(a) Education.

• Ecole Polytechnique (France). Mathematics and Physics M.S. 1994 • Ecole Nationale des Ponts et Chaussées (Corps des Ponts). Civil Engineering M.S. 1997 • University of Paris VI (Jussieu). DEA (Probability) 1997 • Ecole Polytechnique Fédérale de Lausanne. Mathematics Ph.D. (with G. Ben Arous) 2001 • Technion. Post Doc (with D. Ioffe) in Probability Theory 2000/2001

(b) History.

• 2011 - present: Caltech, Professor of Applied & Computational Mathematics and Control & Dynamical Systems. • 2004-2011: Caltech, Assistant Professor of Applied & Computational Mathematics and Control & Dynamical Systems. • 2001-2004: CNRS Research Fellow. • 1994-2001: High Civil Servant in the Corps des Ponts et Chaussées (French Corps of Engineers).

(c) Research areas.

• Mathematics of Machine Learning. • Scientific Machine Learning. Physics Informed Learning. • Game theoretic approaches to numerical analysis, algorithm design and learning. • Homogenization and multiscale analysis. • Uncertainty Quantification. • Stochastic modeling and stochastic analysis. • Robustness/Brittleness of Bayesian inference and machine learning algorithms.

(d) Research grants and contracts.

• DOE award number DE-SC0023163 (SEA-CROGS: Scalable, Efficient and Accelerated Causal Reasoning Operators, Graphs and Spikes for Earth and Embedded Systems). 2022-2025. $150,000/year (Caltech subcontract) • NASA, AIST. Kernel Flows: Emulating Complex Models for Massive Data Sets. 2022-2024. $650,000/year (CoPI, $1560,000/year) • AFOSR, MURI. Machine Learning and Physics-Based Modeling and Simulation. Learning and Meta-Learning of Partial Differential Equations via Physics-Informed Neural Networks: Theory, Algorithms, and Applications (Caltech PI, $380k/year). 2020-2025. • Beyond Limits. Learning Optimal Models. 2020-2023, $601,000 (PI). • NASA/JPL. Earth 2050. 2020-2022, $156,000/year (CoPI). • AFOSR. Grant number FA9550-18-1-0271. Games for Computation and Learning. 2018-2021, $900,000 (PI). • ONR. Grant number N00014-18-1-2363. Toward scalable universal solvers for linear systems. 2018-2022. $840,000 (CoPI). • AFOSR/ DARPA EQUiPS. Grant number FA9550-16-1-0054. Computational Information Games, 2015-2018, $900,000 (PI). • AFOSR. Grant number FA9550-12-1-0389. Scientific Computation of Optimal Statistical Estimators, 2012-2015, $900,000 (PI). • DOE/LANL (Exascale Co-Design Center for Materials in Extreme Environments), 2012-2016, $150,000/year (UQ task). • NSF. OCI-1216643, Scientific Software Innovation Institute for Advanced Analysis of X-Ray and Neutron Scattering Data (SIXNS), 2012-2014, $477,685 (CoPI, UQ task) • NSF. CMMI-092600, Dynamics and Control of Bio-Molecular Systems using Geometric Model Reduction and Stochastic Variational Integrators, 2009-2012, $450000 (PI). • DOE/NNSA. PSAAP, Uncertainty Quantification, ASC Predictive Science Academic Alliance Program ($17 million grant), 2008-2013 (Director of the UQ group). • UTRC, Post Doctoral Grant Fellowship. 2009. • DARPA. DynaRum, Dynamic Network Analysis for Robust Uncertainty Management, 2007-2008. • UTRC. Stochastic Variational Integrators, 2007 (PI)

(i) Professional Affiliations.

• SIAM • AMS

(j) Editorial Activities.

• Current o Mathematics of Computation (MCOM) o SIAM Journal on Numerical Analysis. o International Journal of Uncertainty Quantification. o Journal of Computational Dynamics. o De Gruyter book series on Computational Science and Engineering. o SIAM/ASA journal on Uncertainty Quantification o Foundations of Data Science o The Journal of Machine Learning for Modeling and Computing (JMLMC). • Past o Springer Handbook of Uncertainty Quantification o M2AN Special issue on multiscale problems and techniques

(k) University administration (selected).

