About

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I am a postdoctoral research assistant in the field of applied mathematics in the research group of Prof. Ansgar Jüngel at the Vienna University of Technology.  My research is on partial differential equations and their applications in biology, physics, and chemistry. My focus is on the analysis, modeling and derivation of cross-diffusion in biological systems and multi-species kinetic models, moreover, I am interested in bridging PDE-techniques with probabilistic methods.

Research interests:

  • Entropy methods for diffusive systems
  • Cross diffusion in biological systems
  • Kinetic and diffusive multi-species systems
  • Hypocoercivity in kinetic equations
  • Interactions between kinetic and diffusive PDEs and probability
  • Uncertainty quantification

  Publications and Preprints

  • [12] E. S. Daus, J.-P. Milišić, N. Zamponi: Global existence for a two-phase flow model with cross diffusion. Submitted for publication, 2019. [arXiv]
  • [11] E. S. Daus, M. Gualdani, N. Zamponi: Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation. Submitted for publication, 2018. [arXiv]
  • [10] E. S. Daus, S. Jin, L. Liu: Spectral convergence of the stochastic Galerkin approximation to the Boltzmann equation with multiple scales and large random perturbation in the collision kernel. Submitted for publication, 2018. [arXiv]
  • [9] L. Chen, E. S. Daus, A. Jüngel: Rigorous mean-field limit and cross diffusion. Submitted for publication, 2018, [arXiv]
  • [8] E. S. Daus, J.-P. Milišić, N. Zamponi: Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth. Submitted for publication, 2018. [arXiv]
  • [7] E. S. Daus, A. Jüngel, B. Q. Tang: Exponential time decay of solutions to reaction-cross-diffusion systems of Maxwell-Stefan type. Submitted for publication, 2018. [arXiv]
  • [6] E. S. Daus, L. Desvillettes, H. Dietert: About the entropic structure of detailed balanced multi-species cross-diffusion equations.  To appear in J. Differential Equations 266 (2019), 3861-3882. [DOI] [arXiv]
  • [5] E. S. Daus, L. Desvillettes, A. Jüngel: Cross diffusion systems and fast reaction limits. To appear in Bull. Math. Sci, 2019. [arXiv]
  • [4] E. S. Daus, B. Q. Tang: Trend to equilibrium of renormalized solutions to reaction-cross-diffusion systems. To appear in Appl. Math. Lett. 88 (2019), 81-89. [DOI] [arXiv]
  • [3] X. Chen, E. S. Daus, A. Jüngel: Global existence analysis of cross-diffusion population systems for multiple species. Arch. Rat. Mech. Anal. 227 (2018), no. 2, 715-747. [DOI] [arXiv]
  • [2] M. Briant, E. S. Daus: The Boltzmann equation for a multi-species mixture close to global equilibrium. Arch. Rat. Mech. Anal. 222 (2016), no. 3, 1367-1443.  [DOI] [arXiv]
  • [1]  E. S. Daus, A. Jüngel, C. Mouhot, N. Zamponi: Hypocoercivity for a linearized multi-species Boltzmann system. SIAM J. Math. Anal. 48 (2016), no. 1, 538-568.  [DOI] [arXiv]

Grants and Awards

  • 2019 Junior Trimester Program Kinetic Theory 2019, HIM, Bonn, Germany, Group leader ‘Stochastic-PDE Bridge’.
  • 2018 Oberwolfach Leibniz Travel Grant to Oberwolfach (Seminar), Germany.
  • 2018-2020 Bilateral Reserach Project HR 04/2018 with Croatia, ÖAD- Austrian agency for international cooperation in education and research, Principal Investigator.
  • 2017 Christiana Hörbiger Award, Austria.
  • 2017 Best Paper Award 2016, Faculty of Mathematics and Geoinformation, TU Wien, Austria.
  • 2017 Oberwolfach Leibniz Graduate Student Travel Grant to Oberwolfach (Workshop), Germany.
  • 2016 Invitation to the Mittag-Leffler Institute, Stockholm, Sweden.

Research Visits

Extended research visits:

  • May 12-August 23, 2019: Post-doctoral Fellowship HIM Bonn, Junior Trimester Program Kinetic Theory 2019,  HIM Bonn, Germany.
  • January 01-June 30, 2017: Université Paris Diderot, Institut de Mathématiques de Jussieu- Paris Rive Gauche, Postdoc position funded by Université Sorbonne Paris Cité, France, Project with Laurent Desvillettes.

Short research visits:

  •  March-June 2016, Oct-Dec 2015: Paris Université 6/7, Laboratoire Jacques-Louis Lions, Paris, France. Invited by Ayman Moussa, Laurent Boudin and Laurent Desvillettes.
  • Jan-March 2015: University of Oxford, UK
    Invited by Maria Bruna.
  • June-July 2014: University of Cambridge, UK
    Invited by Clément Mouhot.

Workshops and Conferences

Workshop Organization

  • ‘Probabilistic and variational methods in kinetic theory’, HIM Bonn, May 13-17, 2019 [link]
  • ‘Women in PDEs@Vienna’, University of Vienna, June 17-18, 2019 [link]

