The mapping spaces of the r-truncated versions of the E_n operads appear as the r-th stage of the Taylor tower for long embedding spaces. It has been shown that their rational homotopy groups...

# Publications for year 2019

## Pages

It was recently argued that string theory on {\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4 with one unit (k=1) of NS-NS flux is exactly dual to the symmetric orbifold CFT {\rm Sym}^N(\mathbb{T...

In this article, we prove that the height function associated with the square-ice model (i.e.~the six-vertex model with a=b=c=1 on the square lattice), or, equivalently, of the uniform random...

It was recently shown that string theory on \mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4 with minimal NS-NS flux (k=1) is exactly dual to the symmetric orbifold of T4. Here we show...

For random d-regular graphs on N vertices with 1 \ll d \ll N^{2/3}, we develop a d^{-1/2} expansion of the local eigenvalue distribution about the Kesten-McKay law up to order d^{-3}. This...

Let K be a convex polyhedron and \mathscr F its Wulff energy, and let \mathscr C(K) denote the set of convex polyhedra close to K whose faces are parallel to those of K. We show that, for...

We consider random interlacements on \mathbb{Z}^d, d \ge 3. We show that the percolation function that to each u \ge 0 attaches the probability that the origin does not belong to an infinite...

As a refinement of the Swampland Distance Conjecture, we propose that a quantum gravitational theory in an infinite distance limit of its moduli space either decompactifies, or reduces to an...

The dynamics of DNNs during gradient descent is described by the so-called Neural Tangent Kernel (NTK). In this article, we show that the NTK allows one to gain precise insight into the Hessian...

In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We...

Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show that the...

The main purpose of this paper is to investigate commuting flows and integrable systems on the configuration spaces of planar linkages. Our study leads to the definition of a natural volume form...