Current research interests:
Renormalization group methods, spectral and dynamical problems in quantum field theory.
Scaling limits of quantum dynamics, nonlinear PDEs,
Hamiltonian dynamics.
Mathematical foundations of deep learning. [slides]
Derivation of renormalized Hartree-Fock-Bogoliubov and quantum Boltzmann equations in an interacting Bose gas
(with M. Hott)
Preprint.arXiv (83 pages)
Global L^2 minimization at uniform exponential rate via geometrically adapted gradient descent in Deep Learning
Submitted.arXiv (20 pages)
Non-approximability of constructive global L^2 minimizers by gradient descent in Deep Learning
(with P. Munoz Ewald)
Preprint.arXiv (7 pages)
Geometric structure of Deep Learning networks and construction of global L^2 minimizers
(with P. Munoz Ewald)
Submitted.arXiv (22 pages)
Geometric structure of shallow neural networks and constructive L^2 cost minimization
(with P. Munoz Ewald)
Submitted.arXiv (28 pages)
Quantum Boltzmann dynamics and bosonized particle-hole interactions in fermion gases
(with E. Cardenas)
Submitted.arXiv (70 pages)
On an L^2 critical Boltzmann equation
(with R. Denlinger and N. Pavlovic)
Submitted.arXiv (119 pages)
On the well-posedness and stability of cubic and quintic nonlinear Schrödinger systems on T^3
(with A. Urban)
Ann. H. Poincare, 25 (2), 1657-1692, 2024.Journal (36 pages).
arXiv
On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate
(with M. Hott)
J. Stat. Phys., 190 (4), 85 (2023).Journal (123 pages).
arXiv
Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates
(with R. Denlinger and N. Pavlovic)
Arch. Ration. Mech. Anal., 240 (1), 327-381, 2021.Journal (55 pages).
arXiv
The time-dependent Hartree-Fock-Bogoliubov equations for Bosons
(with V. Bach, S. Breteaux, J. Fröhlich and I.M. Sigal)
J. Evol. Eqs., 22 (2):46, 2022.Journal (43 pages).
arXiv
On the Hartree-Fock-Bogoliubov equations
(with V. Bach, S. Breteaux, J. Fröhlich and I.M. Sigal)
arXiv (12 pages).
Moments and regularity for a Boltzmann equation via Wigner transform
(with R. Denlinger and N. Pavlovic)
Discr. Contin. Dyn. Syst. A, 39 (9), 4979-5015, 2019.Journal
(37 pages).
arXiv
Mean field dynamics of a quantum tracer particle interacting with a boson gas
(with A. Soffer)
J. Funct. Anal., 276 (3), 971-1006, 2019.Journal
(37 pages).
arXiv
Local well-posedness for Boltzmann's equation and the Boltzmann hierarchy via Wigner transform
(with R. Denlinger and N. Pavlovic)
Commun. Math. Phys., 368 (1), 427-465, 2019.Journal
(39 pages).
arXiv
The weak coupling limit for the random Schrödinger equation: The average wave function
(with T. Komorowski and L. Ryzhik)
Arch. Ration. Mech. Anal., 227 (1), 387-422, 2018. Journal
(36 pages).
arXiv
On the scattering problem for infinitely many fermions in dimensions d \geq 3 at positive temperature
(with Y. Hong and N. Pavlovic)
Ann. Inst. H. Poincare (C) Anal. Non Lin., 35 (2), 393-416, 2018.Journal
(24 pages).
arXiv
Global well-posedness of the NLS System for infinitely many fermions
(with Y. Hong and N. Pavlovic)
Arch. Ration. Mech. Anal., 224 (1), 91-123, 2017.Journal (33 pages).
arXiv
Arrest of blowup for the 3-D semi-relativistic Schroedinger-Poisson system with pseudo-relativistic diffusion
(with W. Abou Salem and V. Vougalter)
Rev. Math. Phys. 27 (10), 1550023, 2015.
Journal
(18 pages).
arXiv
On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti
(with C. Hainzl, N. Pavlovic, and R. Seiringer)
Lett. Math. Phys., 104 (7), 871-891, 2014. Journal
(21 pages).
arXiv
Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti
(with C. Hainzl, N. Pavlovic, and R. Seiringer)
Commun. Pure Appl. Math., 68 (10), 1845-1884, 2015.
Journal (40 pages).
arXiv
Derivation in strong topology and global well-posedness of solutions to the Gross-Pitaevskii hierarchy
(with K. Taliaferro)
Commun. PDE, 39 (9), 1658-1693, 2014.
