Institut für Mathematik

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Vita

  • PERSONAL

  • Born in Zagreb, Croatia 1983. Croatian Citizen.

  • EDUCATION

  • Massachusetts Institute of Technology, Ph.D. in Mathematics, June 2011.
  • Advisor: Gigliola Staffilani.
  • Thesis Title: Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger equations.
  • University of California Berkeley, B.A. in Mathematics with Highest Honors, May 2006.
  • University of Zagreb, Mathematics Department, Fall 2002–Spring 2003.

  • EMPLOYMENT

  • Universität Zürich, Postdoctoral researcher, starting September 2016.
  • Advisor: Benjamin Schlein.
  • Eidgenössische Technische Hochschule Zürich, Postdoctoral researcher, September 2014–August 2016. Advisor: Antti Knowles.
  • Mathematical Sciences Research Institute, Berkeley, CA, USA, research member September–October 2015.
  • University of Pennsylvania, Simons Postdoctoral Fellow, 2011-2014.
  • Advisor: Philip Gressman and Robert Strain.
  • Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, visitor, January–February 2012. Host: Felix Otto.

  • PUBLICATIONS

  • Thesis

  • Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations, Ph.D. Thesis, MIT (2011). Advisor: Gigliola Staffilani.
  • Vedran Sohinger

  • Papers

  • 1) Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger equations on S1, Differential and Integral equations, 34 (2011), no. 7-8, 653–718.
  • 2) Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger equations on R, Indiana University Mathematics Journal, 60 (2011), no. 5, 1487–1516.
  • 3) Bounds on the growth of high Sobolev norms of solutions to 2D Hartree equations, Discrete and Continuous Dynamical Systems A, 32 (2012), no. 10, 3733–3771.
  • 4) The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space (with Robert Strain), Advances in Mathematics, 261 (2014), no. 20, 274–332.
  • 5) On the uniqueness of solutions to the 3D periodic Gross-Pitaevskii hierarchy (with Philip Gressman and Gigliola Staffilani), Journal of Functional Analysis, 266 (2014), no. 7, 4705–4764.
  • 6) Randomization and the Gross-Pitaevskii hierarchy (with Gigliola Staffilani), Archive for Rational Mechanics and Analysis, 218 (2015), no. 1, 417–485.
  • 7) Local existence of solutions to Randomized Gross-Pitaevskii hierarchies, Transactions of the American Math- ematical Society, 368 (2016), no. 3, 1759–1835.
  • 8) A rigorous derivation of the defocusing nonlinear Schrödinger equation on T3 from the dynamics of many-body quantum systems, Annales d l’Institut Henri Poincaré C, Analyse Non-Linéaire, 32 (2015), no. 6, 1337– 1365.
  • 9) The Gross-Pitaevskii hierarchy on general rectangular tori (with Sebastian Herr), Archive for Rational Mechanics and Analysis, 220 (2016), no. 3, 1119–1158.
  • 10) Gibbs measures of nonlinear Schrödinger equations as limits of quantum many-body states in dimensions d ≤ 3 (with Jüerg Fröhlich, Antti Knowles, and Benjamin Schlein), preprint (2016), 101 pages. http://arxiv.org/abs/1605.07095.

  • Research Reports

  • 1) On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy (based on joint work with Gigliola Staffilani), Oberwolfach Reports, Vol. 9 (2012), no. 2, 1622–1644.
  • 2) The Gross-Pitaevskii hierarchy on the three-dimensional torus (based on joint work with Philip Gressman
  • and Gigliola Staffilani), Oberwolfach Reports, Vol. 9 (2013), no.3, 2360–2365.

  • Summer School Reports

  • Evolution Equations at the Swiss Federal Institute of Technology, Zürich, Switzerland
  • (summer school report written jointly with Dean Baskin and Jacques Smulevici), in CMI Annual Report 2008,
  • http://www.claymath.org/library.

