# Workshop on Geometry of PDEs and Integrability

14-18 October 2013, Teplice nad Bečvou, Czech Republic

## Topics

• Geometry of integrable systems
• Homological and algebraic methods in geometry of differential equations
• Nonlocal geometry of differential equations and zero curvature representations
• Hamiltonian and Lagrangian formalism
• Computer methods in geometry of differential equations

## Participants and Talks

• Hynek Baran (Opava)
• Pavel Bibikov (Moscow)
• Spherization of 1-jet space ${\displaystyle J^{1}\mathbb {R} ^{n}}$ and point classification of first order partial differential equations, abstract, presentation
• Maciej Błaszak (Poznań)
• Oleksandr Chvartatskyi (Göttingen)
• Pantelis Damianou (Nicosia)
• Adam Doliwa (Olsztyn)
• Gerard Helminck (Amsterdam)
• Darboux transformations for the lower triangular Toda hierarchy and its strict version, abstract, presentation
• Sergei Igonin (Utrecht)
• Lie algebras responsible for zero-curvature representations of (1+1)-dimensional PDEs and some applications to Bäcklund transformations, abstract, presentation
• Jiřina Jahnová (Vodová) (Opava)
• Joseph Krasil'shchik (Opava & Moscow)
• Boris Kruglikov (Tromsø)
• Integrability of dispersionless PDEs in 3D and Einstein-Weyl geometry (joint with Eugene Ferapontov), abstract, presentation
• Valentin Lychagin (Tromsø)
• Irina Markina (Bergen)
• Sub-Riemannian geometry on infinite dimensional manifolds, abstract
• Luigi Martina (Lecce)
• Symmetry reductions of the Skyrme-Faddeev model, presentation
• Michal Marvan (Opava)
• On symmetries and conservation laws of the Gibbons-Tsarev equation (jointly with H. Baran, P. Blaschke, I.S. Krasil'shchik), abstract
• Giovanni Moreno (Opava)
• Flags and polarization in geometric singularites of jets (joint work with Michael Bächtold)
• Oleg Morozov (Tromsø)
• Folkert Müller-Hoissen (Göttingen)
• Binary Darboux transformations in bidifferential calculus, abstract
• Maxim Pavlov (Moscow)
• Integrable Geodesics, abstract
• On the classification of homogeneous differential-geometric third-order Poisson brackets, abstract, presentation
• Juha Pohjanpelto (Corvallis, Oregon)
• Pseudo-groups, moving frames, and invariant variational principles, abstract
• Ziemowit Popowicz (Wroclaw)
• Vladimir Rubtsov (Angers)
• Błażej M. Szablikowski (Poznań)
• Novikov algebras and a classification of multicomponent Camassa-Holm equations, abstract, presentation
• Alexey Samokhin (Moscow)
• Gradient catastrophes for Burgers equation on a finite interval. Numerical and qualitative study, abstract, presentation
• Artur Sergyeyev (Opava)
• Coupling constant metamorphosis, integrability and all that, abstract
• Nikola Stoilov (Göttingen)
• Hamiltonian systems of hydrodynamic type in 2+1 dimensions and their dispersive deformations (joint work with E.V. Ferapontov, V.S. Novikov, and A.V. Odeskii), abstract
• Alexander Vasil'ev (Bergen)
• Alexander Verbovetsky (Moscow)
• Luca Vitagliano (Salerno)
• Petr Vojčák (Opava)
• On nonlocal symmetries for the Krichever-Novikov equation, abstract

## Workshop Location

The workshop will take place in the town Teplice nad Bečvou, Czech Republic. The town is known for its spa, unique Zbrašov aragonite caves (49°31'54"N, 17°44'45"E) and one of the world's deepest underwater caves, the Hranice Abyss (49°31'55"N, 17°45'2.6"E; the confirmed depth of the lake is 373 m, more than 120 m under the sea level).