• Caltech Predictive Science Academic Alliance Program (2008-2013). Director of the Uncertainty Quantification group. • Caltech Computing and Mathematical Sciences (CMS) Department Academic Officer (2010-2013). • Applied and Computational Mathematics Option Representative (2010-2013).

(l) Selected awards and honors.

• Aly Kaufman fellow 2000. • Prix EPFL doctorat 2001. • IMA Editor’s Choice article 2009. • SIAM CSE 2015. Plenary lecturer. • XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications, 2016. Plenary lecturer. • SIAM UQ 2016. Mini-tutorial. • Germund Dahlquist Prize (SIAM). July 2019. • SIAM Fellow 2022.

(m) Selected Interviews.

• HPC Wire: The Masters of Uncertainty (09/2013) • Scientific American. Do we live in a simulation?

(e) Students and Alumni.

• Current Graduate Students o Pau Battle Franch o Matthieu Darcy o Yasamin Jalalian o Théo Bourdais o Jonghyeon Lee • Current Postdocs o Hamed Hamze Bajgiran o Xianjin Yang o Ricardo Miguel Baptista • Alumni o Graduate students ▪ Lei Zhang. (W.P. Carey Ph.D. Prize in Applied Mathematics 2007). Professor at Shanghai Jiaotong University. ▪ Roger Donaldson (co-advised with M. Desbrun, Motorola Solutions). ▪ Leonard Lucas (co-advised with M. Ortiz, US Navy, Pittsburgh). ▪ Molei Tao (co-advised with J. Marsden, W.P. Carey Ph.D. Prize in Applied Mathematics 2011). Associate professor at Georgia Tech. ▪ Gene Ryan Yoo (2020). Quantitative Researcher at Susquehanna International Group. ▪ Florian T. Schäfer (W.P. Carey Ph.D. Prize in Applied Mathematics 2021). Assistant professor at Georgia Tech. ▪ Yifan Chen (W.P. Carey Ph.D. Prize in Applied Mathematics 2023). Counrant Instructor at NYU. o Post Docs ▪ Nawaf Bou Rabee. Associate professor of mathematics at Rutgers. ▪ Ali Lashgari. Truvian Sciences, Inc . ▪ Ufuk Topcu (co-advised). Associate Professor at UT Austin. ▪ Tim Sullivan. Assistant professor at the University of Warwick. ▪ Bamdad Hosseini. Assistant Professor at University of Washington.

(f) Senior research scientists.

• Current JPL researchers on Campus (JROC). o Jouni Susiluoto o Otto M Lamminpaa o Nicolas F Rouquette • Former JPL researchers on Campus (JROC). o Amy Braverman o Peyman Tavallali • Senior Caltech Research Scientists (current and former). o Clint Scovel (retired) o Boumediene Hamzi (former) o Peyman Tavallali (former)

(g) Selected lectures and organized events.

