University of Texas at Austin

1 University Station C1200

Austin,TX, 78712-0257

U.S.A.

- B.S., Mathematics, Ecole Normale Supérieure, rue d'Ulm, PARIS, 1993.

- M.A., Mathematics, Ecole Normale Supérieure, 1995.

- Ph.D., Mathematics, University of Jussieu (Paris 6), 1999. Thesis Advisor: Yann Brenier.

- John T. Stuart Centennial Professor in Mathematics, Department of Mathematics, University of Texas at Austin, from September 2016 to present.

- Affiliated member of ICES, The institute for Computational Engineering and Sciences, from September 2013 to present.

- Professor, Department of Mathematics, University of Texas at Austin, from August 2011 to present.

- Professor, Mathematical Department, University of Oxford, UK, 2010-2011.

- Associate Professor, department of Mathematics, University of Texas at Austin, 2007-2011.

- Assistant Professor, department of Mathematics, University of Texas at Austin, 2003-2007.

- Permanent position of Researcher at the C.N.R.S. (National center of scientific research, France), University of Nice, 1999--2003.

- Fluid mechanics, Navier-Stokes equations.

- Integral operators.

- Hyperbolic conservation laws.

- Kinetic equations, hydrodynamical limits.

- The work of Alexis Vasseur and Cheng Yu has been the topic of a presentation at the Seminaire Bourbaki in IHP, Paris, June 2017.

- Fellow of the American Mathematical Society (class 2016).

- NSF-EPSRC Collaborative Research, 2022-2025.

- NSF-RTG: Co-PI (PI Maggi), Analysis of Partial Dierential Equations, 2019-2024.

- National Science Foundation: Grant award, 2019-2023.

- National Science Foundation: Grant award, 2016-2020.

- National Science Foundation: Grant award, 2012-2016.

- National Science Foundation: Grant award, 2009-2012.

- National Science Foundation: Grant award, 2006-2009.

- Frank Gerth III Faculty fellowship: 2009-2010.

- President's associates centennial teaching fellowship: 2008-2009.

- University of Texas Summer Research Appointment, 2005.

- Young Sam Kwon

Ph.D., University of Texas, 2007

Thesis: Strong Trace for Degenerate Parabolic-Hyperbolic Equations and Applications

Full Professor

Dong-A university, Busan, South Korea.

- Chi-Hin Chan

Ph.D., University of Texas, 2008

Thesis: The De Giorgi's Method as Applied to The Regularity Theory for Incompressible Navier Stokes Equations.

Associate Professor

National Chiao Tung University, Taiwan.

- Craig Michoski

Ph.D., University of Texas, 2009 (co-advised with John F. Stanton, chemistry department)

Thesis: Evolution equations in chemical systems.

Research Scientist

ICES, The university of Texas at Austin.

- Nicholas Leger

Ph.D. University of Texas, 2010

Thesis: A Fragmentation Model for Sprays and L2 Stability Estimates for Shocks Solutions of Scalar Conservation Laws Using the Relative Entropy Method.

Instructional Assistant Professor, Assistant Director of Undergraduate Studies

University of Houston.

- Kyudong Choi

Ph.D. University of Texas, 2012

Thesis: Estimates on derivatives for the Navier-Stokes equations and Holder continuity for integro-differential equations.

Associate Professor

Ulsan National Institute of Science and Technology, South Korea.

- Eric Baer,

Ph.D. University of Texas, 2012 (Co-advised with Prof. Figalli)

Senior Lecturer

The University of Chicago.

- Matt Novack,

Ph.D. University of Texas, 2018

Assistant Professor

Perdue University.

- Sam Krupa,

Ph.D. University of Texas, 2020

Postdoc

Max Planck Institute, Leipzig, Germany.

- Logan Stokols

Postdoc

Duke University.

- Jincheng Yang,
Ph.D. University of Texas, 2022

Postdoc

University of Chicago and IAS Princeton.

- Cheng Yu,

Assistant Professor

University of Florida.

- Moon-Jin Kang,

Assistant Professor

KAIST, South Korea.

- Laurent Lafleche

- Yiran Hu

- William Golding

- Program Director of the Activity Group on Analysis of PDE (SIAG/APDE)

at the Society for Industrial and Applied Mathematics (SIAM), January 2017-December 2018.