This town is close to Hranice na Moravě which has a larger railway station easily reachable from Vienna, Warsaw or Prague.

The accommodation will be provided at the hotels located in Teplice nad Bečvou and the conference itself will take place in a hotel as well.

Cultural events
• On Wednesday, 16 October, excursion is planned to Zbrašov aragonite caves (see above in this section).

Early comers, accompanying persons, and practitioners of absenteeism are encouraged to visit the Hranice Abyss (see above in this section). The way is through the railway station Teplice nad Bečvou (see in section Transport below).

## Conference Costs

There is no conference fee, but the participants must cover all the other expenses. We regret that no financial support is available for this event.

The expected accommodation price will be around 1000 Kč (i.e., ca. 40 EUR) per night per person in a single room with full board. In the case of two people sharing a double room the price will be somewhat lower.

Participants intending to attend the conference dinner will be requested to pay a small fee (it is expected to be around 500 Kč, i.e., ca. 20 EUR).

## Visa

Those in need of a visa to travel to the Czech Republic are kindly requested to contact the organizers as soon as possible so that we can arrange the letters of invitation. It is strongly recommended to apply for a visa well before the trip.

## Transport

The arrival day is Sunday, 13 October 2013, the departure day is Saturday, 19 October 2013.

The following brief information is provided to facilitate easier journey planning. If you need more, do not hesitate to contact the organizers. Timings given below apply to the arrival and departure days.

All data are offered in good faith but without guarantee. Please, verify them against reliable external sources.

The workshop will take place in Penzion Diana (49°31'55"N, 17°44'36"E) situated in Teplice nad Bečvou near Hranice na Moravě (49°33'55"N, 17°44'30"E), a railway node with direct connections to Prague, Brno, Vienna and Warsaw. Detailed timetables are available from www.idos.cz.

From Hranice na Moravě, taking taxi to Teplice nad Bečvou is the fastest and most convenient option. The distance is approximately 5 km. Bus No. 2, which connects Teplice to Hranice, is unavailable on weekends.

Adventurously inclined may wish to continue to Teplice nad Bečvou by a local train (departures from Hranice on Oct. 13 at 11:36, 12:50, 14:50, 16:50, 18:50, 19:47, 21:47, from Teplice on Oct. 19 at 4:56, 6:06, 8:06, 9:06, 13:06, 15:06,17:06). The walking distance from the railway station Teplice nad Bečvou (second stop, 49°31'48"N, 17°44'55"E) to the conference place (Penzion Diana, 49°31'54"N, 17°44'36"E) is approximately 1 km. Follow a red tourist mark, cross the river and walk uphill (look for stairs that begin near a post office); when you reach the main street, Diana is on your left. Or follow the red mark until Sanatorium Moravan, then walk up the street; when you reach the main street, Diana is in front of you.

The nearest airports that have a direct train connection to Hranice na Moravě are