• April 2000: Aussois Congress of Young Probabilists and Statisticians). • November 2000: Technion's Seminar in Probability and Stochastic Processes. • January 2001: "Pole Air" Seminar at ENPC. • February 2001: Orsay Seminar on Probability and Statistics. • April 2001: Israel Mathematics Union Annual Meeting. • April -May 2001: Mini-Course at Technion on Anomalous Diffusion from Perpetual Homogenization. • July 2001: Lyon, First Joint Congress AMS, SMF. • October 2002: Oberwolfach. Stochastic Analysis. • November 2002: Meeting on Particle Methods and Probabilistic Models Applied to the Simulation of the Nuclear Waste Transport Problems. • December 2002: University of Lyon Applied Mathematics Colloquium. • January 2003: ENS Géologie, Nancy: “Modélisation Micro-Macro des Phénomènes Couplés de Transport-Chimie-Déformation en milieux argileux “ • February 2003: Caltech, ACM Colloquium. • March 2003: Congress CIRM. Statistical Mechanics and Probability Theory. • March 2003. University of Neuchâtel Mathematics Seminar. • April 2003: Courant Institute, Probability Seminar. • July 2003: Lisbonne: XIV International Congress on Mathematical Physics. • January 2004: Santiago de Chile, Workshop on Percolation, Particle Systems and Random Media. • April 11, 2004 : USC Applied Math Seminar. • April 24, 2005: Southern California SIAM Symposium. • May 2005: Oberwolfach, Stochastic Analysis and Non-Classical Random Processes. • May 2005: Max Planck Institute: Workshop on Metastability, Aging, and Anomalous Diffusion. Stochastic and Nonlinear Effects in Long Term Dynamics. • July 2005: CIRM. Workshop on Random Homogenization. • March 1, 2006: Caltech, Center for Advanced Computing Research. • March 2006: Banff (Canada), Reaction Diffusion and Free Boundary Problems. • March 31, 2006: USC, Probability Seminar. • July 2006: Los Angeles , 7th World Congress on Computational Mechanics. • January 24, 2007: Chicago University, Mathematics Seminar. • March 19-22, 2007: SIAM Geosciences, Santa Fe. • June 8, 2007: Stanford, Applied Mathematics Seminar. • Oct 2007 : Dynarum Workshop, Caltech. • Nov 2007 : UTRC Seminar. • Nov 2007 : University of Arizona, Mathematics Seminar. • Nov 2007 : Tucson, Dynarum Workshop. • Jan 2008 : Joint Mathematics Meetings in San Diego. • April 2008: University of Maryland, Mathematics Seminar. • April 2008: Structured Integrators Workshop (Stanford). • May 2008: 6th International Conference on Differential Equations and Dynamical Systems. • June 2008: FOCM Meeting, Honk Kong. • July 2008: Stanford UQ Workshop. • August 2008: TST PSAAP, Caltech. • September 15, 2008: University of Chicago, Applied Mathematics Seminar. • October 10-11, 2008: 2nd Workshop on Multiscale and Stochastic Modeling, • Analysis, and Computation. The Michigan Center for Industrial and Applied Mathematics. • October 17, 2008: Purdue University, CCAM Seminar. • October 31, 2008: University of Minnesota, Probability Seminar. • November 6, 2008: Lawrence Livermore National Laboratory, CASC Seminar. • March 2-6, 2009: SIAM CSE Conference (UQ Minisymposium). • March 26-29, 2009: Workshop on Meshless Methods, Generalized Finite Element Methods, and Related Approaches, at the University of Maryland, College Park. • May 4, 2009: Caltech, ACM colloquium. • May 7-8, 2009: Structured Integrators Workshop. • June 2-6, 2009: EPFL: Advances in the Theory of Control, Signals, and Systems, with Physical Modeling. • June 9-12, 2009: Brunel UK, MAFELAP conference. Validation and Robust Prediction in Computational Science. • July 6-11, 2009: Taida Institute for Mathematical Sciences. Taida Mathematics Month, International Conference in Mathematics (Computational and Applied Math), Taiwan. • July 28-30, 2009: PSAAP UQ Workshop (Caltech). • August 10-11 2009: USC Workshop on Stochastic Multiscale Methods. • August 30-Sept 2 2009: SAMSI program on Stochastic Dynamics. • October 7, 2009. UTRC Seminar. • October 9, 2009. Courant Institute of Mathematical Sciences, Applied mathematics seminar. • November 4, 2009. Caltech. E2 Frontiers in Engineering and Applied Science. • Dec 6-11, 2009. Numerical Analysis of Multiscale Computations (BIRS). • March 2, 2010: Caltech CS/IST Lunch Bunch seminar. • April 26-27, 2010. 