- Acting Chair of the Department of Mathematics, January-June 2016.

- Associate Chair, Department of Mathematics, September 2013-January 2017.

- Associate Editor for DIE (Differential and Integral Equations) (From January 2020).

- Associate Editor for Nonlinear Analysis (From March 2020).

- Associate Editor for SIMA (SIAM Journal on Mathematical Analysis) (From January 2016).

- Associate Editor for CMS (Communications in Mathematical Sciences) (from January 2015).

- Associate Editor for M3AS (Math. Models and Methods in Applied Sciences) (From January 2009).

- Member of the Tenure Track search committee, 2020-2021, Math Department.

- Member of the OIET: (Online Instruction Expert Team), since March 2020, Math Department.

- Faculty annual review committee, 2018-19, Math department.

- Postdoc recruitment committee (Chair) 2018-19, Math department.

- Jackson School of Geosciences Appointment Committee (P&T committee), since Sept. 2019.

- 21st Century Research Working Group, 2016-2017, College of Natural Sciences.

- Strategic plan for Seed Funding for Interdisciplinary Research, Summer 2013, College of Natural Sciences.

- Internal review of the Institute for Fusion Studies (IFS), April 2014, College of Natural Sciences.

- Review committee (Chair), 2013-2015, Math department.

- Tenure and Promotion committee, 2011--2014, College of Natural Sciences.

- Tenure and Promotion committee, 2011--2013, Math department.

- Strategic planning committee, 2011--2015, Math department.

- Chair committee, 2011--2017, Math department.

- Hiring committee (Chair), 2012--2013, Math department.

- Faculty annual review committee, 2018, Math department.

- Postdoc recruitment committee 2018, Math department.

- Conference co-organizer at ETH Zurich: When Kinetic Theory meets Fluid Mechanics, July 18-22, 2022.

- Conference co-organizer at AIM: Criticality and stochasticity in quasilinear fluid systems May 2 to May 6, 2022.

- Conference co-organizer at AIM: April 2021-4-5 to 10 (Remote).

- Member of the Organizing Committee for the PSPDE's meeting in Braga, Portugal, December 2015.

- Focus session on Nonlocal Phenomena, co-organized with Peter Bates at X Americas conference on Differential Equations, Buenos Aires, Argentina, 2015-01-16-20.

- Minisymposium co-organizer on "Boltzmann Equations in transport theory" with Prof. Gamba and Prof. Carvalho in the SIAM Conference on Ananlysis of Partial Differential Equations in Houston, December 6-8 2004.

- PDE workshop: Stability Analysis for Nonlinear PDEs, Oxford University (UK), 2022-08-19, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- Conference on Recent Advances in Kinetic Theory and Fluid Dynamics Models, Warsaw (Poland) 2022-08-11, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- Series of Lectures, Pesaro (Italie), 2022-06-12--18, "The Di Giorgi method applied to kinetic equations".

- Colloquium, ENS Paris (France), 2022-06-21, "Stability of discontinuous patterns in inviscid fluid mechanic".

- PDE Seminar, UC Davis, 2022-05-19, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- PDE Seminar, UC San Diego, 2022-05-17, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- Colloquium, Brown University, 2022-04-11, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- Joint mathematical meetings, San Francisco (virtual), 2022-04-07, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- Colloquium, USC California, virtual, 2022-02-07, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- Colloquium, Jiao Tong University Shanghai (China), virtual, 2022-01-05, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- Series of Lectures, KAIST South Korea, virtual, 2021-11, "Stability of discontinuous patterns in inviscid fluid mechanic".

- Colloquium, AIMS Cameroon, virtual, 2021-11-5, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- PDE Seminar, Rutgers University, virtual, 2021-10-29, "Boundary vorticity estimate for the Navier-Stokes equation and control of layer separation in the inviscid limit".

- BIRS conference (Oaxaca), virtual, 2021-09-10, "Uniform stability of viscous shocks for the compressible Navier-Stokes equation".

- BIRS conference (Banff), virtual, 2021-07-30, "Instability of finite time blow-up solutions for incompressible Euler".

- Analysis & PDE Seminar (Stanford), virtual, 2021-05-28, "Stability for discontinuous compressible flows: the theory of a-contraction with shifts".

