is to bring together differential geometers and the people of geometric control theory, working on the equivalence problem for various geometric structures on manifolds, especially nonholonomic distributions, sub-Riemannian  structures, Cauchy-Riemann (CR) structures.  Recent developements in the subject have shown that  the cooperation between these two research communities could be very fruitful.   We hope that the workshop will give an excellent opportunity for the exchanging of ideas and for the better understanding and comparison of different approaches. We also  hope that several days  of intensive discussions will lead to the substantial progress in the already existing collaboration and it will create the new cooperation  between specialists with different background. Also PhD students both local and from abroad are expected to participate in the  workshop, which might be an important stimulus in their education and the preparation of their thesis.

Invited speakers

Dmitri Alekseevsky,  University of Hull, UK, and Masaryk University in Brno, Czech Republic; 

Robert Bryant ,  Duke University, USA; 

Andreas Cap,  University of Vienna and  Erwin Schrodinger Institute  of Mathematical Physics, Austria;

Boris Doubrov, Belorussian State University,  Minsk,  Belarussia;

Maciej Dunajski, University of Cambridge,  UK;

Svetlana Ignatovich, Kharkov National University, Ukraine;

Bronislaw Jakubczyk,  Stefan Banach  International Mathematical Center of Polish Academy of Science, Poland;

Frederic Jean ,  ENSTA, Paris, France;

Alexei Kushner ,  Astrakhan State University and Control Sciences Institute of the Russian Academy of Sciences (Moscow), Russia;

Joseph Landsberg ,  Texas A&M University , USA;

Tohru Morimoto ,  Nara Women University, Japan;

Piotr Mormul ,  Warsaw University, Poland;

Pawel NurowskiWarsaw University, Poland;

Jean-Baptiste PometINRIA, Sophia Antipolis, France;

Jan Slovak, 
Masaryk University in Brno, Czech Republic;

Alexandre Vinogradov, 
University of Salerno, Italy;

Michail Zhitomirskii,  Technion -Israel Institute of Technology, Israel.

The Workshop will be held in SISSA (International School for Advanced Studies), which is part of a scientific campus located near Miramare Castle (see foto above), about 6km from downtown Trieste and enjoys its rather picturesque setting on the hills facing the Adriatic sea.


All participants will live in Adriatico Guesthouse, located on the beautiful see shore in 5-10 minutes walking distance from SISSA.

The address is

Adriatico Guesthouse (AGH)
Via Grignano,
34014 Trieste, Italy
Tel: (+39) 040 2240 112 Switchboard or 040 2240 + extension
Fax: (+39) 040 224 21

You can find the additional information on the webpage of the Guesthouse here.

How to reach Adriatico

1) From the Ronchi Airport (the name of Trieste airport):

You can take the APTbus number 51 to Trieste. The airport is very small, you will see the bus stop in the square on your right, when you go out of the airport building. The buses run every 30 minutes ( at :05 and :35 of each hour). You can find the time table of the buses here

Say the driver that you need to get off in Grignano (as you probably know "gn" is pronounced as soft "n", so it should be pronounced like Grinjano). Grignano is the region (the former village), where SISSA is located, it is a little bit before Trieste. The trip takes about 40 minutes. The bus will stop in Grignano only if you hail the driver, so it is important to inform him in advance.

From the bus stop you should go about 20 meters straight (towards a tunnel), then turn to the right (just before the tunnel) to the narrow street (actually a path) and continue along it down. It will lead you to the see and you will see the Adriatico Guesthouse on your right (see also the map ) .

2) From Trieste train station
Catch bus n. 36 from beside the railway station (buy the bus ticket in the kiosk in the railway station, see the timetable of the bus here) and get down on the last stop, which is exactly in front of the Adriatico Guesthouse. The trip is about 15 minutes (see also the map ).

3) Arriving by car
Exit the highway A4 (Autostrada Venezia-Trieste, E70) in Sistiana and take the road SS14, then after 5-10 minutes you will pass "Hotel Riviera" on your right, about 200 meters after that turn to the right (down). This road will lead you to the see and you will see the Adriatico Guesthouse on your right.

The e-mail addresses for all your questions are ,, and

It takes 5-10 minutes to reach SISSA from Adriatico Guesthouse. Ask the reception there for the explanation (see also the map ).


