פרופ"ח חגי כתריאל

פרופ"ח חגי כתריאל

Assoc. Prof. Haggai Katriel

פרופ"ח חגי כתריאל
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Department
Mathematics
Research Interests
Nonlinear phenomena, Mathematical modeling, Mathematical epidemiology, Nonlinear functional analysis and its applications to differential equations, Spectral theory, Dynamics of forced and coupled oscillators, Stochastic models
Courses
Differential equations, Fourier analysis, algebra 1, functional analysis, mathematical modelling, calculus 2
Current Position
Associate Professor
Contact Information
Email
katriel@braude.ac.il
Telephone
04-9086443
Office
EM411
Education
Ph.D.
1999, Mathematics, Department of Mathematics, The Technion – Israel Institute of Technology, Haifa, Israel
M.Sc.
1993, Mathematics, Department of Mathematics, University of Haifa.
B.Sc.
1990, Mathematics, Department of Mathematics, The Technion – Israel Institute of Technology, Haifa, Israel
Research Areas
• Nonlinear phenomena• Mathematical modeling• Mathematical epidemiology• Nonlinear functional analysis and its applications to differential equations• Spectral theory• Dynamics of forced and coupled oscillators• Stochastic models
Academic Appointments
2011-present Senior Lecturer, ORT Braude College, Department of Mathematics
2009-2011 Research Associate, Biomathematics Unit, Faculty of Life Sciences, Tel-Aviv University.
2007-2008 Humboldt Fellow, Institute of Mathematics, Clausthal Technical University, Germany.
2007 Visiting Scholar, Department of Mathematics, University of British Columbia, Canada (April- June).
2006-2007 Minerva Fellow, Institute of Mathematics, Clausthal Technical University, Germany (May- June)
2003-2006 Postdoctoral research in Mathematics, Landau Fellow, Hebrew University.
2001-2002 Postdoctoral research in Mathematics Education, University of Haifa (Vatat fellowship)
Teaching Experience
ORT Braude College of Engineering:
  • Undergraduate Courses:Ordinary differential equations for electrical engineersOrdinary differential equations for mathematicsFourier analysis Functional AnalysisAlgebra 1
Technion – Israel Institute of Technology:
  • Teaching assistant in courses: Set theory, Modern analysis for electrical engineers, Calculus II, Calculus III, Fourier analysis.
Academic and Professional Awards and Grants
2010 Outstanding poster award at the 1st International Workshop on “Mathematical Methods in Systems Biology”, Tel-Aviv University.
2007 Humboldt postdoctoral fellowship.
1999 Netanyahu Prize for outstanding Phd Dissertation (Technion).
1996 Wolf Foundation prize for doctoral students.
1996 Hanani Prize (Dept. of Mathematics, Technion).
Professional Activities
ORT Braude College:
2011 - Present Member of the Research Committee, ORT Braude College.
2011- Present Member of Organizing Committee, 6th International Conference on Complex Analysis and Dynamical Systems, Naharia, Israel.
2012 - Present Organizer of Research Seminar, Department of Mathematics, ORT Braude College.
Conferences:

1999 Second Symposium on Nonlinear Analysis, Torun, POLAND,. Title: “Periodic solutions of the forced pendulum”.
2005 The Third Israeli Mini-Workshop in Applied and Computational Mathematics, Jerusalem, Title: "Travelling waves in sine-Gordon rings: a topological method".
2006 6th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Poitiers, France,
2006. Title: "Existence of periodic solutions for enzyme-catalyzed reactions with periodic substrate input".
2006 Heat Kernels 06 conference at Blaubauren, Germany,. Title: "Inequalities for moments of eigenvalues using complex analysis".
2008 International Conference on PDEs and Spectral Theory, Goslar, Germany,. Title: “Resonances in the one-dimensional discrete Schroedinger equation”.
2009 Interdisciplinary workshop on periodic oscillations, Granada, Spain. Title: “Oscillators coupled through an environment” (invited plenary lecture). 2010 1st International Workshop on Mathematical Methods in Systems Biology, Tel-Aviv University. Lecture: “Dynamics of oscillators coupled through an environment”, and Poster entitled: Swine flu in the Holy Land – a case country for studying the onset of a pandemic.
2010 28th Israel Symposium on Computational Mathematics, Jerusalem. Title: “Discrete time stochastic age of infection models and their fitting to data”. 2011 Fifth International Conference on Complex Analysis & Dynamical Systems, Akko, Title: "From spectral theory to bounds on zeros of complex functions".
2011 Mathematical Physics, Spectral Theory and Stochastic Analysis, Goslar, Germany. Title: "Random walks and resonances".
2012 Spectral Day, Clausthal, Germany. Title: "Convergence to equilibrium in random market models".
2012 ORT Braude Interdisciplinary Conference, Akko. Title: "Epidemic models with seasonality".