- Seminar (Oxford (UK)), virtual, 2021-05-24, "Stability for discontinuous compressible flows: the theory of a-contraction with shifts".

- Conference in honor of Prof. Dafermos, ICERM (Brown U.), virtual, 2021-05-21, "Stability for discontinuous compressible flows: the theory of a-contraction with shifts".

- Oberseminar Analysis-Probability (Max Planck Institute (Germany)), virtual, 2021-05-11, "Stability of shocks among inviscid limits of Navier-Stokes equation".

- AMS meeting, special session, San francisco, virtual, 2021-05-02, "Instability of finite time blow-up solutions for incompressible Euler".

- Conference in Tours (France), virtual, 2021-03-23, "Stability for discontinuous compressible flows: the theory of a-contraction with shifts".

- Colloquium, George Mason U., virtual, 2021-02-24, "Stability for discontinuous compressible flows: the theory of a-contraction with shifts".

- Conference "Methods and Models of Kinetic Theory", Porto Ercole Italy, virtual, 2021-02-08, "Partial regularity in time for the Landau equation".

- IAS Analysis seminar (princeton), virtual, 2020-12-07, "Stability of discontinuous solutions for inviscid compressible flows".

- Conference in Banff (Canada), virtual, 2020-11-23, "Instability of finite time blow-ups for incompressible Euler".

- Conference in Luminy (France), virtual, 2020-10-26, "Instability of finite time blow-ups for incompressible Euler".

- Series of lecture, University of Pittsburgh, 2020-03-13, "Relative entropy applied to the study of stability to discontinuous solutions of conservation laws, subject to large perturbations".

- Colloquium, University of Florida, 2020-01-13, "Paradoxes and challenges in the modeling of the viscosity for compressible viscous fluids".

- SIAM Meeting, La Quinta (California), 2019-12, "Partial Regularity in Time for the Landau Equation".

- AMS Meeting, Gainesville (Florida), 2019-11-1, "Global existence of entropy solutions to the compressible Navier-Stokes equations with non-linear density dependent viscosities".

- Series of Lecture, Luminy, France, 2019-10, "Relative entropy applied to the study of stability to discontinuous solutions of conservation laws".

- Conference, Local and Nonlocal Trends in Analysis and Geometry, U. of Pittsburgh, 2019-10-11, "Holder regularity up to the boundary for SQG on bounded domains".

- Kinet Conference, University of Wisconsin-Madison, 2019-9-27, "Partial Regularity in Time for the Landau Equation".

- Conference, Oberwolfach, Germany, 2019-08-21, "Why it is so hard to get numerical evidences of possible finite time blow-ups for Euler".

- Conference, University of Cambridge, UK, 2019-07-03, "Why it is so hard to get numerical evidences of possible finite time blow-ups for Euler".

- Kinet Conference, University of Maryland at College Park, 2019-03-05, "De Giorgi holder regularity theory applied to kinetic-type equations".

- Centre International pour la recherche mathematique, Luminy, France, 2018-12-10, "Recent results for the 3D Quasi-Geostrophic Equation".

- Workshop on Nonlinear Waves, University of Illinois at Chicago, 2018-11-10, "Recent results for the 3D Quasi-Geostrophic Equation".

- Colab Conference, The University of Texas at Austin, 2018-11-06, "Partial regularity results for the Landau equation".

- Seminar, Princeton University, 2018-10-15, "The 3D Quasi-geostrophic equation: existence of solutions, lateral boundary conditions and regularity.".

- Seminar, College Station, 2018-08-28, "The 3D quasi-geostrophic equation: Existence, regularity, and boundary conditions".

- Regularity and Blow-up of Navier-Stokes Type PDEs using Harmonic and Stochastic Analysis, Banff, Canada, 2018-08-22, "The 3D quasi-geostrophic equation: Existence, regularity, and boundary conditions".

- Seminar, National Seoul University, South Korea, 2018-08-06, "Contraction property of shocks for conservation laws, and application to asymptotic analysis".

- 2018 UNIST workshop on PDEs in Fluids, UNIST, South Korea, 2018-07-27, "Contraction property of shocks for conservation laws, and application to asymptotic analysis".

- Seminar, University of Grenoble, France, 2018-06-18, "The 3D quasi-geostrophic equation: Existence, regularity, and boundary conditions".

