Low-dimensional topology and geometry have many problems with an easy formulation, but a hard solution. Despite our intuitive feeling that these problems are "hard", lower or upper bounds on algorithmic complexity are known only for some of them...

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Members Seminar

We present an overview of elementary methods to study extensions of modular representations of various types of "groups". We shall begin by discussing actions of an elementary abelian pp-group, E=(Z/p)rE=(Z/p)r, on finite dimensional vector spaces...

In a joint work with Tianyi Zheng we show that the growth function of the first Grigorchuk group satisfies

lnlnvn/lnvn=a,

where a=log2/logx, x being a positive root of the polynomial x3−x2−2x−4. This is done by constructing measures with...

There are striking analogies between topology and arithmetic algebraic geometry, which studies the behavior of solutions to polynomial equations in arithmetic rings. One expression of these analogies is through the theory of etale cohomology, which...

(joint work with Assaf Naor) A key problem in metric geometry asks: given metric spaces X and Y, how well does X embed in Y? In this talk, we will consider this problem for the case of the Heisenberg group and explain its connections to geometric...

You can make a paper Moebius band by starting with a 1 by L rectangle, giving it a twist, and then gluing the ends together. The question is: How short can you make L and still succeed in making the thing? This question goes back to B. Halpern and C...

Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids...