By using the notion of a rigid R-matrix in a monoidal category and the Reshetikhin--Turaev functor on the category of tangles, we review the definition of the associated invariant of long knots...

# Publications

## Pages

Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an...

Recently, string theory on \text{AdS}_3 \times \text{S}^3 \times \mathbb{T}^4 with one unit of NS-NS flux (k=1) was argued to be exactly dual to the symmetric orbifold of \mathbb{T}^4, and in...

Future galaxy clustering surveys will probe small scales where non-linearities become important. Since the number of modes accessible on intermediate to small scales is very high, having a...

We study metastable behavior in a discrete nonlinear Schrödinger equation from the viewpoint of Hamiltonian systems theory. When there are n < \infty sites in this equation, we consider...

In this short paper we determine the effects of structure on the cosmological consistency relation which is valid in a perfect Friedmann Universe. We show that within \LambdaCDM the consistency...

In this paper we provide a universal description of the behavior of the basic operators of the Schwarzian theory in pure states. When the pure states are energy eigenstates, expectation values...

In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension n \leq 9.

This result, that was...

We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation...

In this paper, we analyze a number of architectural features of Deep Neural Networks (DNNs), using the so-called Neural Tangent Kernel (NTK). The NTK describes the training trajectory and...

In this note, we study the action of O(d,d) transformations on the integrable structure of two-dimensional non-linear sigma models via the doubled formalism. We construct the Lax pairs...

Even though we know that physical observations are frame independent, the frame dependence of cosmological perturbations is relatively subtle and has led to confusion in the past. In this paper...