  • AWARDS

  • Good Teaching Award, UPenn, Spring 2013. Good Teaching Award, UPenn, Fall 2011.
  • Vedran Sohinger 3
  • Simons Postdoctoral Fellowship, UPenn, Fall 2011-Spring 2014.
  • Charles and Jennifer Johnson Prize for a paper accepted for publication, MIT, Spring 2011.
  • MIT Presidential Fellowship, Fall 2006.
  • Valedictorian, UC Berkeley Mathematics Department, May 2006.
  • B.A. with Highest Honors, UC Berkeley, May 2006.
  • Phi Beta Kappa (Liberal Arts and Sciences), May 2006 to present.
  • Dorothea Klumpke Roberts Prize for Academic Excellence, UC Berkeley, May 2006.
  • Dean’s Honor List, UC Berkeley.
  • International House Scholarship, UC Berkeley.
  • William Lowell Putnam Mathematical Competition 2005, Honorable Mention, Individual Rank 27th.
  • International Mathematical Olympiad 2001 and 2002, Bronze Medal.

  • PRESENTATIONS

  • Invited Talks

  • University of Warwick, job interview, January 23, 2017.
  • University of Birmingham, job interview, December 8, 2016.
  • The 3rd SwissMAP General Meeting, Engelberg, Switzerland, September 13, 2016.
  • Workshop “Singularity formation and long-time behavior in dispersive PDEs", University of Bonn, March 16, 2016.
  • University of Bielefeld, Oberseminar Analysis, October 30, 2015.
  • University of California Berkeley, Analysis Seminar, October 5, 2015.
  • University of Texas Austin, Analysis Seminar, October 2, 2015.
  • MSRI five minute introduction talk, MSRI, Berkeley, California, September 2015.
  • ETH Analysis Seminar, December 9, 2014.
  • Radcliffe Institute, Workshop "Randomness and Long-Time Dynamics in Nonlinear Evolution Differential Equations", November 2, 2014.
  • University of Bielefeld, Oberseminar Analysis, October 20, 2014.
  • Hausdorff Institute, Workshop on Real Analysis, July 18, 2014.
  • University of Bielefeld, Bielefeld Stochastics Afternoon, April 16, 2014.
  • AMS Spring 2014 Sectional Meeting of the American Mathematical Society, Special Session on
  • Stochastics and PDEs, Albuquerque, NM, April 6, 2014.
  • University of California Los Angeles, Analysis and PDE Seminar, February 21, 2014.
  • University of Rochester, Colloquium, February 11, 2014.
  • Eidgenössische Technische Hochschule Zürich, Postdoctoral Interview, January 23, 2014.
  • Joint Mathematics Meetings, AMS Special Session on Dispersive and Geometric Partial Differential Equations, Baltimore, MD, January 18, 2014.
  • University of Miami, Colloquium, January 16, 2014.
  • SIAM Conference on Analysis of Partial Differential Equations, section on Dynamics of Nonlinear
  • Dispersive Wave Equations, Lake Buena Vista, FL, December 7, 2013.
  • University of Pennsylvania, Analysis Seminar, November 12, 2013.
  • Oberwolfach workshop on Nonlinear Waves and Dispersive Equations, August 15, 2013.
  • University of Zagreb, Probability Seminar, July 9, 2013.
  • Princeton University, Analysis Seminar, February 25, 2013.
  • University of Zagreb, Probability Seminar, December 18, 2012.
  • New York University, Analysis Seminar, November 29, 2012.
  • Massachusetts Institute of Technology, PDE/Analysis Seminar, October 23, 2012.
  • University of Pennsylvania, Analysis Seminar, October 2, 2012.
  • AMS 2012 Fall Eastern Sectional Meeting, Special Session on Microlocal Analysis and Nonlinear Evolution Equations, Rochester, NY, September 22, 2012.
  • University of Texas Austin, 2012/13 Thematic Program on nonlinear Schrödinger equations and Bose gases from a multidisciplinar, integrative perspective, September 17 and September 19, 2012.
  • Conference in honor of Michael Taylor’s 65th birthday, July 19, 2012. Oberwolfach workshop on Nonlinear Evolution Equations, May 17, 2012. Johns Hopkins Analysis Seminar, April 30, 2012.
  • Simons Postdoctoral Fellows Meeting, Stony Brook, April 11, 2012.
  • Drexel University, Applied Mathematics and PDE Seminar, March 20, 2012.
  • University of Pennsylvania, Analysis Seminar, March 13, 2012.
  • SIAM Conference on Analysis of Partial Differential Equations, section Recent Progress on Dispersive Partial Differential Equations, November 14, 2011.
  • AMS 2011 Fall Western Sectional Meeting, Special Session on Harmonic Analysis and Dispersive Partial Differential Equations, Salt Lake City, October 22, 2011.
  • Princeton University, Analysis Seminar, October 3, 2011.
  • SISSA trimester on Nonlinear Hyperbolic PDEs, Dispersive and Transport equations, Trieste, Italy, section on Dispersive equations, July 9, 2011.
  • University of Pennsylvania, Analysis Seminar, February 8, 2011.
  • Max Planck Institute for Mathematics in the Sciences, Leipzig, January 14, 2011.
  • Hausdorff Center for Mathematics, University of Bonn, January 11, 2011.
  • University of California Los Angeles, Analysis and PDE Seminar, October 22, 2010.
  • University of North Carolina Chapel Hill, Analysis/PDE Seminar, September 29, 2010. University of
  • Zagreb, Probability Seminar, June 15, 2010.
  • SIAM conference on Emerging Topics in Dynamical Systems and PDEs, Barcelona, June 3, 2010. New York University Analysis Seminar, May 7, 2010.
  • Brown Department of Applied Mathematics PDE Seminar, March 19, 2010.

