This year very few members of the Students' Mathematical Society US' went to Toruń - which was very unfortunate, as the conference was extraordinary.

The leading topic of the conference was the game theory and rough analysis - topic not too widespread in Poland, especially in Silesia, but not only interesting, but also modern and developing. Organisers invited specialists from these branches of mathematics: professor Lech Górniewicz (the director of the Julius Paweł Schauder Centre of Nonlinear Research), professor Andrzej Nowak, professor Sławomir Plaskacz and doctor Agnieszka Wiszniewska-Matyszkiel, who gave series of lectures. The J.P.Schauder Centre of Nonlinear Research took scientific patronage over the conference.

Professor Lech Górniewicz's talk ("Some problems of multi-valued analysis") began innocently, from the outline of the history of Polish mathematics, but after a short while we ventured into the selection problem (with Michael's, Fryszkowski and Ryll-Nardzewski theorems about the existence of measurable selections), the fixed point problem (here the theorems of Lefchetz, Kakutani, Eilenberg, Dugundji and Górniewicz appeared, along with notions of AR, ANR), and at the end we arrived to the topic of differential inclusions. The talk was especially interesting for the people present at this year's Andrzej Lasota In Memoriam talk - it was on the same topic, laid in a more student-friendly way.

Professor Sławomir Plaskacz told us about the differential games - non-anticipative strategies, the problem of existence of a value for the payment function, the principle of dynamic programming, the steering problem. We learned about some qualities of normal and tangent cones (with the special case of Bouligand cone), we considered the invariant solutions of differential games, also those changing in time. Professor presented the topic in an original way, not by the super- and subdifferential, but through normal cones.

As it turned out during the conference, many participants never had anything to do with game theory. Hence doctor Agnieszka Wiszniewska-Matyszkiel began her talk with defining the notion of a game, the Nash equilibrium, the Pareto efficiency, strategies and their profiles. We considered games with zero sum and not, we considered minimax, games in the normal form, mixed strategies and applications of game theory in economy. We've learned the strategies in dynamic games (the open loop, the feedback and closed loop) and the tools of optimal steering and the problem of dynamical optimisation: the maximum rule of Pontryagin and the Bellman equation.

Professor Andrzej Nowak focused not only on relaying the substance of his lectures, but also to point out to the participants possible directions of research in game theory and its rich literature. The lectures themselves concerned stochastic games, but not only them - we talked about the minimax, von Neumann, Nash, Ionescu-Tulcea and measurable selector theorems, we considered cooperative games with a special mention to the Shapley quantity, discounted games and not.

There were certainly fewer students talks this year - but the intensity of the professor's once did not let anyone feel too little mathematics. In the voting for the best talk the participants chose the "Existence of economical equilibrium" of Łukasz Rzepnicki.

Organisers took care not only of the scientific part;) - during the afternoons and evenings one could go with them to planetarium, visit all the neighbouring student clubs or beer worlds.

To sum it up - interesting topic, interesting talks, great talkers, splendid atmosphere and perfect organisation - it remains to put the Summer School of Mathematics in Toruń to our annual agendas of summer trips :)

Pictures made by organisers may be found at picasaweb.google.com/…/TorunskaLetniaSzkoAMatematyki2011#