

Research activities 
 Gaussian multiplicative chaos, multifractal random measures and their applications,
 Liouville field theory and 2d quantum gravity,
 Probabilistic representation of fully developed turbulence,

Publication list 
51The Virasoro structure and the scattering matrix for Liouville conformal field theory with G. Baverez, C. Guillarmou, A. Kupiainen and V. Vargas .
50Segal's axioms and bootstrap in Liouville theory with C. Guillarmou, A. Kupiainen and V. Vargas .
49Probabilistic construction of simplylaced Toda conformal field theories with B. Cerclé and V. Vargas.
48Conformal bootstrap in Liouville Theory with C. Guillarmou, A. Kupiainen and V. Vargas, to appear in Acta Mathematica .
47The semiclassical limit of Liouville conformal field theory with H. Lacoin and V. Vargas, to appear in Annales de la faculté des sciences de Toulouse .
46A probabilistic approach of ultraviolet renormalisation in the boundary SineGordon model with H. Lacoin and V.Vargas, to appear in Probability Theory and Related Fields.
45Path integral for quantum Mabuchi Kenergy with H. Lacoin and V.Vargas, to appear in Duke Math. Journal.
44On a skewed and multifractal unidimensional random field, as a probabilistic representation of Kolmogorov's views on turbulence with L.Chevillard, C.Garban and V.Vargas, in Annales Henri Poincaré 20, pages 36933741(2019).
43The Tail expansion of Gaussian multiplicative chaos and the Liouville reflection coefficient with V.Vargas, in Annals of Probability Volume 47, Number 5 (2019), 30823107.
42Integrability of Liouville theory: proof of the DOZZ Formula with A.Kupiainen and V.Vargas, in Annals of Mathematics Pages 81166 from Volume 191 (2020), Issue 1.
41Liouville Quantum Gravity and Polyakov's formulation of 2d string theory with C.Guillarmou and V.Vargas, Publications mathématiques de l'IHES (2019) p175.
40Lecture notes on Gaussian multiplicative chaos and Liouville Quantum gravity with V.Vargas.
39Local conformal structure of Liouville quantum gravity with A.Kupiainen and V.Vargas, in Communications in Mathematical Physics 371, 1005Ð1069 (2019).
38Renormalizability of Liouville Quantum Gravity at the Seiberg bound, with F.David, A.Kupiainen and V.Vargas, Electron. J. Probab. Volume 22 (2017), paper no. 93, 26 pp.
37Liouville Quantum Gravity on the complex tori, with F.David and V.Vargas, Journal of Mathematical Physics 57, 022302 (2016).
36Continuity estimates for the complex cascade model on the phase boundary, with T. Madaule and V.Vargas, 2015.
35Liouville quantum gravity on the unit disk, with Y. Huang and V.Vargas, 2015.
34Liouville quantum gravity on the Riemann sphere, with F.David, A.Kupiainen and V.Vargas, Commun. Math. Phys. (2016) 34269.
33Logcorrelated Gaussian fields: an overview, with B.Duplantier, S.Sheffield and V.Vargas, volume in honor of JeanMichel Bismut 65th Anniversary.
32KPZ formula derived from Liouville heat kernel, with N.Berestycki, C.Garban and V.Vargas, Journal of London Mathematical Society (2016) 94 (1) : 186208.
31Liouville heat kernel: regularity and bounds, with P.Maillard, V.Vargas and O.Zeitouni, Ann. Inst. H. Poincaré Probab. Statist. Volume 52, Number 3 (2016), 12811320.
30Semiclassical limit of Liouville Field Theory, with H.Lacoin and V.Vargas, Journal of Functional Analysis, vol 273, Issue 3, 1 2017, Pages 875916.
29Liouville Brownian motion at criticality, with V.Vargas, Potential Analysis 43 (2) 149
(2015).
28The glassy phase of complex branching Brownian motion , with T.Madaule and V.Vargas, Commun. Math. Phys. (2015) 3341157.
27Glassy phase and freezing of logcorrelated Gaussian potentials , with T.Madaule and V.Vargas, Ann. Appl. Probab. 26 (2016), no. 2, 643690.