  • Poster presentations

  • Workshop “Probability and asymptotic analysis in strongly coupled systems”, University of Bonn, January 12, 2015.

  • Expository Talks

  • UPenn Friday Pizza Seminar, "The nonlinear Schrödinger equation", Spring 2014.
  • MIT Pure Math Graduate Student Seminar, "Low regularity solutions of nonlinear dispersive equations", Spring 2010 .
  • MIT Pure Math Graduate Student Seminar, "Counting the number of lattice points in Euclidean balls", Fall 2008.
  • MIT Applied Math Student Seminar, "Solitary wave solutions to the Nonlinear Schrödinger equation", Spring 2008.

  • Undergraduate research

  • "Orbits under wreath products"
  • University of California Berkeley, Subfactor seminar, September 2005.

  • CONFERENCES AND WORKSHOPS

  • The 3rd SwissMAP General Meeting, Engelberg, Switzerland, September 11–13, 2016.
  • Oberwolfach workshop on Nonlinear Evolution Problems, Oberwolfach, Germany, May 29–June 4, 2016.
  • Singularity formation and long-time behavior in dispersive PDEs, University of Bonn, March 14–18, 2016. Probability and asymptotic analysis in strongly coupled systems, University of Bonn, January 11–15, 2016.
  • New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems, Semester program at the MSRI, Berkeley, CA, USA, September-October 2015.
  • Geometric non-linear analysis: Conference on the occasion of Michael Struwe’s 60th birthday, ETH Zürich, June 8-12, 2015.
  • Symposium: 50 years of Mathematics at the FIM, ETH Zürich, June 3-8. 2015.
  • Frontiers in Analysis and Probability, Strasbourg / Zürich meeting, University of Strasbourg, France, February 19-21, 2015.
  • Workshop on Randomness and Long-Time Dynamics in Nonlinear Evolution Differential Equations, Radcliffe Institute, Cambridge, MA, November 1-3, 2014.
  • Harmonic Analysis & Partial Differential Equations: Recent & Developments and Future Directions: A conference in honor of C. E, Kenig, University of Chicago, September 19-21, 2014.
  • Workshop on Real Analysis, part of Trimester on Harmonic Analysis and Partial Differential Equations at the Hausdorff Institute in Bonn, Germany, July 14-18, 2014.
  • AMS 2014 Spring Western Sectional Meeting, University of New Mexico, Albuquerque, NM, April 5-6, 2014.
  • Joint Mathematics Meetings, Baltimore, MD, January 15-18, 2014.
  • SIAM Conference on Analysis of Partial Differential Equations, Lake Buena Vista, FL, December 7-10, 2013.
  • Oberwolfach workshop on Nonlinear Waves and Dispersive Equations, Oberwolfach, Germany, August 11-17, 2013.
  • The Global Behavior of Solutions to Critical Nonlinear Wave Equations: A conference in honor of Carlos Kenig, Kansas State University, Manhattan, KS, June 17-21, 2013.
  • The Sixteenth Rivière-Fabes Symposium on Analysis and PDE, University of Minnesota, April 19-21, 2013. AMS 2012 Fall Eastern Sectional Meeting, Rochester Institute of Technology, Rochester, NY, September
  • 22-23, 2012.
  • Partial Differential Equations: Analytic and Geometric Aspects, in honor of Michael Taylor’s 65 Birthday, University of North Carolina, Chapel Hill, July 16-20, 2012.