- Seminar, University of Lille, France, 2018-06-14, "The 3D quasi-geostrophic equation: Existence, regularity, and boundary conditions".

- PDE seminar, University of Houston, 2018-03-02, "Uniform stability of shocks with respect to the viscosity, for the viscous shallow water equation.".

- Joint CMU-Pitt Colloquium, University of Pittsburgh, 2018-02-09, "Global solutions to the compressible Navier-Stokes equation with degenerate viscosity coefficients".

- Nonlocal PDE, Clay Mathematics Institute, Oxford, UK, University, 2017-09-28, "Regularity theory for a family of Integral-differential operators".

- Nonlocal School on Fractional Equations NSFE 2017, Iowa State University, 2017-08-18, "Regularity theory for a family of Integral-differential operators".

- Equadiff 2017, Bratislava, Slovakia, 2017-07-25, "The quantum Navier-Stokes equation and its semiclassical limit".

- Lecture on the Quasi-geostrophic equation, University of Chicago, 2017-06.

- Advanced School & Workshop on Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability, ICTP, Trieste, Italy, 2017-05-25, "Global regularity of solutions to the 4-species quadratic diffusion-reaction system in any space dimension".

- Seminar, The University of Kansas, 2017-04-06, "Global solutions to the compressible Navier-Stokes equation with degenerate viscosities".

- Conference on Current Developments in Mathematical Fluid Dynamics, Brown University, 2017-01-25, "Recent results on the 3D quasi-geostrophic equation".

- Seminar, Capital Normal University, Beijing, China, 2016-12-05, "Global existence of solutions for the compressible Navier-Stokes equation".

- Lecture on the quasi-geostrophic equation, The Chinese academia of Sciences, Beijing, China, 2016-12.

- Seminar, University of Wisconsin-Madison, 2016-11-14, "Recent results on the 3D quasi-geostrophic equation".

- Conference on Transport phenomena in collective dynamics: from micro to social hydrodynamics, ETH, Zurich, Switzerland, 2016-11-03, "Recent results on the 3D quasi-geostrophic equation".

- Colloquium, Rice University, Houston, 2016-09-08, "Recent results for the quasi-geostrophic equation".

- 7th European Congress of Mathematics, Berlin, Germany, 2016-07-20, "Global solutions to 3D compressible Navier-Stokes equations with degenerate viscosities".

- Asymptotic behavior of systems of PDE arising in physics and biology, University of Lille, 2016-06-15, "Global Existence of Solutions to the 3D Navier-Stokes Equations with Degenerate Viscosities".

- Conference-Calculus of Variations and Nonlinear Partial Differential Equations, Columbia University, NY, 2016-05-25, "Holder regularity for hypoelliptic kinetic equations with bounded measurable coefficients".

- Colloquium, PennState, Department of Mathematics, 2016-03-29, "Relative entropy and stability for Conservation Laws".

- Advances in Kinetic and Fluid Dynamics Transport: Analysis and Approximations, ICES, The University of Texas at Austin, 2016-02-24, "Holder regularity for hypoelliptic kinetic equations with rough diffusion coefficients".

- Mini workshop on modeling, analysis, computation and application of kinetic problems, Brown University, 2016-02-05, "Holder regularity for hypoelliptic kinetic equations with rough diffusion coefficients".

- 2016 Joint Mathematics meetings, Seattle, Washington, 2016-01-9, "Global weak solutions to the inviscid 3D quasi-geostrophic equation".

- Particle Systems and PDE's - IV, University of Minho, Braga, Portugal, 2015-12-17, "Global Existence of Solutions to the 3D Navier-Stokes Equations with Degenerate Viscosities".

- SIAM Conference on PDE, Scottsdale, Arizona, 2015-12-08, "Global Existence of Solutions to the 3D Navier-Stokes Equations with Degenerate Viscosities".

- Analysis seminar, Rutgers University, New Brunswick, 2015-10-14, "Regularity theory for the Surface Quasi-Geostrophic Equation".

- PDE seminar, Laboratoire Jacques-Louis Lions, Paris 6, La Sorbonne, Paris, France, 2015-06-26, "Théorie de régularité pour une famille d'opérateurs intégraux-différentiels".

- XEDP seminar, Ecole Polytechnique, Paris, France, 2015-06-23, "Existence of Global Solutions for 3D Compressible Navier-Stokes".