6th Annual Structured Integrators Workshop (UCSD). • May 24-28, 2010. International Centre for Mathematical Sciences in Edinburgh, • Scotland. SPDE-UQ workshop. • June 28- July 10, 2010: Indian Institute of Mathematical Sciences (Bangalore-India). International Workshop on Multiscale Analysis and Homogenization. (Course on Homogenization with Non-Separated Scales) • July 12 - July 14, 2010: Indian Institute of Mathematical Sciences (Bangalore-India). International Conference on Multiscale Analysis and Homogenization (Plenary) • July 22-24, 2010: Dynamical Systems and Control. Corfu, Greece (Plenary). • September 13-17, 2010. Conference on Highly Oscillatory Problems. Isaac Newton Institute, Cambridge. • September 27-30, 2010. Istitut Henri Poincare (Paris). Hybrid Simulations of • Dynamical Systems and Applications to Molecular Dynamics. (3-Hours Course). • November 10, 2010. UT Austin. Math/ICES Center of Numerical Analysis Seminar. • November 11, 2010. UT Austin. Mathematical Physics Seminar. • January 24 - 28, 2011: Random Media: Homogenization and Beyond. (IPAM Workshop). • Feb 3, 2011. University of Arizona Mathematics Colloquium. • February 28 - March 4, 2011. SIAM CSE11 (Reno, NV). Mini-Symposium on "Numerical Methods for Stochastic Computation and Uncertainty Quantification." • March 10-12, 2011. Third "Frontier Probability Days" (FPD11). University of Utah. • March 14, 2011. Applied Math and Analysis Seminar, Duke University. • March 21-24, 2011. SIAM Geosciences Meeting. Multiscale Aspects of Wave Propagation. Long Beach, CA, USA. • March 27-April 1 2011. Stochastic Multiscale Methods (BIRS Workshop in Banff). • April 15, 2011. USC probability seminar. • April 18, 2011. Penn State University. • June 13-15, 2011. Santa Fe, New Mexico. Uncertainty Quantification and Multiscale Materials Modeling. • July 18-22, 2011. ICIAM 2011 (Vancouver, BC). Minisymposium on "Mathematical and Numerical Aspects of Uncertainty Quantification." • July 18-22, 2011. ICIAM 2011 (Vancouver, BC). Minisymposium on “Numerical Solution of Stochastic PDEs.” • July 25-28, 2011. WAVES 2011 (Vancouver, BC). Minisymposium on Multiscale methods for wave propagation. • August 1-5, 2011. USA/South America symposium on Uncertainty Quantification. Rio de Janeiro, Brazil. • October 19, 2011. USC AME Seminar. • October 22-23, 2011. 2011 Fall AMS Western Section Meeting, "Inverse Problems and Homogenization", Salt Lake City, UT • November 5, 2011. University of Illinois at Urbana-Champaign. Aerospace Engineering Seminar series. • November 10, 2011. SAMSI. High Dimensional Approximation for Uncertainty Quantification. • December 9, 2011. LATP, Marseille. Probability and Statistics seminar. • December 12-16, 2011. Workshop on Multiscale Systems: theory and applications. Warwick University. • March 16, 2012. Center for Control, Dynamical systems and Computation (CCDC) at UCSB. • March 19, 2012, ICME Colloquium, Stanford. • April 3-5, 2012. SIAM UQ12 conference. Raleigh. • July 30-Aug 2, 2012. AFOSR. Arlington. • October 9-11, 2012. ICERM, Brown. Workshop on Uncertainty Quantification. • October 24, 2012. LLNL. • December 3-7, 2012. IPAM. Workshop on Computational Methods for Multiscale Modeling of Materials Defects. • March 17-23, 2013. Oberwolfach. Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization, (organizer). • April 28-May 1, 2013. UT Austin Institute for Computational Engineering and Sciences. Workshop on Multiscale Modeling. • May 15, 2013. Stanford applied math seminar. • June 9-12, 2013. SIAM '13 Conference on Math Aspects of Materials Science (Philadelphia). Aspects of Homogenization: Analysis and Applications. • September 16-20, 2013. Heraklion, Greece. International Conference on Applied Mathematics (Plenary). • March 31-April 3, 2014: SIAM UQ 14, Savannah, Georgia, USA, mini-symposium on "Numerical methods for uncertainty quantification of coupled problems". • May 28-31, 2014. Shanghai Jiao Tong University. Workshop on “Multiscale Problems from Physics, Biology and Materials Science” • June 22 - June 28, 2014. Oberwolfach. Computational Multiscale Methods. • June 30 - July 1, 2014. Computations in infinite dimensions: challenges in a continuous world. Kavli Royal Society International Centre at Chicheley Hall. • September 1-4, 2014. Burg Schnellenberg, Germany. IUTAM symposium on “Innovative numerical approaches for materials and structures in multi-field and multi-scale problems.” • September 10, 2014. Berkeley Applied Math Seminar. • March 14-18, 2015. SIAM Conference on Computational Science and Engineering (CSE15). Plenary. • July 1, 2015. SIAM Conference on Mathematical and Computational Issues in the Geosciences. • July 22-24, 2015. Cambridge, UK. IEEE International Conference on Computer • Science and Education 2015 (IEEE ICCSE). Keynote. • August 19-21, 2015. USC. Fourth QUEST UQ Summer School (tutorial). • November 6-8, 2015. University of Texas at Dallas. Texas Analysis and Mathematical Physics Symposium 2015. • January 19 - 22, 2016. IPAM. Uncertainty Quantification for Multiscale Stochastic Systems and Applications. • April 5-8, 2016. EPFL. SIAM UQ 2016. Mini-tutorial. • May 30 – June 2, 2016. City University of Hong Kong. International Conference on Applied Mathematics. • June 18-20, 2016. 4th CAM-ICCM Workshop, Multiscale and Large-scale Scientific Computing, Chinese University of Hong Kong (CUHK). • August 1-5, 2016. RWTH Aachen University (Germany). XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Plenary. • January 4, 2017. AIAA SciTech. DARPA Efficient Quantification of Uncertainty in Physical Systems. • February 27-March 3, 2017. SIAM CSE 2017, EQUiPS minisymposia. • April 3-7, 2017, IPAM workshop "Multiphysics, Multiscale, and Coupled Problems in Subsurface Physics". • April 10-14, 2017, “Multiscale Problems: Algorithms, Numerical Analysis and Computation” Hausdorff Trimester Program. • June 5-10, 2017. ICERM. Probabilistic Scientific Computing: Statistical inference approaches to numerical analysis and algorithm design (co-organizer). • June 19-23, 2017. Dynamics, aging and universality in complex systems (in honor of Gérard Ben Arous). • September 12-15, 2017. Complex High-Dimensional Energy Landscapes Tutorials. • October 30, 2017. Computing@PNNL seminar series. • Januray 24, 2018. Stanford applied math seminar. • March 26, 2018: University of Notre Dame. Center for Informatics and Computational Science Colloquium. • April 5, 2018: John Hopkins University, seminar. • April 6, 2018: Applied Math Colloquium, UMBC. • April 10, 2018: Jussieu (Paris VI). Seminaire du Laboratoire de Probabilités, Statistique et Modélisation. • April 11-13, 2018. The Alan Turing Institute, London. SAMSI Workshop on Probabilistic Numerics. • April 20, 2018: Institut de Mathematiques de Marseille. Séminaire Probabilités et Statistique. • April 23-27, 2018: BIRS, Numerical Analysis and Approximation Theory meets Data Science. • June 4-7, 2018. The Fields Institute. Conference on Multiscale Problems in Materials and Biology (co-organizer). • July 10, 2018. SIAM AN 2018, MS100 Machine Learning for Scientific Computing. • July 24, 2018. WCCM 2018, MS104. • November 5-7, 2018, RICAM (Linz), Multivariate Algorithms and Information-Based Complexity. • March 11-15, 2019. Oberwolfach, Uncertainty Quantification. • March 12, 2019. Max-Planck, Leipzig. • March 27-29, 2019. Center of Mathematical Sciences and Application at Harvard University. Workshop on machine learning for Multiscale Model reduction. • June 9-15, 2019. Oberwolfach, beyond numerical homogenization (one week course). • June 24-26, 2019. Crete, Greece. UNCECOMP 2019: Machine learning approaches to UQ. • July 22, 2019 SciCADE 2019, Innsbruck Austria. plenary Lecturer. • July 29-Aug 2, 2019. Oberwolfach, Computational Multiscale Methods. • May 18-22, 2020. IPAM. Stochastic Analysis Related