  • Oberwolfach workshop on Nonlinear Evolution Equations, Oberwolfach, Germany, May 13-19, 2012.
  • Evolution Equations: A Workshop in Honor of Terence Tao, Northwestern University, May 4-6, 2012.
  • Simons Foundation Postdoctoral Fellows Meeting, Simons Center for Geometry and Physics, Stony Brook, NY, April 10-13, 2012.
  • SIAM Conference on Analysis of Partial Differential Equations, San Diego, CA, November 14-18, 2011.
  • ICERM conference on Boltzmann models in Kinetic theory, ICERM, Brown, Providence, RI, November 7-11, 2011.
  • AMS 2011 Fall Western Sectional Meeting, Salt Lake City, October 22-23, 2011.
  • SISSA trimester on Nonlinear Hyperbolic PDEs, Dispersive and Transport equations, Trieste, Italy, section on Dispersive equations, July 7-14, 2011.
  • The Fourteenth Rivière-Fabes Symposium on Analysis and PDE, University of Minnesota, April 15-17, 2011. SIAM Conference: Emerging Topics in Dynamical Systems and PDEs, Barcelona, Spain, May 31-June 4,
  • 2010.
  • The Thirteenth Rivière-Fabes Symposium on Analysis and PDE, University of Minnesota, April 23-25, 2010.
  • Workshop on Nonlinear dispersive and geometric evolution equations: Singularities and Asymptotics,
  • Pacific Institute for the Mathematical Sciences, Vancouver, Canada, August 17-28, 2010
  • Conference Ondes Non-linéaires et Dispersion, Institut Henri Poincaré, Paris, France, June 22-26, 2009.
  • The power of Analysis, Birthday conference for Charles Fefferman, Princeton May 4-8, 2009.
  • Clay Mathematics Institute Summer School on Evolution Equations, ETH, Zurich, Switzerland June 23-July 18, 2008.
  • The Eighth International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Spain, June 16-20, 2008.
  • Nonlinear Waves, Conference in honor of Walter Strauss, Brown University, May 8 - 11, 2008.
  • MIT Women in Mathematics: A Celebration, Massachusetts Institute of Technology, April 12-13, 2008.
  • Teaching

  • COURSES

  • At UZH

  • Introduction to Nonlinear Dispersive Equations (Master's level), Fall 2016, instructor.

  • At ETH

  • Introduction to Harmonic Analysis (Master’s level), Spring 2016, instructor.
  • Introduction to Harmonic Analysis (Master’s level), Spring 2015, instructor.

  • At UPenn

  • Math 240: Calculus III, Fall 2013, instructor.
  • Math 425: Partial Differential Equations (Undergraduate Level), Spring 2013, instructor. Math 644:
  • Partial Differential Equations (Graduate Level), Fall 2011, instructor.

  • At MIT

  • 18.152: Introduction to PDE, Fall 2010, grader.
  • 18.155: Differential Analysis, Fall 2010, grader.
  • 18.03: Ordinary Differential Equations, Spring 2010, recitation instructor.
  • 18.02: Multivariable Calculus, Fall 2009, recitation instructor.
  • 18.06: Linear Algebra, Fall 2008, recitation instructor.
  • 18.075: Advanced Calculus for Engineering, Spring 2008, grader.
  • 18.101: Analysis II, Fall 2007, grader.
  • 18.704: Undergraduate Seminar in Algebra and Number Theory, Spring 2007, grader.

