My research concerns the mathematical aspects of classical and quantum field theory, with a particular emphasis on gravity (general relativity). On the physics side, I am interested in the formulation of quantum gravity as a field theory, focusing on the problems of causality and observables in quantum gravity. I am also interested in various mathematical topics that play a role in my work, including the following: geometry of PDEs, jet bundles, conservation laws, symmetries, symplectic and Poisson geometry, homological algebra, supergeometry, infinite dimensional analysis, synthetic differential geometry, category theory.

I have helped organize the mini-symposium QFT Day in Milan: mathematical aspects of renormalization (poster PDF, SVG). I had helped organize the Mathematical Physics Seminar in Trento. It has been on hiatus, but has been recently revived here.


Address: Igor Khavkine
Institute of Mathematics, AS ČR
Žitná 25
115 67   Praha 1
Czech Republic

Last updated: 19 Dec 2020

Curriculum Vitae

Full CV as a PDF file.

Habilitation: Docent (Geometry & Analysis) Czech Republic
Abilitazione: II Fascia – 01/A4, MAT/07 (Fisica Matematica) Italy
Qualification: MCF25 (Mathématiques Pures) France
Staff Researcher:
Department of Algebra, Geometry and Mathematical Physics at the Institute of Mathematics of the Czech Acadey of Sciences (Prague, Czech Republic).
Researcher at the Department of Mathematics, University of Milan (Statale).
Researcher at the Department of Mathematics, University of Rome 2 (Tor Vergata).
Researcher at the Department of Mathematics, University of Trento.
Researcher at the Institute for Theoretical Physics, Utrecht University, in the former Quantum Gravity group of Dr. Renate Loll. Funding: NSERC PDF, NWO VENI fellowship.
Degree in Applied Mathematics and Theoretical Physics from The University of Western Ontario, under the supervision of Dr. J. Daniel Chirstensen. Title: Computer simulation of spin foam models of quantum gravity
Degree in Theoretical Physics from The University of Toronto, under the supervision of Dr. Hae-Young Kee. Title: Formation of electronic nematic phase in interacting systems
Degree in Theoretical Physics from Concordia University, Montreal.


Essentially all of my papers are available from the arXiv preprint server.

Preprints and in preparation


  1. Reducing triangular systems of ODEs with rational coefficients, with applications to coupled Regge-Wheeler equations
    I. Khavkine
    Diff Geom Appl 70 101632 (2020) [arXiv, doi]
  2. Conformal Killing Initial Data
    A. García-Parrado, I. Khavkine
    J Math Phys 60 122502 (2019) [arXiv, doi]
  3. Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation
    I. Khavkine
    Class Quant Grav 36 185012 (2019) [arXiv, doi]
  4. IDEAL characterization of higher dimensional spherically symmetric black holes
    I. Khavkine
    Class Quant Grav 36 045001 (2019) [arXiv, doi]
  5. On Wick polynomials of boson fields in locally covariant algebraic QFT
    I. Khavkine, A. Melati, V. Moretti
    Ann H Poincaré 20 929 (2019) [arXiv, doi]
  6. Approaches to linear local gauge-invariant observables in inflationary cosmologies
    M.B. Fröb, T.-P. Hack, I. Khavkine
    Class Quant Grav 35 115002 (2018) [arXiv, doi]
  7. Explicit triangular decoupling of the separated vector wave equation on
    Schwarzschild into scalar Regge-Wheeler equations

