Vincent Vargas
 

Welcome to my Web Page!
 

Research

Teaching

Consulting

 

 

Future Events: lectures on the DOZZ formula!

I am giving a series of lectures on our recent probabilistic proof of the DOZZ formula (joint with A. Kupiainen and R. Rhodes): DOZZ stands for Dorn-Otto-Zamolodchikov-Zamolodchikov. You can find this formula in wikipedia and our proof here. The lectures will be given at the IHES during october-november 2017.

Research

I am currently a CNRS Research fellow at the DMA (mathematics departement of the Ecole Normale supérieure of Paris). I am interested in applied and theoretical probability. More specifically, my research topics are: directed polymers, Gaussian multiplicative chaos, Liouville quantum gravity (or Liouville field theory), turbulence, modeling and forecasting volatility. More precisely, I have spent most of my time developing the theory of Gaussian multiplicative chaos and its applications. For the past few years, I have been defining the path integral approach to Liouville Quantum gravity (on all Riemann surfaces) and trying to prove that this approach coincides with the conformal bootstrap approach. If you want to contact me, here are my coordinates:

My current and past PhD students:

 

My coauthors are Romain Allez, Julien Barral, Nathanael Berestycki, Jean-Philippe Bouchaud, Laurent Chevillard, Francis Comets (PhD advisor), Francois David, Tung-Lam Dao, Jean Duchon, Bertrand Duplantier, Christophe Garban, Colin Guillarmou, Antti Kupiainen, Hubert Lacoin, Thomas Madaule, Pascal Maillard, Rémi Rhodes, Raoul Robert, Scott Sheffield, Julien Sohier and Ofer Zeitouni (feel free to visit their web page!). I was also coordinator of the ANR project (French research grant) entitled CHAMU (2010-2014). Here is a list of my publications:

    Publications in Gaussian Multiplicative Chaos, Branching Random Walks or Liouville Quantum Gravity

  1. A. Kupiainen, R. Rhodes, V. Vargas (2017), Integrability of Liouville theory: proof of the DOZZ Formula, preprint submitted.
  2. C. Guillarmou, R. Rhodes, V. Vargas (2017), Polyakov's formulation of 2d bosonic string theory, preprint submitted.
  3. A. Kupiainen, R. Rhodes, V. Vargas (2015), Local Conformal structure of Liouville Quantum Gravity, preprint submitted.
  4. F. David, A. Kupiainen, R. Rhodes, V. Vargas (2015), Renormalizability of Liouville Quantum Gravity at the Seiberg bound, preprint submitted.
  5. F. David, R. Rhodes, V. Vargas (2015), Liouville Quantum Gravity on the complex tori, Journal of Mathematical Physics.
  6. T. Madaule, R. Rhodes, V. Vargas (2015), Continuity estimates for the complex cascade model on the phase boundary, preprint submitted.
  7. Y. Huang, R. Rhodes, V. Vargas (2015), Liouville Quantum Gravity on the unit disk, Annales de l'IHP.
  8. F. David, A. Kupiainen, R. Rhodes, V. Vargas (2014), Liouville Quantum Gravity on the Riemann sphere, Communications in Mathematical Physics.
  9. N. Berestycki, C. Garban, R. Rhodes, V. Vargas (2014), KPZ formula derived from Liouville heat kernel, Journal of the London Mathematical Society.
  10. P. Maillard, R. Rhodes, V. Vargas, O. Zeitouni (2014), Liouville heat kernel: regularity and bounds, Annales de l'IHP.
  11. H. Lacoin, R. Rhodes, V. Vargas (2014), Large deviations for random surfaces: the hyperbolic nature of Liouville Field Theory, Journal of Functional Analysis.
  12. R. Rhodes, V. Vargas (2013), Liouville Brownian motion at criticality, Potential Analysis.
  13. T. Madaule, R. Rhodes, V. Vargas (2013), The glassy phase of complex branching Brownian motion, Communications in Mathematical Physics.
  14. T. Madaule, R. Rhodes, V. Vargas (2013), Glassy phase and freezing of log-correlated Gaussian potentials, Annals of Applied Probability.
  15. H. Lacoin, R. Rhodes, V. Vargas (2013), Complex Gaussian multiplicative chaos, Communications in Mathematical Physics.
  16. R. Rhodes, V. Vargas (2013), Gaussian multiplicative chaos and applications: a review, Probability Surveys.
  17. R. Rhodes, V. Vargas (2013), Spectral dimension of Liouville quantum gravity, Annales de l'IHP Physique théorique.
  18. C. Garban, R. Rhodes, V. Vargas (2013), On the heat kernel and the Dirichlet form of Liouville Brownian Motion, Electronic Journal of Probability.
  19. C. Garban, R. Rhodes, V. Vargas (2013), Liouville Brownian motion, to appear in Annals of Probability.
  20. B. Duplantier, R. Rhodes, S. Sheffield, V. Vargas (2012), Renormalization of Critical Gaussian Multiplicative Chaos and KPZ, Communications in Mathematical Physics.
  21. B. Duplantier, R. Rhodes, S. Sheffield, V. Vargas (2012), Critical Gaussian multiplicative chaos: convergence of the derivative martingale, Annals of Probability.
  22. J. Barral, R. Rhodes, V. Vargas (2012), Limiting laws of supercritical branching random walks, C.R.A.S. 350, 535-538 (2012).
  23. J. Barral, X. Jin, R. Rhodes, V. Vargas (2012), Gaussian multiplicative chaos and KPZ duality, Communications in Mathematical Physics.
  24. R. Rhodes, J. Sohier, V.Vargas (2012), Star-scale invariant random measures, Annals of Probability.
  25. R. Allez, R. Rhodes, V. Vargas (2012), Lognormal scale invariant random measures , Probability Theory and Related Fields.
  26. R. Allez, R. Rhodes, V. Vargas (2012), Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure , ESAIM P&S.
  27. R. Rhodes, V. Vargas (2011), Optimal transport for multifractal random measures. Applications , Annales de l'I.H.P.
  28. R. Rhodes, V. Vargas (2009), Multidimensional Multifractal Random Measures , Electronic Journal of Probability.
  29. R. Rhodes, V. Vargas (2008), KPZ formula for log-infinitely divisible multifractal random measures, ESAIM P&S 15, 358-371 (2011).
  30. R. Robert, V. Vargas (2008), Gaussian Multiplicative Chaos revisited, Annals of Probability 38 (2), 605-631 (2010)

