Małe Ciche Niskowymiarowe
Tatra conference in Low-dimensional topology Polish version

About
Getting there
Conditions
Mountains
Programme
Financial support
How to apply
About
The Conference Małe Ciche Niskowymiarowe (Small Quiet Low-dimensional: Małe Ciche, that is, small quiet, is the name of the village the conference takes place in) will be held in Małe Ciche from 08/16 (Sunday) through 08/22 (Saturday). The aim of the conference is to introduce students and young researchers into the field of low-dimensional topology. We plan a few talks given by experts and also some introductory students' talks. This is because we believe the best way to learn something is by trying to explain it to someone else.

The exact conference is not yet fixed. We know that one or two days will be devoted to hiking, but this heavily depends on the weather.

We do not expect any preliminary knowledge in low-dimensional topology.
Getting there.
  • The standard way to get to Małe Ciche is through Zakopane.
  • Getting to Zakopane is straightforward. There are buses and trains from Cracow and many other places in Poland. Even though there are direct trains and buses from basically any place in Poland, it might be actually more convenient (albeit more expensive) to go to Cracow and change to a bus going to Zakopane.
  • In Zakopane one can take a local bus to Małe Ciche or a cab. There are usually plenty of buses departing from the large square right outside of the train station. The exact place from where the buses to Małe Ciche depart changes quite often, so it is best to ask "Małe Ciche?"
  • A group of between six and ten can take a bus, a group of three of four can share a taxi. Sometimes this pays off, the distance is not big.
  • The Polish website suggests another option, of taking the bus going to Morskie Oko and getting off at Zazadnia (from where it is a 20 minutes walk). We do not recommend this, unless you travel in a group with at least one Polish speaker.
  • The actual building (address: Małe Ciche 73) is located near the chairlift, very close to the southern edge of the village. On getting out of the bus, you'll most likely be near the church. Follow the road you came on, going in the directions of mountains (that is, southwards). Take the last street to the left before the bridge (do not cross the bridge). The street goes uphill, take second left (there is a mirror for cars on the junction). After 50 meters or so, you'll see a large building on the left. The entire distance from the church to the building is less than 500 meters.
  • Anoter option is to take a car, but note that the main street from Nowy Targ to Zakopane (route 47) has heavy traffic. A better option is to take route 49.
  • If the weather is good, expect heavy traffic near all entry points to the National Park between 9am and 3pm, that is at route 958 between Kiry and Zakopane, and at route 960 near the border (on the Polish side).
  • Last summer, after a heavy thunderstorm, some parts of the road just outside the house were destroyed. Driving uphill requires caution, otherwise the car's suspension could be damaged. This should be fixed by now, but it might happen that another heavy rainfall destroys some other part!
  • There shouldn't be any problems with parking.
Local conditions
  • The participants are accommodated in a local cottage. This is not a hotel, the standard is lower (no towels for example), but so its the price. It is also a nice adventure. And the food is at the same place.
  • The rooms are for 2, 3 or 4 persons, usually the rooms are with bathrooms, some are not.
  • The accommodation includes three meals per day: breakfast around 8am, lunch around 1pm (this is the main meal in Poland) and dinner around 7pm. Usually the meals are good. If you have special requests (no meat, no milk etc.), please let us know while registering.
  • The house has 3 floors, usually the rooms are on the second and third floor. If you have problems climbing stairs, please let us know, we can arrange for a room on the ground floor.
  • During a hiking day, there are usually two meals: in the morning and in the evening.
  • In the village there are two shops (around 10 minutes walk from the house), a good pizzeria and a church.
  • There is a possibility of playing soccer. However, the nearest flat place is outside of the village, around 1.5 km from the house.
  • Note that there might be problems with mobile phones: the rooms might be out of range. Going out of the house and 10 meters uphill usually solves the problem.
Programme



Topics:
  1. Constructions of three and four manifolds (Dehn surgeries, branched covers, Kirby calculus).
  2. Smooth invariants: Seiberg--Witten and Heegaard Floer
  3. Contact structures
Lecturers
  • Adam Baranowski
  • Jozsef Bodnar
  • Maciej Borodzik
  • Jakub Pawlikowski
  • Wojciech Politarczyk
  • Gergo Pinter
  • Bruno Stonek
  • Magdalena Zielenkiewicz

Maciej Borodzik (2 hours)
It will be an introductory lecture about knot theory and the theory of 3-manifolds. A knot is just a smooth embedding of a circle into a three-dimensional space or S^3. Knots can be used to construct 3-manifolds - there exist strong connections between knot invariants and invariants of three-dimensional manifolds.

