We consider the adjacency operator of the Linial-Meshulam model for random simplicial complexes on n vertices, where each *d*-cell is added independently with probability p to the...

# Publications

## Pages

Numerical simulations are a versatile tool providing insight into the complicated process of structure formation in cosmology. This process is mainly governed by gravity, which is the dominant...

We study the structure of Brownian loop-soup clusters in two dimensions. Among other things, we obtain the following decomposition of the clusters with critical intensity: When one conditions a...

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a...

The moduli space of canonical divisors (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. We define a proper moduli space of twisted canonical...

We describe simple properties of some soups of unoriented Markov loops and of some soups of oriented Markov loops that can be interpreted as a spatial Markov property of these loop-soups. This...

We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences...

We show that the Hochschild-Pirashvili homology on wedges of circles produces new representations of Out(F_n) that do not factor in general through GL(n,Z). The obtained representations are...

We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations...

Using convex integration we give a constructive proof of the well-known fact that every continuous curve in a contact 3-manifold can be approximated by a Legendrian curve.

Wilson lines in gauge theories admit several path integral descriptions. The first one (due to Alekseev-Faddeev-Shatashvili) uses path integrals over coadjoint orbits. The second one (due to...

On the identity component of the universal Teichmüller space endowed with the Takhtajan–Teo topology, the geodesics of the Weil–Petersson metric are shown to exist for all time. This component...