Publications
Refereed Papers
  1. G. Katriel, Mountain pass theorems and global homeomorphism theorems. Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994), no. 2, 189--209.
  2. G. Katriel, Surjection results for Fredholm mappings with singularities. Nonlinear Anal. 23 (1994), no. 10, 1273--1275.
  3. G. Katriel, Are the approximate and the Clarke subgradients generically equal? J. Math. Anal. Appl. 193 (1995), no. 2, 588--593.
  4. G. Katriel, Many periodic solutions for pendulum-type equations. Nonlinear Anal. 34 (1998), no. 5, 687--699.
  5. G. Katriel, Uniqueness of periodic solutions for asymptotically linear Duffing equations with strong forcing. Topol. Methods Nonlinear Anal. 12 (1998), no. 2, 263--274.
  6. G. Katriel, A uniqueness theorem for two-point boundary value problems. Appl. Anal. 74 (2000), no. 3-4, 261--274.
  7. G. Katriel, Periodic solutions of the forced pendulum: exchange of stability and bifurcations. J. Differential Equations 182 (2002), no. 1, 1--50.
  8. G. Katriel, Solution of Rubel’s question about differentially algebraic dependence on initial conditions. Illinois J. Math. 47 (2003), no. 4, 1261-1272.
  9. G. Katriel, Stability of synchronized oscillations in networks of phase-oscillators, Discrete and Continuous Dynamical Systems B 5 (2005) 353-364.
  10. G. Katriel, Existence of travelling waves in discrete sine-Gordon rings, SIAM J. Math. Anal. 36 (2005) 1434-1443.
  11. R. Fattal, O.H. Hald, G. Katriel & R. Kupferman Global stability of equilibrium manifolds, and "peaking" behavior in quadratic differential systems related to viscoelastic models, J. Non-Newton. Fluid Mech. 144 (2007) 30-41.
  12. G. Katriel, Existence of periodic solutions for enzyme-catalyzed reactions with periodic substrate input, Discrete & Continuous Dynamical Systems - Supplements (September 2007), 551-557.
  13. G. Katriel, Existence, uniqueness, and multiplicity of rotating fluxons in annular Josephson Junctions, Differential & Integral Equations, 20 (2007), 1167—1184.
  14. G. Katriel, R. Kupferman & E. Titi Global Existence and long-time limit for a class of nonlinear infinite dimensional dynamical systems. J. Differential Equations 245 (2008), 2771-2784.
  15. M. Demuth & G. Katriel, Eigenvalue inequalities in terms of Schatten norm bounds on differences of semigroups, and application to Schroedinger operators, Annales Henri Poincaré Math. Phys 9 (2008), 817-834.
  16. G. Katriel, Synchronization of oscillators coupled through an environment, Physica D 237 (2008), 2933-2944.
  17. M. Demuth, M. Hansmann & G. Katriel, On the discrete spectrum of non-selfadjoint operators, J. Functional Analysis 257 (2009), 2742-2759.
  18. M. Demuth & G. Katriel, On finiteness of the sum of negative eigenvalues of Schrödinger operators, Bull. Kerala Math.Assoc. 2009, Special Issue, 87--104.
  19. G. Katriel & L. Stone, Pandemic dynamics and the breakdown of herd immunity, PLoS ONE 5(3): e9565 (2009).
  20. Huppert A., Katriel H., Yaari R., Barnea O., Roll U., Stern E., Balicer R. and Stone L. (2010). Mathematical Models as a Tool for Studying and Developing Strategies in the Case of a Pandemic Influenza Outbreak. Harefuah, 149:4-8 (in Hebrew, English abstract).
  21. G. Katriel, Epidemics with partial immunity to reinfection, Mathematical Biosciences 228 (2010), 153-159.
  22. M. Hansmann & G. Katriel, Inequalities for the eigenvalues of non-selfadjoint Jacobi operators, Complex Analysis & Operator Theory 5 (2011), 197-218.
  23. O. Barnea, R. Yaari, G. Katriel & L. Stone, Modelling seasonal influenza in Isreal, Math. Bioscience & Engineering 8 (2011), 561-573.
  24. G. Katriel , R. Yaari, A. Huppert, U. Roll & L. Stone, Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study, J. Roy. Soc. Interface 8 (2011), 856-867.
  25. U. Roll, L. Stone, G. Katriel, R. Yaari , O. Barnea , E. Mendelson, M. Mandelboim, A. Huppert , Onset of a pandemic: characterizing the initial phase of the swine flu (H1N1) epidemic in Israel, BMC Infectious Diseases 11 (2011).
  26. G. Katriel, Note on `Age, influenza and disease dynamics' by A.L. Greer, A.Tuite & D.N. Fisman, Epidemiology and Infection 189 (2011).
  27. G. Katriel, The size of epidemics in populations with heterogeneous susceptibility, J. Math. Biology 65 (2012), 237-262.
  28. G. Katriel & L. Stone, Attack rates of seasonal epidemics, Mathematical Biosciences 235 (2012), 56-65.
  29. M. Hansmann, G. Katriel, From spectral theory to zeros of holomorphic functions, Bulletin London Math. Soc. 45 (2013), 103-110.
  30. A. Huppert, O. Barnea, G. Katriel, R. Yaari, U. Roll, and L. Stone, Modeling and Statistical Analysis of the Spatio-temporal Patterns of Seasonal Influenza in Israel, PloS ONE 7 (2012), e45107.
  31. G. Katriel, Stochastic discrete-time age-of-infection epidemic models, International Journal of Biomathematics 6 (2013), 1250066.
  32. A. Huppert, G. Katriel, Mathematical modelling and prediction in infectious disease epidemiology, Clin. Microbiol. Infection 19 (2013), 999-1005.
  33. R. Yaari, G. Katriel, A. Huppert, J.B. Axelsen, L. Stone, Modelling seasonal influenza: the role of weather and punctuated antigenic drift, J. R. Soc. Interface 10 (2013), 20130298.
  34. M. Demuth, M. Hansmann, G. Katriel Lieb-Thirring type inequalities for Schroedinger operators with a complex-valued potential, Integral Equations & Operator Theory 75 (2013), 1-5.
  35. G. Katriel, Existence of periodic solutions for the periodically-forced SIR model, Nonlinear Oscillations 16 (2013), 359-366.
  36. G. Katriel, Gambler's ruin probability - a general formula, Probability and Statistics Letters 83 (2013), 2205-2210.
  37. G. Katriel, Convergence to an exponential distribution in a random market model, Applicable Analysis 6 (2014) 1256-1263.
  38. O. Barnea, A. Huppert, G. Katriel, L. Stone, Spatio-Temporal synchrony of Influenza in cities across Israel: the "Israel is one city" hypothesis, PLoS ONE 9 (2014), e91909.
  39. G. Katriel, Gambler's Ruin: The Duration of Play, Stochastic Models 30 (2014), 251-271.  
  40. D. Burg, D. Malkinson, G. Katriel, L. Wittenberg, Modeling the dynamics of soil erosion and vegetative control - catastrophe and hysteresis, Theoretical Ecology 8, 67-79 (2015).
  41. G. Katriel, Directed Random Market: the equilibrium distribution, Acta Applicandae Mathematicae, 139, 95-103 (2015).
  42. M. Demuth, F. Hanauska, M. Hansmann, G. Katriel, Estimating the number of eigenvalues of linear operators on Banach spaces, J. Functional Analysis 268, 1032-105 (2015).
  43. G. Katriel, The Immediate Exchange model: an analytical investigation, Eur. Phys. J. B 88: 19 (2015).
  44. A. Zvuloni, Y.Artzi-Randrup, G. Katriel, Y. Loya, L. Stone, Modeling the impact of white-plague coral disease in climate change scenarios, PloS Comput. Biol. 11, e1004151 (2015).
  45. R. YaariG. KatrielL. StoneE. MendelsonM. MandelboimA. Huppert, Model-based reconstruction of an epidemic using multiple datasets: understanding influenza A/H1N1 pandemic dynamics in Israel, J. Roy. Soc. Interface 13, 2016099 (2016).
  46. T. Gadrich, G. Katriel, A mechanistic stochastic Ricker model: analytical and numerical investigations, Int. J. Bifurcation Chaos 26, 1650067 (2016)
  47.  R. Yaari, E. Kaliner, I. Grotto, G. Katriel, J. Moran-Gilad, D. Sofer, E. Mendelson, E. Miller, A. Huppert, Modeling the spread of polio in an IPV-vaccinated population: lessons from the 2013 silent outbreak in southern Israel, BMC Medicine 14:95 (2016).
  48. G. Katriel, A quantitative discounted central limit theorem using the Fourier metric, Statistics & Probability Letters 145 (2019), 321-326.
  49. M. Ben-Artzi, G. Katriel, Spline functions, the biharmonic operator, and approximate eigenvalues, Numerische Math. 141 (2019), 839-879.