  • Seminar Courses

  • Undergraduate seminar for Putnam Exam preparation, UPenn, Fall 2012.
  • Course on Nonlinear Dispersive Equations, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, January-February, 2012.

  • Reading Groups

  • Organizer of student reading group on the use of U and V function spaces in nonlinear dispersive
  • equations, MIT, Spring 2011.
  • Organizer of student reading group on KAM Theory, MIT, Fall 2009.

  • High school teaching

  • Olympiad training for high school students in Croatia, 2003–2010.

  • COMMITTEE WORK

  • Chair of the Prize Committee at UPenn in the academic year 2012–2013.
  • Member of the Prize Committee at UPenn in the academic year 2013–2014.
  • Member of Ph. D. Thesis Defense Committee for Taisong Jing (UPenn), 2014.

  • JOURNALS REFEREED

  • Dynamics of Partial Differential Equations.
  • Probability Theory and Related Fields.
  • International Mathematics Research Notices.
  • Annales scientifiques de l’École normale supérieure. Analysis and PDE.
  • SIAM Journal on Mathematical Analysis.
  • Annales de l’Institut Henri Poincaré (C), Analyse Non Linéaire.
  • Discrete and Continuous Dynamical Systems, Series A.
  • Journal of Mathematical Analysis and its Applications.
  • Journal of Functional Analysis.
  • Proceedings of the American Mathematical Society. Physica D.
  • Communications in Pure and Applied Analysis.

  • MEMBERSHIP

  • American Mathematical Society.
  • Croatian Mathematical Society.
  • Phi Beta Kappa.

  • LANGUAGE SKILLS

  • Croatian: native speaker.
  • English: fluent.
  • German: B1.
  • French: basic knowledge.

Forschung

  • In my Ph.D. thesis I proved upper bounds on the growth of high Sobolev norms of solutions of nonlinear Schrödinger equations using almost conserved quantities. In my subsequent work I considered the Gross-Pitaevskii hierarchy on a periodic domain with the aim of studying uniqueness of solutions to this system. In addition, I have studied the non cut-off Boltzmann equation. More recently, I have worked on the derivation of Gibbs measures of nonlinear Schrödinger equations from many-body dynamics.
  • Thesis:
  • Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations, Ph.D. Thesis, MIT (2011). Advisor: Gigliola Staffilani.
  • Papers:
  • 1) Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger equations on S1, Differential and Integral equations, 34 (2011), no. 7-8, 653–718.
  • 2) Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger equations on R, Indiana University Mathematics Journal, 60 (2011), no. 5, 1487–1516.
  • 3) Bounds on the growth of high Sobolev norms of solutions to 2D Hartree equations, Discrete and Continuous Dynamical Systems A, 32 (2012), no. 10, 3733–3771.
  • 4) The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space (with Robert Strain), Advances in Mathematics, 261 (2014), no. 20, 274–332.
  • 5) On the uniqueness of solutions to the 3D periodic Gross-Pitaevskii hierarchy (with Philip Gressman and Gigliola Staffilani), Journal of Functional Analysis, 266 (2014), no. 7, 4705–4764.
  • 6) Randomization and the Gross-Pitaevskii hierarchy (with Gigliola Staffilani), Archive for Rational Mechanics and Analysis, 218 (2015), no. 1, 417–485.
  • 7) Local existence of solutions to Randomized Gross-Pitaevskii hierarchies, Transactions of the American Math- ematical Society, 368 (2016), no. 3, 1759–1835.
  • 8) A rigorous derivation of the defocusing nonlinear Schrödinger equation on T3 from the dynamics of many-body quantum systems, Annales d l’Institut Henri Poincaré C, Analyse Non-Linéaire, 32 (2015), no. 6, 1337– 1365.
  • 9) The Gross-Pitaevskii hierarchy on general rectangular tori (with Sebastian Herr), Archive for Rational Mechanics and Analysis, 220 (2016), no. 3, 1119–1158.
  • 10) Gibbs measures of nonlinear Schrödinger equations as limits of quantum many-body states in dimensions d ≤ 3 (with Jüerg Fröhlich, Antti Knowles, and Benjamin Schlein), preprint (2016), 101 pages. http://arxiv.org/abs/1605.07095.