Adam Baranowski A wild world of 4-manifolds (2 hours)
Every student knows, that every continuous function can be approximated by smooth functions. But can every homeomorphism be approximated by a sequence of diffeomorphisms? It seems to be possible, but there exist homeomorphic manifolds which are not diffeomorphic. Moreover, there exist homeomorphisms of four-dimensional space, which cannot be uniformly approximated by diffeomorphisms. To "see" such phenomenon we need at least four dimensions, but in five or more dimension problems become easier. In this sequence of lectures we will talk about constructions of 4-manifolds.

Wojciech Politarczyk Jones polynomial and Khovanov homologies (3 hours)
Jones polynomial is a very interesting knots' invariant, which was discovered by accident in eighties of XX century. Khovanov homology are a generalisation of Jones polynomial. Although the definision is very easy combinatorially, we don't know, why these homologies have so strong properties.

Jakub Pawlikwoski Introduction to plumbing calculus (2 hours)

Gergo Pinter Singularities and three-manifolds (2 hours)

Bruno Stonek Characteristic classes (2 hours)

Magdalena Zielenkiewicz Quick trip through homologies of manifolds (2 hours)

Jozsef Bodnar Brieskorn manifolds -- singularities and low dimensional topology (3 hours)
Brieskorn singularity is a hypersurface singular at the origin having an equation in several complex variables given by the sum of some powers of the variables. Brieskorn manifolds are defined by taking the intersection of this hypersurface with a sphere centered at the origin. Despite of their simple definition, these manifolds have many remarkable properties. Just to mention a few: we can find among them all the possible smooth structures on the 7 dimensional topological sphere (28 altogether), and in dimension 3, the Poincare sphere was a close witness of the birth of the concept of fundamental group and the famous Poincare conjecture. The aim of this lecture is to give a brief introduction to some of the concepts of singularity theory and low dimensional topology (Milnor fibers, links, plumbing representation, surgeries, homology spheres), mainly working on concrete examples provided by Brieskorn singularities and manifolds.

Expenses
  • The cost of the conference is 490 PLN. This is around 120 Euro or 35000 Huf.
  • We expect some financial support for participants. If you need support, please let us know.
Mountains
  • This section contains important informations which might affect your safety.
  • Małe Ciche is located around 1km north of the border of Tatra Mountains National Park.
  • The organizers do not provide guides and do not take responsibility for safety of the excursions.
  • There are lots of possibilities for hiking: starting from a very easy hike to Rusinowa Polana, through medium length trips (Murowaniec, Dolina Pięciu Stawów, Kasprowy Wierch), up to hard and very hard excursions.
  • The rescue in Polish mountains is free, however if you plan on going to the Slovakian part, it is a good idea to buy an insurance. This also matters if you go on a hike on Polish side and accidentally fall onto the Slovakian.
  • No matter how experienced you are, please keep in mind that safety is important and hiking is serious . In particular:
    • It will be August. But it doesn't mean that the temperature will not drop below freezing, there won't be snowstorms etc. There shouldn't be any snowfall, but especially in the high mountains, you never know.
    • T-storms will always be an issue. Every year a dozen of tourists gets struck by a lightning. Such accidents can be fatal. Always check the weather forecast (like here ) before going. Try to set off early in the morning (8 am is not early), so that in the early afternoon you start descending from high peaks. The T-storms occur mostly in the afternoon, you might avoid lots of problems. If weather forecast predict T-storms, better stay at home or go into a valley.
    • Wherever you go, please inform someone where are you going and what is the estimated time of return. If your plans change, inform about it.
    • Always have a backup plan. Just in case.
    • Remember that the distance on a map looks shorter than in reality. On some trails (like Orla Perć), a few hundred meters is much harder to walk through than the whole 9 kilometers road to Morskie Oko.
    • Usually maps have distance given in minutes. This is reasonable, not always accurate. If a distance is 60 minutes, maybe you can walk it in 45, but not in 15. It can, however, take more than 2 hours as well.
    • Beware of jams on most popular peaks (Świnica, Giewont, Rysy). Set off very early if you don't want to waste 2 hours.
    • Consult an expert before going out. As a rule of thumb, trails up to 2012 m of altitude are `safe', higher peaks usually are more `advanced', require using of hands while climbing etc. Keep in mind that the beginning of a trail usually is at altitude 1000m. Getting to 2100m means at least 1100m elevation gain and usually over 30km of overall distance to walk.
    • It's getting dark pretty quickly after the sunset, you might meet a bear if you are in the dark in the mountains.
    • Unless you really know what you're doing, never ever get off a marked trail.
    • A 5-years old child can walk 27 km in high mountains (reaching summits of height above 2100m). But it does not imply you can do that as well.
To apply for the conference, write an e-mail to Maciej Borodzik. The address is mcboro, then the usual sign, then mimuw.edu.pl.


Organizers: Maciej Borodzik and Jakub Pawlikowski