  Talk 1: Open problems in knot theory that everyone can try to solve. Knot
theory is more than two hundred years old; the first scientists who considered
knots as mathematical objects were A.Vandermonde (1771) and C.F.Gauss (1794).
However, despite the impressive grow of the theory, there are simply formulated
but fundamental questions, to which we do not know answers. I will discuss
today several such open problems, describing in detail the 20 year old
Montesinos-Nakanishi conjecture. Our problems lead to sophisticated
mathematical structures (I will describe some of them in tomorrows talks), but
today's description will be absolutely elementary. Talk 2: Lagrangian
approximation of Fox $p$-colorings of tangles. The talk will culminate in the
introduction of the symplectic structure on the boundary of a tangle in such a
way that tangles yields Lagrangians in the symplectic space. Talk 3: Historical
Introduction to Skein Modules. I will discuss, in my last talk of the
conference, skein modules, or as I prefer to say more generally, algebraic
topology based on knots. I would like to discuss today, in more detail, skein
modules related to the (deformations) of 3-moves and the Montesinos-Nakanishi
conjecture but first I will give the general definition and I will make a short
tour of the world of skein modules.