    I. Khavkine
    J Phys: Conf Ser 986 012006 (2018) [arXiv, doi]
  8. IDEAL characterization of isometry classes of FLRW and inflationary spacetimes
    G. Canepa, C. Dappiaggi, I. Khavkine
    Class Quant Grav 35 035013 (2018) [arXiv, doi]
  9. Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
    F. Bussola, C. Dappiaggi, H.R.C. Ferreira, I. Khavkine
    Phys Rev D 96 105016 (2017) [arXiv, doi]
  10. The Calabi complex and Killing sheaf cohomology
    I. Khavkine
    J Geom Phys 113 131 (2017) [arXiv, doi]
  11. Cohomology with causally restricted supports
    I. Khavkine
    Ann H Poincaré 17 3577 (2016) [arXiv, doi]
  12. Analytic dependence is an unnecessary requirement in renormalization of locally covariant QFT
    I. Khavkine, V. Moretti
    Commun Math Phys 344 581 (2016) [arXiv, doi]
  13. Local and gauge invariant observables in gravity
    I. Khavkine
    Class Quant Grav 32 185019 (2015) [slides, arXiv, doi]
  14. Recurrence relation for the 6j-symbol of suq(2) as a symmetric eigenvalue problem
    I. Khavkine
    Int J Geom Methods Mod Phys 12 1550117 (2015) [arXiv, doi]
  15. Algebraic QFT in curved spacetime and quasifree Hadamard states: an introduction
    I. Khavkine, V. Moretti
    Book chapter in Advances in Algebraic Quantum Field Theory, R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds.) (Springer, 2015) [arXiv, doi]
  16. Topology, rigid cosymmetries and linearization instability in higher gauge theories
    I. Khavkine
    Ann H Poincaré 16 255 (2015) [arXiv, doi]
  17. Covariant phase space, constraints, gauge and the Peierls formula
    I. Khavkine
    Int J Mod Phys A 29 1430009 (2014) [arXiv, doi]
  18. Quantum astrometric observables II: time delay in linearized quantum gravity
    B. Bonga, I. Khavkine
    Phys Rev D 89 024039 (2014) [arXiv, doi]
  19. Presymplectic current and the inverse problem of the calculus of variations
    I. Khavkine
    J Math Phys 54 111502 (2013) [arXiv, doi]
  20. Quantum astrometric observables I: time delay in classical and quantum gravity
    I. Khavkine
    Phys Rev D 85 124014 (2012) [arXiv, doi]
  21. Comment on `Hawking radiation from fluctuating black holes'
    I. Khavkine
    Class Quant Grav 28 038001 (2011) [arXiv, doi]
  22. Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations
    I. Khavkine, R. Loll, P. Reska
    Class Quant Grav 27 185025 (2010) [arXiv, doi]
  23. Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model
    J.D. Christensen, I. Khavkine, E.R. Livine, S. Speziale
    Class Quant Grav 27 035012 (2010) [arXiv, doi]
  24. Evaluation of new spin foam vertex amplitudes
    I. Khavkine
    Class Quant Grav 26 125012 (2009) [arXiv, doi]
  25. Dual Computations of Non-abelian Yang-Mills on the Lattice
    J.W. Cherrington, J.D. Christensen, I. Khavkine
    Phys Rev D 76 094503 (2007) [arXiv, doi]
  26. q-Deformed spin foam models of quantum gravity
    I. Khavkine, J.D. Christensen
    Class Quant Grav 24 3271 (2007) [arXiv, doi]
  27. Supercurrent in Nodal Superconductors
    I. Khavkine, H.-Y. Kee, K. Maki
    Phys Rev B 70 184521 (2004) [arXiv, doi]
  28. Formation of Electronic Nematic Phase in Interacting Systems
    I. Khavkine, C.-H. Chung, V. Oganesyan, H.-Y. Kee
    Phys Rev B 70 155110 (2004) [arXiv, doi]
  29. Strong-field molecular alignment for quantum logic and quantum control
    E.A. Shapiro, I. Khavkine, M. Spanner, and M.Yu. Ivanov
    Phys Rev A 67 013406 (2003) [doi]


Synthetic PDEs (thumbnail)
Talk given at the Geometry of Differential Equations Seminar (slides, ), Independent University of Moscow (online). Based on the joint work arXiv:1910.08756 with S. Aksteiner, L. Andersson, T. Bäckdahl, and B. Whiting.
Synthetic PDEs (thumbnail)
Talk given at the Differential Geometry Seminar, Charles University, Prague. Based on the joint work arXiv:1701.06238 with Urs Schreiber.
Projet de recherche (thumbnail)
A presentation (slides) of selected aspects and projects from my research program. (in French)
QG: exercise (thumbnail)
Talk (slides) given at the Quantum Gravity in Perspective workshop (31 May – 1 Jun 2013), Munich, Germany.
time delay (thumbnail)
Talk (slides) given at the UC Davis Joint Theory Seminar, Davis, USA.
q-deformed (thumbnail)
Talk (slides) given at the LOOPS'07 conference (25 – 30 Jun 2007), Morelia, Mexico.


My MathOverflow profile.

clock (thumbnail)
A visualization of the phenomenon tackled in the papers on the influence of the quantum gravitational vacuum on astrometric observables (time delay, angular position, image distortion). Not to scale! This is an artistst's conception... where the artist is also the scientist. ;)
Zorn's lemma A whimsical illustration of the hypotheses and conclusion of Zorn's Lemma.
polar duality Polar or convex duality maps hyperplanes in a vector space to points of the dual space. Thus, any figure can be mapped to its dual, its envelope of tangents. In particular, the unit balls of p-norm and q-norms (1/p + 1/q = 1) are dual to each other. Click to play around with a Java applet or to see animations for p=1 or p=∞.
temperature vs. coldness A simple Java applet to illustrate the idea of negative temperature. For some special systems, adding heat, past a certain point, will make the temperature climb up to +∞ and then jump to -∞. The basic idea is that, while the temperature T changes discontinuously, the physically more natural parameter coldness β = 1/T remains continuous.