# Publications for year 2019

## Pages

Saturday, 2 November, 2019
Thomas Willwacher

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...

arXiv:1911.00709
Friday, 1 November, 2019
Lorenz Eberhardt, Matthias R. Gaberdiel, Rajesh Gopakumar

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...

arXiv:1911.00378
Thursday, 31 October, 2019
Hugo Duminil-Copin, Matan Harel, Benoit Laslier, Aran Raoufi, Gourab Ray

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...

arXiv:1911.00092
Wednesday, 23 October, 2019
Matthias R. Gaberdiel, Jeremy A. Mann

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...

arXiv:1910.10427
Tuesday, 22 October, 2019
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles, Horng-Tzer Yau

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...

arXiv:1910.10121
Monday, 21 October, 2019
Alessio Figalli, Yi Ru-Ya Zhang

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...

arXiv:1910.09515
Thursday, 10 October, 2019
Alain-Sol Sznitman

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...

arXiv:1910.04737
Wednesday, 2 October, 2019
Seung-Joo Lee, Wolfgang Lerche, Timo Weigand

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...

arXiv:1910.01135
Tuesday, 1 October, 2019
Arthur Jacot, Franck Gabriel, Clément Hongler

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...

arXiv:1910.02875
Thursday, 26 September, 2019
Marcos Marino, Tomas Reis

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...

arXiv:1909.12134
Wednesday, 25 September, 2019
Tobias Diez, Tudor S. Ratiu

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...

arXiv:1909.11551
Friday, 20 September, 2019
Tudor S. Ratiu, Nguyen Tien Zung

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...

arXiv:1909.09707