    Publications in Turbulence:

  1. L. Chevillard, R. Rhodes, V. Vargas (2012), Gaussian multiplicative chaos for symmetric isotropic matrices, Journal of Statistical Physics 150, 678-703 (2013).
  2. L. Chevillard, R. Robert, V. Vargas (2009), A Stochastic Representation of the Local Structure of Turbulence, Europhys. Lett. 89, 54002 (2010).
  3. R. Robert, V. Vargas (2006), Hydrodynamic turbulence and intermittent random fields, Communications in Mathematical Physics 284 (3), 649-673 (2008).

    Publications in Finance:

  1. V. Vargas, T.L. Dao, J.P. Bouchaud (2012), Skew and implied leverage effect: smile dynamics revisited, to appear in International journal of applied and theoretical finance.
  2. J.P. Bouchaud, L. De Leo, V. Vargas, S. Ciliberti (2012), Smile in the low moments, RISK Magazine, 64-67 July (2013).
  3. J.C. Domenge, R. Rhodes, V. Vargas (2011), Forecasting volatility in the presence of Leverage Effect, preprint.
  4. J. Duchon, R. Robert, V. Vargas (2008), Forecasting volatility with the multifractal random walk model, Mathematical Finance 22 (1), 83-108 (2012).

    Publications in Homogenization or Directed Polymers:

  1. R. Rhodes, V. Vargas (2009), Scaling limits for symmetric Ito-Levy processes in random medium, Stochastic Processes and their applications.
  2. V. Vargas (2008), Strong localization and macroscopic atoms for directed polymers, Probability Theory and Related Fields.
  3. F. Comets, V. Vargas (2007), Majorizing multiplicative cascades for directed polymers in random media, ALEA.
  4. V. Vargas (2006), A local limit theorem for directed polymers in random media: the continuous and the discrete case, Annales de l'I.H.P .

 

Teaching

I use to give a course (in french) entitled "Modele limite lognormal de Mandelbrot et ses applications en finance" for the master MASEF (financial mathematics) and the master EDPMAD (applied mathematics). This course can be seen as an introduction to econophysics (pioneered by Benoit Mandelbrot, J.P. Bouchaud and M. Potters among others). Here are the slides:

    Slides of "Modele limite lognormal de Mandelbrot et ses applications en finance":

  1. Cours1, an introduction to econophysics.
  2. Cours2, an introduction to Gaussian multiplicative Chaos.
  3. Cours3, an introduction to option pricing theory.
I also give a course (in french) entitled "Phenomenologie des Marches financiers" in the third year of ENSAE, Paris Graduate school of Economics, Statistics and Finance. Here are the slides:

    Slides of "Phenomenologie des Marches financiers":

  1. Cours1, an introduction to econophysics.
  2. Cours2, an introduction to option pricing theory.
  3. Cours3, an introduction to Random matrices.

 

Consulting

During the period 2007-2013, I was a consultant in volatility arbitrage for the French hedge fund Capital Fund Management. Capital Fund Management is a quantitative hedge fund based in Paris that is specialized in arbitrage strategies. The arbitrage strategies are elaborated by PHD's in physics and mathematics and implemented by IT specialists.

I am currently a member of the board of Capital Fund Management's research foundation: the web page is here.

Past Events

I was co-organizing a trimester at the Institut Henri Poincaré (IHP). The trimester was on statistical physics and took place on the period january 2015-april 2015. Feel free to visit the web site here.

I co-organized with J. Bouttier, I. Corwin and R. Rhodes a two week workshop on the two KPZs. It took place in september 2016 at the IESC in Cargese, Corsica. The web site of the workshop is here.