26Complex Gaussian multiplicative chaos , with H.Lacoin and V.Vargas, Commun. Math.
Phys. (2015) 337 : 569.
25Gaussian multiplicative chaos and applications: a review , with V.Vargas, Probab. Surveys 11 (2014),
p. 315392.
24Spectral dimension of Liouville quantum gravity , with V.Vargas, Ann. Henri Poincaré (2014) 15 : 2281.
23On the heat kernel and the Dirichlet form of Liouville Brownian motion , with C.Garban and V.Vargas, Electron. J. Probab. 19 (2014), paper no. 96, 25 pp
22Liouville Brownian motion , with C.Garban and V.Vargas, Ann. Probab. vol 44, Num 4
(2016), 30763110.
21Renormalization of critical Gaussian multiplicative chaos and KPZ formula , with B.Duplantier, S.Sheffield and V.Vargas, Commun. Math. Physics, 2014, Volume 330, Issue 1, pp 283330.
20Gaussian multiplicative chaos for symmetric isotropic matrices , with L.Chevillard and V.Vargas, Journal of Statistical Physics, February 2013, Volume 150, Issue 4, pp 678703.
19Critical Gaussian multiplicative chaos: Convergence of the derivative martingale , with B.Duplantier, S.Sheffield and V.Vargas, Annals of Probability, Volume 42, Number 5 (2014), 17691808.
18Limiting laws of supercritical branching random walks , with J.Barral and V.Vargas, Comptes rendus  Mathematique 350 (2012) pp. 535538.
17Gaussian multiplicative chaos and KPZ duality , with J.Barral, X. Jin, and V.Vargas, Comm. in Math. Physics, October 2013, Volume 323, Issue 2, pp 451485.
16Levy multiplicative chaos and star scale invariant random measures, with J.Sohier and V.Vargas, Annals of Probability, Volume 42, Number 2 (2014), 689724.
15Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure, with R.Allez and V.Vargas, to appear in ESAIM PS.
14Lognormal scale invariant random measures, with R.Allez and V.Vargas, Probability Theory and Related Fields, April 2013, Volume 155, Issue 34, pp 751788.
13Optimal transportation for multifractal random measures, applications, with V.Vargas, Annales de l'Institut Henri Poincaré PS, Volume 49, Number 1 (2013), 119137.
12Forecasting volatility in the presence of leverage effect, with J.C. Domenge and V.Vargas.
11Critical homogenization of ItôLevy process driven SDEs in random medium, with B. Sow, Stochastic Analysis and Applications, Volume 29, Issue 5, 2011.
10Multidimensional Multifractal Random Measures, with V.Vargas, Electronic Journal of Probability, 2010, Vol 15, 241258.
9Scaling limits for symmetric ItôLévy processes in random medium, with V.Vargas, Stochastic Processes and their Applications, volume 119, no 12, 2009.
8KPZ formula for loginfinitely divisible multifractal random measures, with V. Vargas, ESAIM PS, 2011, Vol 15, 358371.
7Stochastic Homogenization of Reflected Diffusion Processes, Electronic Journal of Probability, 2010, vol 15, 9891023.
6Homogenization of periodic semilinear parabolic degenerate PDEs, with E. Pardoux and B. Sow, Annales de l'Institut Henri Poincaré ANL, Vol 26, Issue 3, MayJune 2009, 978998.
5Stochastic Homogenization of Quasilinear PDEs with a spatial degeneracy, with F. Delarue, Asymptotic Analysis, 2009, 61, 6190.
4Homogenization of locally ergodic diffusions with possibly degenerate diffusion matrix, Annales de l'Insitut Henri Poincaré PS, Volume 45, Number 4 (2009), 9811001.
3Diffusion in a Locally Stationary Random Environment, Probability Theory and Related Fields, Vol 143, No 34, 2009, p. 545568.
2Homogenization of spacetime dependent and degenerate random flows II, Annales de l'Institut Henri Poincaré (PS) 2008, vol. 44, n.4, p. 673692.
1Homogenization of spacetime dependent and degenerate random flows,
Stochastic Processes and their Applications, 117 (2007), pages 15611585.