- PDE seminar, University of Savoie, Chambery, France, 2015-06-19, "Existence of Global Solutions for 3D Compressible Navier-Stokes".

- The fourth international conference on nonlinear evolutionary partial differential equations-theories and applications, Jiao Tong University, Shanghai, China, 2015-06-04, "Existence of Global Solutions for 3D Compressible Navier-Stokes".

- Conference-Calculus of Variations and Nonlinear Partial Differential Equations, Austin, Texas, 2015-05-27, "Regularity theory for non local operators".

- International Conference on Local and Nonlocal Nonlinear Partial Differential Equations, NYU at Shanghai, China, 2015-04-24, "Regularity theory for non local operators".

- Conference on PDEs and Free Boundary Problems, University of Pittsburgh, 2015-03-12, "Global weak solutions to the inviscid 3d quasi-geostrophic equation".

- PDE seminar, Princeton University, 2015-02-26, "Global weak solutions to the inviscid 3d quasi-geostrophic equation".

- X Americas conference on Differential Equations, Buenos Aires, Argentina, 2015-02-19, "Regularity theory for non local operators".

- Particle Systems and PDE's - III, University of Minho, Braga, Portugal, 2014-12-19, "Study of shocks via entropy methods".

- Conference "Revisiting decades of conservation laws", Valpré, Lyon, France, 2014-10-5, "Shocks and layers in compressible fluid mechanics".

- PDE seminar, University of Houston, 2014-09-12, "Shocks and layers in compressible fluid mechanics".

- PDE seminar, Chung-Ang University, Seoul, South Korea, 2014-07-30, "Shocks and Layers".

- Lecture, National Seoul University, South Korea, 2014-07-28, "The De Giorgi method applied to fluid mechanics".

- Seminar, Academia of Sciences of the Czech Republic, Prague, Czech Republic, 2014-07-15 2014-07-18, "Shocks and Layers".

- CIMI Workshop, Toulouse, France, 2014-06-18, CIMI Workshop, Toulouse, France. New trends in modeling, control, and inverse problems. "Shocks and Layers". New trends in modeling, control, and inverse problems. "Shocks and Layers".

- Kinetics, non standard diffusions and stochastics: emerging challenges in the sciences, University of Texas at Austin, 2014-05-15, "De Giorgi regularity method applied to Hamilton Jacobi".

- Lecture, Chiao-Tung University, Taiwan, 2014-05-08, "Partial regularity for the Navier-Stokes equation and higher derivatives estimates." "Partial regularity for the Navier-Stokes equation and higher derivatives estimates."

- Analysis seminar, University of Chicago, 2014-04-09, "C alpha regularity for Hamilton-Jacobi equations".

- International Conference on Recent Advances in PDEs and Applications, Levico Terme, Italy, 2014-02-20, "Relative entropy, contraction of shock in $L^2$, and applications".

- UCLA Colloquium. UCLA, Los Angeles, CA. 2014-01-23, "The Stability of Shocks in Inviscid Compressible Flows and the Second Law of Thermodynamics".

- SIAM Minisymposium on New Developments with Entropic Solutions to Nonlinear Conservation Laws. 2014 joint mathematics meetings. Baltimore, MA. 2014-01-16, "Relative entropy, contraction of shock in L^2, and applications".

- SIAM Conference on Analysis of PDE, Lake Buena Vista, Florida, 2013-12-07 2013-12-10 , "Relative entropy and contraction to extremal shocks".

- Analysis seminar, Princeton University, 2013-12-02, "Regularity theory for a class of fully nonlinear integral operators".

- Red-Raider Mini-symposium, Aspects of Fluid Dynamics, Texas Tech University, Lubbock, TX, 10-25 10-27 2013, "Relative entropy applied to shocks for Conservation Laws and applications".

- Seminar, Capital Normal University, Beijing, China, September 25, 2013, "Stability of shocks for conservation laws".

- Lecture, Morningside center, Academia of Sciences of China, Beijing, China, September 16-27,2013, 'The De Giorgi method for elliptic and parabolic equations and applications'.

- Workshop "Recent Advances in PDEs and Fluids", Stanford University, August 5-18, 2013 ``Relative entropy, stability of shocks for conservation laws, and applications to asymptotic limits".