to Hamilton-Jacobi PDEs. • 27-31 July 2020. Institut Mittag-Leffler. New trends in numerical multiscale methods and beyond. • September 1st, 2020. JPL Colloquium. • September 21 - October 2, 2020. The Fields Institute. Second Symposium on Machine Learning and Dynamical Systems (pre-recorded + plenary live). • September 30 - October 2, 2020. CECAM workshop on Multiscale simulations of soft matter: New method developments and mathematical foundations. • November 2, 2020. One World Seminar in Numerical Analysis. • November 16, 2020, UC Irvine, applied math seminar. • January 27-30: IEEE CCWC 2021, keynote. • February 22, 2021. Keller colloquium, Caltech. • March 2, 2021. Sayas Numerics Seminar, UMD. • March 3, 2021: Freie Universität Berlin. Minisymposium on Kernel Methods for Multiscale Problems. • March 18, 2021: Fisk Distinguished Speaker Series, university of Wyoming. • March 25, 2021: Applied Mathematics & Statistics seminar at Johns Hopkins University. • July 12-16, 2021. Institut Mittag-Leffler.New trends in numerical multiscale methods and beyond. • September 21, 2021. University of Naples Federico II • October 8, 2021. FAU Erlangen-Nürnberg • October 24-29, 2021. Probabilistic Numerical Methods - From Theory to Implementation. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Germany. • March 3, 2022. e-seminar for Scientific Machine Learning. • March 14-18, 2022. SIAM conference on Analysis of Partial Differential Equations (PD22), Berlin, Germany. Minisymposium on Disordered media and Homogenization. • March 18, 2022. University of Pittsburgh. e-seminar for Scientific Machine Learning. • March 18, 2022. University of Wyoming. Fisk Distinguished Speaker series. • April 4-8, 2022. Adaptivity, High Dimensionality and Randomness. The Erwin Schrödinger Institute (ESI) in Vienna. • April 11, 2022. PhILMs Webinar Series. • April 12-15, 2022. SIAM Conference on Uncertainty Quantification. Minisymposium on PDE-constrained optimization under uncertainty. Atlanta, USA. • April 20, 2022. One world seminar on the mathematics of machine learning. • April 26, 2022. Applied Math seminar at UMass Amherst. • April 27, 2022. Applied math seminar at UC Berkeley. • April 29, 2022. Applied Math Seminar, Florida International University (FIU). • May 6, 2022. UCSD MAE seminar. • May 16-20, 2022. PDE-constrained Bayesian inverse problems: Interplay of spatial statistical models with Machine Learning in PDE discretizations. The Erwin Schrödinger Institute (ESI). • July 11-15, 2022. SIAM Annual Meeting22. Pittsburgh, Pennsylvania. • Aug 29-Sep 2, 2022. IMSI (Chicago). Expressing and Exploiting Structure in Modeling, Theory, and Computation with Gaussian Processes • Sep 26-30, 2022. SIAM MDS22 (San Diego). Data-Driven Methods in Scientific Computing. • Dec 19-21, 2022. Caltech. International Conference on New Trends of Computational and Data Sciences. • Feb 9, 2023. AI for science workshop at Caltech. • Feb 20-20, 2023. Differential Equations for Data Science 2023 (DEDS2023). • Apr 6-7, 2023. data-driven middling of physical systems at USC. • May 19-20, 2023. MaSAG conference, Rome, Italy. • May 22-25, 2023. Inaugural CAMDA conference to be held in College Station, TX. • May 30 - Jun 1, 2023. ECCOMAS-IACM thematic conference “Math 2 Product (M2P): Emerging Technologies in Computational Science for Industry, Sustainability" and Innovation, Sicily. • June 5-9, 2023. ICERM's workshop “Mathematical and Scientific Machine Learning" • June 12-17. Data Science and Machine Learning Summer School (Emilia Romagna, Italy) • June 3-18, 2023. Isaac Newton Institute for Mathematical Sciences in Cambridge. Mathematical and Statistical Foundation of Future Data-Driven Engineering. • July 23-27, 2023. Albuquerque, New Mexico. 17th US National Congress on Computational Mechanics (USNCCM). • Aug 20-25, 2023. Tokyo. ICIAM 2023. Machine learning in infinite dimensions. • Nov 2nd, 2023, University of Washington. Boeing Applied Mathematics Colloquium series. • Feb 27 – Mar 1st, 2024. SIAM UQ24. Plenary.

