Three talks in Cuautitlan under the general title: Topología algebraica basada sobre nudos

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.

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