- Contributed talk at a special session of the 2013 SIAM annual meeting, July 8-12, 2013, ``Relative entropy, stability of shocks for conservation laws, and applications to asymptotic limits".

- PDE seminar, University of Nice, France, June 2013, ``Relative entropy, stability of shocks for conservation laws, and applications to asymptotic limits".

- Quantum Systems: A Mathematical Journey from Few to Many Particles, University of Maryland, May 13 - 16, 2013, ``Relative entropy, stability of shocks for conservation laws, and applications to asymptotic limits".

- Symposium on Blow-up vs. Regularity for Fluid Equations, City University of New York, May, 2nd, 2013, ``Relative entropy, stability of shocks for conservation laws, and applications to asymptotic limits".

- Spring Central Sectional Meeting Iowa State University, Ames, April 26th-28th, 2013, ``Relative entropy, stability of shocks for conservation laws, and applications to asymptotic limits".

- Workshop on Kinetic PDEs: Analysis and Computation, Iowa State University, April 25th - 26th, 2013, ``Relative entropy applied to the stability of shocks for fluid mechanics".

- Mathflows 2012, Porquerolles, France, October 21-26th, 2012, ``Relative entropy applied to the stability of shocks for fluid mechanics".

- Model reduction in continuum thermodynamics: Modeling, analysis and computation, Banff, Canada, September 16th- September 21st, 2012, ``Relative entropy applied to the stability of shocks for fluid mechanics".

- Partial differential equations in the social and life science: emergent challenges in modeling, analysis, and computations, Banff, Canada, March 31st- April 5th, 2012, ``Relative entropy applied to shocks for the compressible Euler equation".

- Mathematical Aspects of Hydrodynamics, MFO Oberwolfach (Germany), August 12th - August 18th, 2012, ``Relative entropy applied to shocks for the compressible Euler equation".

- Closing plenary lecture at the14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Padova (Italy), June 25-29, 2012, ``Relative entropy applied to shocks for the compressible Euler equation".

- Nonlocal Operators: Analysis, Probability, Geometry and Applications, Bielefeld (Germany), July 9th - 14th, 2012, ``Integral Variational Problems".

- Seminar at the University of Toulouse (France), June 19, ``Integral Variational Problems".

- 5th Symposium on Analysis and PDEs, Perdue University, May 20-23, 2012, ``Regularity theory for nonlocal variational problems".

- Workshop on Hyperbolic conservation laws and infinite-dimensional dynamical systems, University of Pittsburgh, March 30 - April 1, 2012. ``Relative entropy applied to shocks for the compressible Euler equation".

- Colloquium, University of Maryland, March 14th, ``De Giorgi methods applied to regularity issues in Fluid Mechanics".

- Symposium on 3D Euler equation and Navier-Sokes equation, City University of New York, October 27th, 2011, ``Drift diffusion equation with fractional diffusion and the Surface Quasigeostrophic equation".

- Hyperbolic Conservation laws and related analysis, ICMS Edinburgh (UK), ``L^2 Stability of shocks for conservation laws".

- oxPDE-Royal Society International Seminars, Entropy and Convexity for Nonlinear Partial Differential Equations 16-17 June 2011, Kavli Royal Society International Centre (UK), "Integral variational problems".

- Oxbridge PDE Days, Oxford University (UK), 26 and 27 April 2011, "Regularity theory for nonlinear integral operators".

- Conference in Honour of the 70th birthday of Prof. Bardos, University of Nice, 21-25 February 2011, "Relative entropy method applied to the stability of shocks for systems of conservation laws".

- Newton Institute seminar, Cambridge University (UK), September 7 2010, "Relative entropy method applied to the stability of shocks for systems of conservation laws".

- Partial Differential Equations in Kinetic Theories: Tutorials for Graduate Students, Cambridge University (UK), August 25-26 2010, "Regularity theory for non linear singular integral operators based on De Giorgi techniques".

- Partial Differential Equations & Fluid Mechanics 2010, University of Warwick (UK), 5th-9th July 2010, "Regularity of Solutions of Some Non Linear Integral Variational Problems".

- International Summer School on Mathematical Fluid Dynamics, Levico Terme, Italy, "The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics".

- Seminar, June 11 2010, Universite Pierre et Marie Curie (Paris 6), France, "Conservation laws, relative entropy, and shocks".

