School of Mathematics

I will describe several old and new applications of topological and algebraic methods in the derivation of combinatorial results. In all of them the proofs provide no efficient solutions for the corresponding algorithmic problems. Finding such...

I'll review recent progress on properties of 3-manifold groups, especially following from geometric properties. Then I'll discuss some open questions regarding 3-manifold groups, including their profinite completions, torsion in covers, orderability...

In [kal89], Kaltofen proved the remarkable fact that multivariate polynomial factorization can be done efficiently, in randomized polynomial time. Still, more than twenty years after Kaltofen's work, many questions remain unanswered regarding the...

Agenda: http://www.ias.edu/math/wgso3m/agenda

A knot is a closed curve embedded in the three-dimensional space, like a rope whose two ends are joined together. As usual in Topology, two knots are equivalent if one can be deformed into the other by continuous moves, where stretching and...

Vapnik's fundamental theorem of statistical learning establishes a computational equivalence between optimization (empirical risk minimization) and learning in the statistical setting. Is the same true for learning in games? We give a precise answer...

We produce examples of non-trivial Hamiltonian fibrations that are not detected by previous methods (the characteristic classes of Reznikov for example), and improve theorems of Reznikov and Spacil on cohomology-surjectivity to the level of...

I will describe how the notion of Lagrangian cobordism, introduced by Arnold in 1980, offers a systematic perspective on the study of Lagrangian topology. There are three aspects that will be emphasized: the relations with the triangulated structure...

Venkatesh has recently proposed a fascinating conjecture relating motivic cohomology with automorphic forms and the cohomology of arithmetic groups. I'll describe this conjecture, and discuss its connections with the local geometry of eigenvarieties...