Contact
Email: rf tod sehi ta aramaluo
Office: BAML 6, IHÉS
35 route de Chartres
91440 BuressurYvette, France
Research

Delocalization of the height function of the sixvertex model,
with Hugo DuminilCopin, Alex Karrila, Ioan Manolescu,
preprint
We show that the height function of the sixvertex model, in the parameter range $a=b=1$ and $c\ge 1$, is delocalized with logarithmic variance when $c\le 2$. This complements the earlier proven localization for $c>2$. Our proof relies on RussoSeymourWelsh type arguments, and on the local behaviour of the free energy of the cylindrical sixvertex model, as a function of the unbalance between the number of up and down arrows.

Rotational invariance in critical planar lattice models,
with Hugo DuminilCopin, Karol Kajetan Kozlowski, Dmitry Krachun, Ioan Manolescu,
preprint
In this paper, we prove that the large scale properties of a number of twodimensional lattice models are rotationally invariant. More precisely, we prove that the randomcluster model on the square lattice with clusterweight $1\le q\le 4$ exhibits rotational invariance at large scales. This covers the case of Bernoulli percolation on the square lattice as an important example. We deduce from this result that the correlations of the Potts models with $q\in\{2,3,4\}$ colors and of the sixvertex height function with $\Delta\in[1,1/2]$ are rotationally invariant at large scales.

Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems,
with
Marc Lelarge,
J Stat Phys 173, 917–940 (2018)
In two papers Franz, Leone and Toninelli proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution and a general distribution. Panchenko and Talagrand simplified the proof and generalized the result of for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks and allows to bypass the arguments in based on the study of the SherringtonKirkpatrick (SK) model.

Abstract Interpretation with HigherDimensional Ellipsoids and Conic Extrapolation,
with
Arnaud Venet,
CAV 2015: 415430
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higherdimensional ellipsoids to automatically discover symbolic quadratic invariants within loops, using loop counters as implicit parameters. In order to obtain nontrivial invariants, the diameter of the set of values taken by the numerical variables of the program has to evolve (sub)linearly during loop iterations. These invariants are called ellipsoidal cones and can be seen as an extension of constructs used in the static analysis of digital filters. Semidefinite programming is used to both compute the numerical results of the domain operations and provide proofs (witnesses) of their correctness.
Teaching
 2020  2022: TA, Math316 (Probability), L3 Math, Université ParisSud
 2020  2022: Facilitator, MISS (science workshop for children), Université ParisSud
 2019  2020: TA, Math151 (Calculus), L1 PCST, Université ParisSud
 2017  2019: math oral examination in CPGE: MP*, Lycée Blaise Pascal, Orsay