Book Chapters
  1. L. Stone, F. Hilker & G. Katriel, SIR Models, in Encyclopedia of Theoretical Ecology, A. Hastings & L. Gross (eds.), University of California Press, 2012.
Conference Proceedings and Abstracts
  1. M. Demuth, M. Hansmann, G. Katriel, Eigenvalues of non-selfadjoint operators: a comparison of two approaches, Proceedings of Mathematical Physics, Spectral Theory and Stochastic Analysis, Goslar, 2013, Birkhauser.
Other Publications
Professional Reports:
  1. G. Katriel, On the number of solutions of nonlinear equations. Ph.D. Dissertation. Advisor: Professor A. Ioffe, The Technion – Israel Institute of Technology, Haifa, Israel, 1999.
  2. G. Katriel, Global nonsmooth analysis. M.Sc. Thesis. Advisor: Professor A. Ioffe,, University of Haifa, December, 1993.
  3. G. Katriel, Synchronization in model networks of class I neurons, 2003 http://arxiv.org/abs/nlin.AO/0309041.
  4. G. Katriel, From Rolle’s theorem to the Sturm-Hurwitz theorem, 2003, http://arxiv.org/abs/math/0308159.
  5. G. Katriel, Periodic travelling waves in the theta model for synaptically connected neurons, 2003, http://arxiv.org/abs/nlin.PS/0409052.
  6. G. Katriel, Asymptotic behavior of random walks with a jump at the origin, 2011, http://arxiv.org/abs/1108.5621 .
  7. G. Katriel, Meromorphic continuation for generating functions of iteratively defined sequences, 2012.