Scientific Talks

  • 11/2018 ‘Nonlinear Phenomena in Stockholm: Kinetic meets Dispersive’, KTH, Sweden
  • 10/2018 Oberwolfach Seminar ‘Optimal Transportation and hydrodynamics’, Germany
  • 09/2018 ‘MAFRAN days  2018’, Cambridge, UK
  • 06/2018  Seminar at the Simons Semester PDES&SPDEs, Banach Center Warsaw, Poland
  • 05/2018 ‘Theory and Numerics of kinetic equations’, Saarbruecken, Germany
  • 05/2018 Oberseminar Dynamics, TU Munich, Germany
  • 01/2018 Seminar at the University of Mannheim, Germany
  • 12/2017 Oberwolfach ‘Classical and quantum mechanical models of many-particle systems’
  • 10/2017  Seminar at the University of Zagreb, Croatia
  • 09/2017  ‘MAFRAN days’, Cambridge, UK
  • 05/2017 ‘Cross diffusion and kinetic equations in biology’, WPI Vienna, Austria
  • 03/2017 ‘Franco-Italian meeting on kinetic theory and singular parabolic equations’, Paris 7
  • 02/2017 Groupe de travail ‘Modélisation numérique et image’, Paris 5, MAP5, France
  • 01/2017 DK NPDE Winterschool, Reichenau an der Rax, Austria
  • 11/2016 Seminar at the Institut Mittag-Leffler, Stockholm, Sweden
  • 05/2016: Conference ‘Mathematical Topics in Kinetic Theory’, Cambridge, UK
  • 11/2015:  Seminar of the Doctoral School LJLL, Paris 6, France
  • 09/2015: Workshop ‘Multiscale transport of particles’, WPI Vienna, Austria
  • 07/2015: Seminar des Lehrstuhls f. Mathematik IV, Universität Mannheim, Germany
  • 07/2015: ‘Kinetic equations and defect dynamics’, HCB Bonn, Germany
  • 07/2015: Conference ‘Equadiff 2015’, Lyon, France
  • 05/2015: Workshop ‘Mathematical problems in kinetic theory’, CHL Rennes, France
  • 02/2015: WCMB Group Meeting, Oxford, UK
  • 02/2015: SIAM Student Chapter Conference, Oxford, UK

Attended Workshops

  • Workshop ‘Nonlinear Phenomena in Stockholm: Kinetic meets Dispersive’. KTH Stockholm, Sweden, 19.11.-21.11.2018.
  • Oberwolfach Seminar “Optimal Transportation and Hydrodynamics”, Oberwolfach, Germany, 14.10.-20.10.2018
  • “MAFRAN days” 2018, Mathematical Frontiers in the Analysis of many-particle systems, Centre for Mathematical Sciences Cambridge, 24.09.-26.09.2018
  • Lluis Santalo Summer School 2018 on ’Interactions between PDE and probability’,
    Santander, Spain, 13.08.-17.08.2018. (Poster presentation)
  • Simons Semester PDEs/SPDEs and Functional Inequalities, Banach Center Warsaw, Poland, 18.06.-22.06.2018
  • Workshop “Theory and Numerics of kinetic equations”, Saarbrücken, Germany, 28.05.-30.05.2018
  • Workshop Stochastic Partial Differential Equations,  CIRM, Luminy, France, 14.05.-18.05.2018.
  • Workshop on kinetic and fluid partial differential equations, Paris Descartes and Paris Diderot,  Paris, France, 07.03.-09.03.2018.
  • Oberwolfach Workshop ‘Classical and quantum mechanical models of many-particle systems’, Germany, 03.12.-09.12.2017
  • Workshop “MAFRAN Days: Mathematical Frontiers in Many-particle Systems”, University of Cambridge, UK, 15.09.-27.09.2017
  • Workshop “Cross diffusion and kinetic equations in biology”, WPI Vienna, 10.05.-12.05.2017
  • Workshop “Women in PDEs@Karlsruhe”, Karlsruhe, Germany, 27.04.-28.04.2017
  • KIBORD “Franco-Italian meeting on kinetic theory and singular parabolic equations”, Paris 7, France, 16.03.-17.03.2017
  • “Forefront of PDEs: Modelling, Analysis and Numerics”,  TU Vienna, 12.12.-14.12.2016
  • Thematic Semester Research Program “Interactions between Partial Differential Equations and Functional Inequalities”,  Institute Mittag-Leffler, Stockholm, Sweden, 04.11.-12.11.2016
  • Workshop “Kinetic equations”, Paris 6, France, 01.06.2016
  • “Mathematical topics in kinetic theory”, Cambridge, UK, 09.05.-13.05.2016
  • “Workshop on complex systems of reaction-diffusion”, Paris 7, France, 24.03.-25.03.2016
  • WPI Workshop “Multiscale Transport of particles”, Vienna, Austria, 14.09.-16.09.2015
  • Hausdorff School “Nonlinear evolutions: Kinetic equations and defect dynamics”, Bonn, Germany, 12.07.-17.07.2015
  • Equadiff 2015, Lyon, France, 01.07.-10.07.2015
  • Vienna PDE Day, TU Vienna, Austria, 16.06.2015
  • Collective dynamics in gradient flows and entropy driven structures, L’Aquila, Italy, 31.05.-08.06.2015
  • Workshop „Mathematical Problems in kinetic theory“, Rennes, France, 25.05.-30.05.2015
  • Conference “Kinetic Equations”, CIRM, Marseille, France, 10.11.-14.11.2014
  • ESI Vienna “Scaling limits and effective theories in classical and quantum mechanics”, Austria, 22.09.-26.09.2014
  • ESI Vienna “Scaling limits and effective theories in classical and quantum mechanics”, Austria, 22.09.-26.09.2014
  • DK NPDE Summer School, Weissensee, Austria, 14.09.-20.09.2014
  • Joint Summer School IGDK 1754 and DK NPDE, Graz, Austria, 07.09.-11.09.2014
  • VII Edition “Summer School M&MKT14 Porto Ercole”, Porto Ercole, Italy, 07.06.-14.06.2014
  • Conference “Advances in nonlinear PDEs”, TU Vienna, Austria, 02.06.-03.06.2014
  • KI-NET Conference, London, UK, 19.05.-23.05.2014
  • OCCAM + ESGI, Oxford, UK, 31.03.-11.04.2014

 

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