Journal (35 pages).
arXiv
On the generalized semi-relativistic Schroedinger-Poisson system in R^n
(with W. Abou Salem and V. Vougalter)
Doc. Math., 18, 343 - 357, 2013.Journal
(16 pages).
arXiv
Existence and nonlinear stability of stationary states for the semi-relativistic Schroedinger-Poisson system
(with W. Abou Salem and V. Vougalter)
Ann. H. Poincare, 15 (6), 1171 - 1196, 2014.
Journal
(25 pages).
arXiv
Effective dynamics of an electron coupled to an external potential in non-relativistic QED
(with V. Bach, J. Faupin, J. Fröhlich and I.M. Sigal)
Ann. H. Poincare, 14 (6), 1573-1597, 2013.Journal
(25 pages).
arXiv
On the well-posedness of the semi-relativistic Schroedinger-Poisson system
(with W. Abou Salem and V. Vougalter)
Dynamics of PDE, 9 (2), 121-132, 2012.
Journal (12 pages).
arXiv
Multilinear Morawetz identities for the Gross-Pitaevskii hierarchy
(with N. Pavlovic and N. Tzirakis)
Contemp. Math., 581, 39 - 62, 2012. Book article (23 pages).
arXiv
On the Dynamics of a Fermi Gas in a Random Medium with Dynamical Hartree-Fock Interactions
IMS Lecture Notes Series (National University of Singapore), Vol. 24, 2013.
Book article.
Derivation of the cubic NLS and Gross-Pitaevskii hierarchy
from manybody dynamics
in d=3 based on spacetime norms
(with N. Pavlovic)
Ann. H. Poincare, 15 (3), 543 - 588, 2014. Journal
(46 pages).
arXiv
A lower bound on blowup rates for the 3D incompressible Euler equation
and a single exponential Beale-Kato-Majda type estimate
(with N. Pavlovic)
Commun. Math. Phys., 314 (1), 265 - 280, 2012. Journal (15 pages).
arXiv
Charge Transport in Random Media and Boltzmann Limits for Single Particle and Manybody Models
RIMS Kokyuroku Bessatsu B21, 63 - 108, 2011. Preprint (45 pages)
Local decay in non-relativistic QED
(with J. Faupin, J. Fröhlich and I.M. Sigal)
Commun. Math. Phys., 309 (2), 543 - 582, 2012.Journal
(40 pages).
arXiv
Recent results on the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies
(with N. Pavlovic)
Math. model. nat. phenom. Vol. 5, No. 4 (2010).
Issue on spectral problems,
dedicated to the memory of M. Birman (V. Volpert, A. Laptev et al., eds.).
Journal.
Boltzmann limit for a homogenous Fermi gas with dynamical
Hartree-Fock interactions in a random medium
(with I. Rodnianski)
J. Stat. Phys., 142 (5), 1000 - 1051, 2011. Journal (52 pages).
arXiv.
A new proof of existence of solutions for focusing and defocusing Gross-Pitaevskii hierarchies
(with N. Pavlovic)
Proc. Amer. Math. Soc., 141, 279-293, 2013.
Journal (15 pages).
mp_arc.
Higher order energy conservation and global wellposedness of solutions for
Gross-Pitaevskii hierarchies
(with N. Pavlovic)
Commun. PDE, 39 (9), 1597-1634, 2014.
Journal (37 pages).
arXiv.
Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies
(with N. Pavlovic and N. Tzirakis)
Ann. Inst. H. Poincare (C) Anal. Non-Lin., 27 (5), 1271-1290, 2010. Journal
(24 pages).
arXiv.
On the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies
(with N. Pavlovic)
Discr. Contin. Dyn. Syst. A, 27 (2), 715 - 739, 2010.
Journal (25 pages).
arXiv.
The quintic NLS as the mean field limit of a Boson gas with three-body interactions
(with N. Pavlovic)
J. Funct. Anal., 260 (4), 959-997, 2011.
Journal (39 pages).
arXiv.
Quantitative estimates on the hydrogen ground state energy in non-relativistic QED
(with J.-M. Barbaroux, V. Vougalter and S. A. Vugalter)
Ann. H. Poincare, 11 (8), 1487-1544, 2010.
Journal (58 pages),
arXiv.
