We will present some results on upper and lower bounds for hitting probabilities of random fields in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. Applications to several examples of stochastic partial differential equations will be discussed.

10:30-11:30

**Ilse Fischer **
(University of Vienna)
*Refined enumerations of alternating sign matrices *

12:00-13:00

**Bohumír Opic **
(Academy of Sciences, Prague)
*Embeddings of Bessel-potential-type spaces into generalized Hölder spaces involving k-modulus of smoothness *

The lecture is based on a joint work with Amiran Gogatishvili and Júlio S. Neves.

15:00-16:00

**Joan Porti **
(Universitat Autònoma de Barcelona)
*Ricci flow and geometrization of three manifolds *

16:30-17:30

**Jiří Matoušek **
(Charles University, Prague)
*Hardness of embedding simplicial complexes in R^{d}*

18:00-19:00

**Jakob Yngvason **
(University of Vienna)
*Quantum gases in fast rotation and vortices *

Brown and Adams representability theorems for cohomology theories originated in algebraic topology. They have been extended to other algebraic and geometric contexts, where they have been successfully applied (Grothendieck duality in algebraic geometry, Auslander-Reiten theory in representation theory, motivic cohomology?). Nevertheless, there are still many open questions with potentially striking applications. We will introduce the audience to what is known and report on recent advances.

16:30-17:30

**Ľubomír Snoha **
(Matej Bel University, Banská Bystrica)
*Minimal sets in discrete dynamics - results, tools, open problems *

18:00-19:00

**Aleksander Malnič **
(University of Ljubljana)
*Covering space techniques in graph theory *

the primary incentive was the final solution of the long standing Heawood's Map Colour Problem.

In the talk I will review some results covering this topic.