- Plenary lecture, Emerging Topics in Dynamical Systems and Partial Differential Equations, DSPDEs 10, June 1 2010, Barcelona, Spain, "Regularity of solution to a class of nonlinear integral operators".

- Workshop Nonlinear Analysis and PDEs, April 16 2010, Austin, Texas, "Conservation laws, relative entropy, and shocks".

- Seminar, February 24 2010, Stanford University, "Regularity theory for a family of nonlinear integral equations".

- Colloquium of the Center for Applied Mathematical Sciences, February 2 2010, University of Southern California, Los Angeles, "The partial regularity results for Navier-Stokes revisited".

- France-China summer institute on mathematics, January 6 2010, Morningside Institute, Beijing, China, "Estimates on higher derivatives for the Navier-Stokes equation".

- Seminar, December 2 2009, University of Houston, "Global regularity for a class of systems of reaction-diffusion equations".

- FRG annual meeting, Kinetic Description of Multiscale Phenomena, September 25 2009, University of Maryland, "Global regularity for a class of systems of reaction-diffusion equations".

- Workshop on Regularity problems in hydrodynamics, August 4 2009, PIMS Vancouver, Canada, "Estimates on higher derivatives for the Navier-Stokes equation".

- IMA Summer program on Conservation laws, July 29 2009, University of Minnesota, "Global regularity for a class of Reaction-Diffusion systems".

- Workshop on Mathematical Aspects of Hydrodynamics, July 20 2009, Oberwolfach, Germany, "Estimates on higher derivatives for the Navier-Stokes equation".

- Workshop on Applied Math, July 3 2009, Bilbao, Spain, "Estimates on higher derivatives for the Navier-Stokes equation".

- Conference on Kinetic equations, June 25 2009, Banff, Canada, "Global regularity for a class of Reaction-Diffusion systems".

- Seminar, June 9 2009, University of Pisa, Italy, "Estimates on higher derivatives for the Navier-Stokes equation".

- College de France, Paris, June 5 2009, "Recent Results in Fluid Mechanics".

- Lecture at the Kazov School on Fluid Mechanics (former Paseky School), Kazov, Czech Republic, 23-29 May 2009, "Application of De Giorgi methods to Fluid Mechanics".

- Riviere-Fabes Symposium, University of Minnesota, April 18 2009, "Recent Results in Fluid Mechanics".

- AIM Workshop on the 3D Euler and 2D SQG equations, Palo Alto, April 6 2009, "Global regularity for the SQG equation in the critical case".

- Minisymposium "non linear fluid equations" in the SIAM Conference on Nonlinear Waves and Coherent Structures (NW08), July 24 2008, Roma, "Higher derivatives estimates for the Navier-Stokes equation".

- Seminar, The Academy of Sciences of the Czech Republic, June 2008, "Higher derivatives estimates for the Navier-Stokes equation".

- Seminar, University of Chicago, March 5 2008, "Higher derivatives estimates for the Navier-Stokes equation".

- Seminar, UBC Vancouver Canada, January 9 2008, "A bound from below for the temperature in compressible Navier-Stokes equations".

- Minisymposium Kinetic Theory and Interacting Particle Systems, SIAM Conference on Analysis of Partial Differential Equations, Phoenix, December 10-12 2007, "Regularity Result for Drift-Diffusion Equations with Fractional Laplacian".

- Seminar, Georgia Tech, November 6 2007,"C^a regularity for the quasi-geostrophic equation in the critical case".

- Seminar, University of Maryland, October 30 2007, "C^a regularity for the quasi-geostrophic equation in the critical case".

- Special Session on Nonlinear Conservation Laws and Related Problems, AMS Meeting, Chicago, October 5-6 2007, "A bound from below for the temperature in compressible Navier-Stokes equations".

- Seminar, Technische Universitat (Vienna, Austria), June 5 2007, "C^a regularity for the quasi-geostrophic equation in the critical case".

- Seminar, Academy of Sciences of the Czech Republic (Prague, Czech Republic), May 23 2007, "A bound by below for the temperature for Navier-Stokes".

- Seminar, University of Chicago, April 11 2007, "C^a regularity for the quasi-geostrophic equation in the critical case".

- Seminar, College Station, February 14 2007, "A new proof of partial regularity for Navier-Stokes equations".