Boltzmann limit and quasifreeness for a homogenous Fermi gas in a weakly disordered random medium
(with I. Sasaki)
J. Stat. Phys., 132 (2), 329-353, 2008.
Journal (25 pages).
arXiv.
Infraparticle scattering states in non-relativistic QED - II. Mass shell properties
(with J. Fröhlich and A. Pizzo)
J. Math. Phys., 50 (1), 012103, 2009. Journal (34 pages).
arXiv
Infraparticle scattering states in non-relativistic QED - I. The Bloch-Nordsieck paradigm
(with J. Fröhlich and A. Pizzo)
Commun. Math. Phys., 294 (3), 761 - 825, 2010. Journal (65 pages).
arXiv
Infrared renormalization in non-relativistic QED and scaling criticality
J. Funct. Anal., 254 (10), 2555 - 2647, 2008.
Journal (93 pages).
arXiv.
On the ground state energy of the translation invariant Pauli Fierz model
(with J.-M. Barbaroux, V. Vougalter and S. A. Vugalter)
Proc. Amer. Math. Soc., 136 (20), 2008.
Journal (8 pages).
arXiv.
Coherent infrared representations in non-relativistic QED
(with J. Fröhlich)
Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday.
Proc. Symp. Pure Math., AMS, 25 - 45, 2007
(refereed research article, 21 pages).
arXiv.
The renormalized electron mass in non-relativistic QED
(with V. Bach, J. Fröhlich and I. M. Sigal)
J. Funct. Anal., 243 (2), 426 - 535, 2007.
Journal (110 pages).
arXiv.
Convergence in higher mean of a random Schrödinger to a linear Boltzmann evolution
Comm. Math. Phys., 267, 355-392, 2006.
Journal (38 pages).
arXiv.
Localization lengths for Schrödinger operators on Z^2 with decaying random potentials
Int. Math. Res. Notices, 2005:54, 3341-3373, 2005.
Journal (33 pages).
arXiv.
Localization lengths and Boltzmann limit for the Anderson model at small disorders in dimension 3
J. Stat. Phys., 120 (1-2), 279-337, 2005.
Journal (59 pages).
arXiv.
Long-time dynamics and localization lengths in the 3-D Anderson model at weak disorders
Proceedings of the International Congress on Mathematical Physics 2003, World Scientific, 2005.
Critical manifolds and stability in Hamiltonian systems with non-holonomic constraints
J. Geom. Phys., 49 (3-4), 418 - 462, 2004.
Journal (45 pages).
arXiv.
Smooth Feshbach map and operator-theoretic renormalization group methods
(with V. Bach, J. Fröhlich and I. M. Sigal)
J. Funct. Anal., 203 (1), 44-92, 2003.
Journal (49 pages).
mp_arc.
The decay of unstable noncommutative solitons
(with J. Fröhlich and J. Walcher)
Comm. Math. Phys., 237 (1-2), 243-269, 2003.
Journal (27 pages).
arXiv.
Binding conditions for atomic N-electron systems in non-relativistic QED
(with J.-M. Barbaroux and S. A. Vugalter)
Ann. H. Poinc., 4 (6), 1101 - 1136, 2003.
Journal (36 pages).
arXiv.
The increase of binding energy and enhanced binding in non-relativistic QED
(with V. Vougalter and S. A. Vugalter)
J. Math. Phys., 44 (5), 1961-1970, 2003.
Journal (10 pages).
arXiv.
The Haag-Lopuszanski-Sohnius theorem
(with J. Fuchs)
Concise encyclopedia of supersymmetry, J. Bagger, S. Duplij, W. Siegel (eds.), Kluwer, 2003.
Dynamical behaviour of a constrained system near a singularity of the configuration space
(with H. Brauchli)
Proc. 4th World Congr. Comp. Mech. (WCCM IV), Buenos Aires, 1998.
Renormalization group methods: Landau-Fermi liquid and BCS superconductor
(with J. Fröhlich and M. Seifert)
LXII Les Houches summer schools, Elsevier, 1996.
arXiv
Operator-theoretic infrared renormalization and construction of dressed
one-particle states in non-relativistic QED
Ph.D. Thesis, Diss-ETH 14203, 2001.
arxiv (139 pages)
Non-holonomy, critical manifolds and stability in constrained Hamiltonian systems
Ph.D. Thesis, Diss-ETH 13017, 1999.
arXiv (52 pages)
Aspects of the theory of non-relativistic matter, coupled to the quantized electromagnetic field
Diploma Thesis ETH, 1996.pdf.