Computer Science/Discrete Mathematics

What can we say on a convex body from seeing its projections? In the 80s, Lutwak introduced a collection of measurements that capture this question. He called them the affine quermassintegrals. They are affine invariant analogues of the classical...

Let X and Y be normed spaces. In functional analysis, a ``theorem on factorization through L2'' refers to the following type of statement: 

Every bounded linear operator A mapping X to Y (i.e. sup_x ||A(x)||_Y/||x||_X

Such factorization...

Let C be a class of groups. (For example, C is a class of all finite groups, or C is a class of all finite symmetric groups.) I give a definition of approximations of a group G by groups from C. For example, the groups approximable by symmetric...

What combinatorial properties are likely to be satisfied by a random subspace over a finite field? For example, is it likely that not too many points lie in any Hamming ball of fixed radius? What about any combinatorial rectangle of fixed side...

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups $Sym(n)$ (in the sofic case) or the finite dimensional unitary...

A recent line of work has focused on the following question: Can one prove strong unconditional lower bounds on the number of samples needed for learning under memory constraints? We study an extractor-based approach to proving such bounds for a...