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 am a co-organizer of the Prague-Hradec Králové seminar on Cohomology in algebra, geometry, physics and statistics
(
,
recorded lectures).
In 2017, I have helped organize the mini-symposium QFT
Day in Milan: mathematical aspects of renormalization (poster PDF, SVG).
In 2014–2015, I had helped organize the Mathematical Physics Seminar in Trento.
During 2016–2019 it was reprised here here.
Contact
Last updated: 14 Oct 2024
Curriculum Vitae
Full CV as a PDF file.
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Habilitation:
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Docent (Geometry & Analysis) Czech Republic
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Abilitazione:
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II Fascia – 01/A4, MAT/07 (Fisica Matematica) Italy
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Qualification:
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MCF25 (Mathématiques Pures) France
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Staff Researcher:
2017–
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Department of Algebra, Geometry and Mathematical Physics at the Institute of Mathematics of the Czech Acadey of Sciences (Prague, Czech Republic).
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Postdoc:
2016–2017
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Researcher at the Department of
Mathematics, University of Milan (Statale).
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Postdoc:
2016–2016
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Researcher at the Department of
Mathematics, University of Rome 2 (Tor Vergata).
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Postdoc:
2013–2015
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Researcher at the Department of
Mathematics, University of Trento.
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Postdoc:
2009–2013
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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.
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PhD:
2004–2008
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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
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MSc:
2002–2004
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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
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BSc:
1999–2002
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Degree in Theoretical Physics from Concordia University, Montreal.
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Papers
Essentially all of my papers are available from the
arXiv preprint server.
Preprints and in preparation
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IDEAL characterization of vacuum pp-waves
I. Khavkine, D. McNutt, L. Wylleman (2024)
[arXiv]
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The K-distribution of random graph C∗-algebras
B. Jacelon, I. Khavkine (2023)
[arXiv]
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Synthetic geometry of differential equations: I. Jets and comonad structure
I. Khavkine, U. Schreiber (2017)
[arXiv, nLab]
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A polynomial action for gravity with matter, gauge-fixing and ghosts
I. Khavkine (2015)
[arXiv]
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Characteristics, Conal Geometry and Causality in Locally Covariant Field Theory
I. Khavkine
(2012) [arXiv]
Published
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Closed conformal Killing-Yano Initial Data
A. García-Parrado, I. Khavkine
Class Quant Grav 39 105002 (2022)
[arXiv,
doi]
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On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
M.B. Fröb, I. Khavkine, T. Málek, V. Pravda
Eur Phys J C 82 215 (2022)
[arXiv,
doi]
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Explicit triangular decoupling of the separated Lichnerowicz tensor wave equation on Schwarzschild into scalar Regge-Wheeler equations
I. Khavkine
SIGMA 18 011 (2022)
[arXiv,
doi]
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Compatibility complex for black hole spacetimes
S. Aksteiner, L. Andersson, T. Bäckdahl, I. Khavkine, B. Whiting
Commun Math Phys 384 1585 (2021)
[arXiv,
doi]
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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]
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Conformal Killing Initial Data
A. García-Parrado, I. Khavkine
J Math Phys 60 122502 (2019)
[arXiv,
doi]
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Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation
I. Khavkine
Class Quant Grav 36 185012 (2019)
[arXiv,
doi]
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IDEAL characterization of higher dimensional spherically symmetric black holes
I. Khavkine
Class Quant Grav 36 045001 (2019)
[arXiv,
doi]
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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]
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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]
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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]
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IDEAL characterization of isometry classes of FLRW and inflationary spacetimes
G. Canepa, C. Dappiaggi, I. Khavkine
Class Quant Grav 35 035013 (2018)
[arXiv,
doi]
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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]
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The Calabi complex and Killing sheaf cohomology
I. Khavkine
J Geom Phys 113 131 (2017)
[arXiv,
doi]
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Cohomology with causally restricted supports
I. Khavkine
Ann H Poincaré 17 3577 (2016)
[arXiv,
doi]
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Analytic dependence is an unnecessary requirement in
renormalization of locally covariant QFT
I. Khavkine, V. Moretti
Commun Math Phys 344 581 (2016)
[arXiv,
doi]
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Local and gauge invariant observables in gravity
I. Khavkine
Class Quant Grav 32 185019 (2015)
[slides, arXiv, doi]
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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]
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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]
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Topology, rigid cosymmetries and linearization instability in higher gauge theories
I. Khavkine
Ann H Poincaré 16 255 (2015)
[arXiv, doi]
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Covariant phase space, constraints, gauge and the Peierls formula
I. Khavkine
Int J Mod Phys A 29 1430009 (2014)
[arXiv, doi]
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Quantum astrometric observables II: time delay in linearized quantum gravity
B. Bonga, I. Khavkine
Phys Rev D 89 024039 (2014)
[arXiv, doi]
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Presymplectic current and the inverse problem of the calculus of variations
I. Khavkine
J Math Phys 54 111502 (2013)
[arXiv, doi]
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Quantum astrometric observables I: time delay in classical and quantum gravity
I. Khavkine
Phys Rev D 85 124014 (2012)
[arXiv, doi]
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Comment on `Hawking radiation from fluctuating black holes'
I. Khavkine
Class Quant Grav 28 038001 (2011)
[arXiv, doi]
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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]
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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]
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Evaluation of new spin foam vertex amplitudes
I. Khavkine
Class Quant Grav 26 125012 (2009)
[arXiv, doi]
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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]
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q-Deformed spin foam models of quantum gravity
I. Khavkine, J.D. Christensen
Class Quant Grav 24 3271 (2007)
[arXiv, doi]
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Supercurrent in Nodal Superconductors
I. Khavkine, H.-Y. Kee, K. Maki
Phys Rev B 70 184521 (2004)
[arXiv, doi]
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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]
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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]