Airport state code web page distance
Ostrava cz osr www.airport-ostrava.cz/en 50 km
Brno cz brq www.brno-airport.cz/en 110 km
Katowice pl ktw www.katowice-airport.com/en 175 km
Pardubice cz ped www.airport-pardubice.cz 200 km
Vienna at vie www.viennaairport.com 260 km
Prague cz prg www.prg.aero/en 340 km
Prague
Because of its good air and railway connectivity, Prague is the recommended destination of your flight. The transport between the airport and the railway station Praha hlavní nádraží is provided by regular Airport Express bus and taxi. Hourly express trains make the distance from Prague to Hranice na Moravě in slightly more than 3 hours. The last of these direct trains departs from Prague at 20:16; the first arrives to Prague at 7:55. However, direct trains on this route are operated by two distinct companies and care must be taken not to mix them up.
The majority of the direct express connections have their number prefixed with Ex or R and are operated by the national railway company České dráhy; tickets offices are everywhere in the main hall of the Prague railway station. The ticket costs 275 CZK. Departures from Prague are at 5:16, 6:16, 7:16, 8:16, 9:16, 10:16, 11:16, 12:16, 13:16, 14:16, 15:16, 16:16, 16:47, 18:16, 18:47, 20:16. Departures from Hranice are at 4:41, 5:34, 6:41, 7:34, 8:41, 9:41, 10:41, 11:39, 12:41, 13:41, 14:41, 15:41, 16:41, 17:41, 18:41, 19:38. Tickets can be bought online at www.cd.cz/eshop.
Be aware that trains which have their number prefixed with IC and followed with RegioJet are operated by a private company Student Agency; passengers without a valid RegioJet ticket are not allowed to enter them. The RegioJet trains are subject to compulsory reservation, but offer a free wifi and refreshments. RegioJet tickets are available online (either from www.regiojet.cz or click "KUP!" in www.idos.cz) or from a separate ticket office RegioJet in the lower basement of the Prague railway station (and are likely to be sold out). Departures from Prague are at 7:12, 9:12, 11:12, 13:12, 15:12, 16:12, 17:12, 19:12. Departures from Hranice are at 6:32, 7:32, 8:32, 10:32, 12:32, 14:32, 16:32, 18:32. Prices vary, but are comparable to České dráhy.
Vienna
Despite good air connectivity, Vienna is more difficult to reach from the location of the workshop. There are two direct express EC trains from Wien Meidling to Hranice na Moravě (destination Warszawa, departure 7:42, 13:32) and from Hranice na Moravě to Wien Meidling (arrival 14:24, 20:17); travelling time is less than 3 hours. For indirect connections see www.idos.cz. Connections through Břeclav have the expected travelling time of 3 hours; others (through Brno) are considerably longer.
For the timetable of the hourly bus Flughafen Wien (airport) -- Wien Meidling see www.oebb.at/busplan2013/118700.pdf. Student Agency www.studentagency.eu) runs a regular bus service between the Vienna airport and Brno (see below); the stop in Brno is in walking distance from the railway station (5 min).
Pardubice
The airport is close to the railway station (4 km) and reachable by local bus No. 8, fourth stop from the railway station. All express trains from Prague (see above) to Hranice make a stop in Pardubice, the departure (arrival) time being approx. 1 hour later (earlier) than Prague's.
Katowice
Wizz air, Ryanair and Lufthansa fly from Katowice to a number of european destinations. For bus service to the railway station (≈ 50 min) see www.pkm.katowice.pl/pyrzowice.php. Direct trains to Hranice na Moravě depart from Katowice at 9:12, 13:12, 15:12; from Hranice na Moravě arrive to Katowice at 12:30, 14:30, 18:30. The travelling time is 2:20 h.
Brno
On Saturdays, UTair flies to Moscow Vnukovo (↗12:15, ↘13:15). Bus 76 to railway station Brno hlavní nádraží (the distance is 13 km) departs every 30 min. Taxi costs 500 CZK ≈ 20 EUR.
There are hourly direct express "R" trains from Brno to Hranice na Moravě between 7:02 and 21:02 except at 8 and 10 o'clock, and from Hranice na Moravě to Brno between 5:19 and 21:19 except at 6, 10, 12 and 18 o'clock. The travelling time is 1:40 h, the price is 161 CZK.
Ostrava
There are daily flights to Prague (↗13:00, ↘13:30). Due to proximity (50 km), taxi to Teplice nad Bečvou may be an affordable option.
Alternatively, take taxi to the railway station Studénka (which is much closer than Ostrava). Direct express "R" trains to Hranice (20 min, 52 CZK, 2nd stop) depart every two hours between 8:58 and 20:58.

### Some important words in Czech

airport = letiště
railway station = nádraží, vlakové nádraží, vlaková zastávka
platform = nástupiště
track = kolej
departure = odjezd
arrival = příjezd
delay = zpoždění