Preliminary schedule (PDF version)
Wednesday December 13
9:00-10:00 Registration
Morning Session
10:00-10:50 Tohru Morimoto (Nara Women University, Japan) Representations of Graded Lie Algebras and Differential Equations on Filtered Manifolds
10:50-11:40 Dmitri Alekseevsky (University of Hull, UK) Homogeneous bi-Lagrangian manifolds of semisimple group and generalized Gauss decompositions
Coffee Break
12:00-12:35 Frederic Jean (ENSTA, Paris, France) Generic results for horizontal and singular curves of rank-varying distributions
Afternoon Session
14:30-15:20 Bronislaw Jakubczyk (Stefan Banach International Mathematical Center, Warsaw, Poland) Invariants of vector distributions of corank 2
15:20-15:55 Aleksei Kushner (Astrakhan State University and Control Sciences Institute of the Russian Academy of Sciences, Moscow, Russia) Invariants of almost-product structures and geometry of Monge-Ampere and Jacobi equations
15:55-16:30 Svetlana Ignatovich (Kharkov National University, Ukraine) Realizable growth vectors and normalization of homogeneous approximations of affine control systems
Thursday December 14
Morning Session
9:00-9:50 Alexandre Vinogradov (University of Salerno, Italy) Classification problem and scalar differential invariants
9:50-10:40 Joseph Landsberg (Texas A&M University, USA) Rigidity and flexibility of homogeneous varieties
10:40-11:00 Coffee Break
11:00-11:35 Igor Zelenko (SISSA, Trieste, Italy) Canonical frames for vector distributions of rank two and three
11:35-12:10 Boris Doubrov (Belorussian State University, Minsk, Belarussia) Equivalence and invariants of scalar variational problem of higher order
Afternoon Session
14:30-15:20 Andreas Cap (University of Vienna and Erwin Schrodinger Institute of Mathematical Physics, Austria)
Parabolic geometries determined by subbundles in the tangent bundle
15:20-15:55 Maciej Dunajski (University of Cambridge, UK) Doubrov invariants, twistor theory and exotic holonomy
16:00-18:00 Poster Session (see here the list of the participants and titles of their presentations)
Friday December 15
Morning Session
9:00-9:50 Jan Slovak (Masaryk University in Brno, Czech Republic) Inclusions of parabolic geometries on a manifold
9:50-10:40 Michail Zhitomirskii (Technion - Israel Institute of Technology, Israel) Exact normal form for (2,5) distributions
10:40-11:00 Coffee Break
11:00-11:35 Piotr Mormul (Warsaw University, Poland) How to stratify special multi-flag and geometrically encode the emerging strata
11:35-12:10 Jean-Baptiste Pomet (INRIA, Sophia Antipolis, France) Average control system and Finsler geometry (common work with Alex Bombrun)
Afternoon Session
14:30-15:05 Josef Silhan (Masaryk University in Brno, Czech Republic) The conformal Killing equation on forms - prolongations and applications
15:10-16:00 Pawel Nurowski (Warsaw University, Poland) GL(2,R) geometries and ODE
Jiro Adachi (Hokkaido University, Sapporo, Japan) Relative local stability for Engel structures
Francesca Chittaro (SISSA, Trieste, Italy) An estimate for the entropy of Hamiltonian flows
Dorel Fetcu (Technical University of Iassy, Romania)
Explicit formulas for biharmonic submanifolds in 3-dimensional Sasakian space forms (jointly with Cezar Oniciuc)
Jaroslav Hrdina (Masaryk University in Brno, Czech Republic)

Hiroyuki Kamada (Miyagi University of Education, Japan and University of South Denmark, Odense, Denmark) Quaternionic Analog of CR structure and its pseudoconvexity
Woichech Krynski (Banach Mathematical Center, Poland)
Characteristic vector fields of distributions - determination theorems
Velichka Milousheva (Institute of Mathematics and Informatics, Bulgarian Academy of Science) On the geometry of hypersurfaces of conullity two in Euclidean spaces
Marian Ioan Munteanu (University “Al. I. Cuza”, Iasi, Romania) TBA
Svyatoslav Pavlichkov (Kharkov National University, Ukraine)
Generalized triangular forms: coordinate-free description and backstepping
Marek Rupniewski (Banach Mathematical Center, Poland)
Determinacy of affine distributions by their singular curves
Katja Sagershnig (University of Vienna, Austria)
An explicit formula for Nurowskis conformal structure
Ulysse Serres (U. Dini University, Firenze, Italy)
Gauss-Bonnet inequalities and Hopf theorem for Zermelo’s problem
Valery Yumaguzhin (Program Systems Institute of RAS, Pereslavl’-Zalessky, Russia) Differential Invariants of classical generic Monge-Amp`ere equations of hyperbolic type
Vojtech Zadnik (Masaryk University in Brno, Czech Republic) TBA
Lenka Zalabova (Masaryk University in Brno, Czech Republic) TBA

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