(h) Teaching.

• April -May 2001: Mini-Course at Technion on Anomalous Diffusion from Perpetual Homogenization. • February-April 2002: CMI, Université de Provence: Homogénéisation Perpétuelle et Diffusions Anormales. • August 2004: Mahdia (Tunisia), Course on Homogenization (summer school). • 2004-2005: Caltech, Partial Differential Equations (ACM 201 a and b). • 2005-2006: Caltech, Markov Chains (ACM 216). • 2005-2006: Caltech, Stochastic Differential Equations. (ACM 217) • 2006-2007: Caltech, Introduction to Probability Theory and Applications (ACM 116). • 2006-2007: Caltech, Large Deviations and Concentration of Measure (ACM 256). • 2007-2008: Caltech, Introduction to probability theory and applications (ACM 116). • 2007-2008: Caltech, Markov Chains (ACM 216). • 2008-2009: Caltech, Introduction to Probability Theory and Applications (ACM/EE 116). • 2008-2009: Caltech, Markov Chains (ACM 216). • 2009-2010: Caltech, Introduction to Probability Theory and Applications (ACM/EE 116). • 2009-2010: Caltech, Introduction to Optimization (ACM 113). • June 28- July 10, 2010, Indian Institute of Mathematical Sciences (Bangalore, India): Course on Homogenization with Non-Separated Scales at the International Workshop on Multiscale Analysis and Homogenization. • September 27-30, 2010: Institut Henri Poincaré (Paris): Simulation of Hybrid Dynamical Systems and Applications to Molecular Dynamics (3-hour lecture). • 2010-2011: Caltech, Introduction to Probability Theory and Applications (ACM/EE 116, 100 enrolled students) • 2010-2011: Caltech, Advanced Topics in Optimization (ACM 213). • 2011-2012: Caltech, Introductory Methods of Applied Mathematics (ACM 95/100b: Ordinary Differential Equations). • 2012-2013: Caltech, Markov Chains (ACM 216). • 2012-2013: Caltech, Stochastic Differential Equations and martingales (ACM 217). • 2013-2014: Caltech, Introduction to Probability Theory and Applications (ACM/EE 116). • 2013-2014: Caltech, Markov Chains (ACM 216). • 2014-2015: Caltech, Introduction to Probability Theory and Applications (ACM/EE 116). • 2014-2015: Caltech, Markov Chains (ACM 216). • 2015-2016: Caltech, Introduction to Probability Theory and Applications (CMS/ACM 116). • 2015-2016: Caltech, Markov Chains (ACM 216). • 2016-2017: Caltech, Introduction to Probability and Random Processes (CMS/ACM/EE 117). • 2016-2017: Caltech, Markov Chains (ACM 216). • 2017-2018: Caltech, Introduction to Probability and Random Processes (CMS/ACM/EE 117). • 2017-2018: Caltech, Markov Chains (ACM 216). • 2018-2019: Caltech, Introduction to Probability and Random Processes (CMS/ACM/EE 117). • 2018-2019: Caltech, Markov Chains (ACM 216). • June 2019. Oberwolfach seminar (Beyond numerical homogenization). • 2019-2020. Caltech, Stochastic processes and regression (ACM 118). • 2019-2020: Caltech, Markov Chains (ACM 216). • 2020-2021: Caltech, Stochastic processes and regression (ACM 118). • 2020-2021: Caltech, Markov Chains (ACM 216). • 2021-2022: Caltech, Stochastic processes and regression (ACM 118). • 2021-2022: Caltech, Markov Chains (ACM 216). • 2022-2023: Caltech, Stochastic processes and regression (ACM 118). • 2022-2023: Caltech, Markov Chains (ACM 216). • 2023-2024: Caltech, Stochastic processes and regression (ACM 118). • 2023-2024: Caltech, Markov Chains (ACM 216).