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| 1999 | Diploma in Theoretical Physics, ETH-Zurich | | 1999--2002 | Graduate studies in mathematical physics | | 2002 | Ph.D. from Institute of Theoretical Physics, ETH-Zurich | | 2002-–2003 | Courant Instructor at the Courant Institute, New York University | | 2003-–2004 | Instructor at Stanford University | | 2004-–2005 | NSF postdoctoral fellow at Stanford | | 2005–-2006 | NSF postdoctoral fellow at Harvard | | 2006–-2007 | Assistant Professor (tenure-track) at UC Davis | | 2007-–2008 | Research fellow at LMU Munich, supported by Kovalevskaja Award | | 2007--2010 | University Lecturer at DPMMS, Cambridge | | 2010-- | Hausdorff Chair (W3), Bonn |
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My research field is mathematical physics. I am very interested in the dynamical properties of quantum mechanical systems (quantum dynamics). In the last years, I have been working on the derivation of effective evolution equations for interacting many body systems; see [4,5,6,7,8], as well as on the study of the behavior of the solutions of these macroscopic evolution equations.
Another subject I have been working on is the derivation of Lieb-Robinson bounds for the time evolution of anharmonic lattice systems; these bounds establish the locality of the dynamics; see [9].
I am also interested in the study of the spectral properties of random matrices; in particular, in the last years, I have been working to establish the universality of the local eigenvalue statistics for ensembles of Wigner matrices; see [1,2,3].
Another class of questions I have been trying to understand are related with scattering theory for models of non-relativistic matter coupled to quantized radiation fields; see [10].
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[ 1] László Erdos, Benjamin Schlein, Horng-Tzer Yau
Wegner estimate and level repulsion for Wigner random matrices
Int. Math. Res. Not. IMRN (3): 436--479
2010
ISSN: 1073-7928[ 2] László Erdos, José Ramirez, Benjamin Schlein, Terence Tao, Van Vu, Horng-Tzer Yau
Bulk universality for Wigner Hermitian matrices with subexponential decay
Math. Res. Lett. , 17: (4): 667--674
2010
ISSN: 1073-2780[ 3] László Erd{\Ho}s, Benjamin Schlein, Horng-Tzer Yau
Universality of Random Matrices and Local Relaxation Flow
Accepted for publication in \it Inventiones Mathematicae. Preprint arxiv:0907.5605
2009[ 4] László Erdos, Benjamin Schlein, Horng-Tzer Yau
Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems
Invent. Math. , 167: (3): 515--614
2007
ISSN: 0020-9910
DOI: 10.1007/s00222-006-0022-1[ 5] László Erdos, Benjamin Schlein, Horng-Tzer Yau
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
Ann. of Math. (2) , 172: (1): 291--370
2010
ISSN: 0003-486X
DOI: 10.4007/annals.2010.172.291[ 6] László Erdos, Benjamin Schlein, Horng-Tzer Yau
Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential
J. Amer. Math. Soc. , 22: (4): 1099--1156
2009
ISSN: 0894-0347
DOI: 10.1090/S0894-0347-09-00635-3[ 7] Igor Rodnianski, Benjamin Schlein
Quantum fluctuations and rate of convergence towards mean field dynamics
Comm. Math. Phys. , 291: (1): 31--61
2009
ISSN: 0010-3616
DOI: 10.1007/s00220-009-0867-4[ 8] Alessandro Michelangeli, Benjamin Schlein
Dynamical collapse of boson stars
Accepted for publication in \it Communications in Mathematical Physics. Preprint arXiv:1005.3135
2010[ 9] Bruno Nachtergaele, Hillel Raz, Benjamin Schlein, Robert Sims
Lieb-Robinson bounds for harmonic and anharmonic lattice systems
Comm. Math. Phys. , 286: (3): 1073--1098
2009
ISSN: 0010-3616
DOI: 10.1007/s00220-008-0630-2[ 10] J. Fröhlich, M. Griesemer, B. Schlein
Asymptotic completeness for Compton scattering
Comm. Math. Phys. , 252: (1-3): 415--476
2004
ISSN: 0010-3616
DOI: 10.1007/s00220-004-1180-x |
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| 2006 | Sofja Kovalevskaja Award from the Alexander von Humboldt foundation | | 2009 | ERC Starting Grant | | 2009 | Young Scientist Prize in Mathematical Physics (IUPAP) |
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| 2006 | International Congress Mathematical Physics (ICMP), Rio | | 2008 | Annual meeting of DPG, Freiburg | | 2008 | Annual meeting of DMV, Erlangen | | 2009 | ICMP, Prag | | 2010 | Annual meeting DPG, Bonn | | 2010 | QMath 11 | | 2011 (plan) | ICIAM, Vancouver | | 2011 (plan) | Annual meeting DMV, Koeln |
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ERC Project ''Mathematical Aspects of Quantum Dynamics'' (2009--2014).
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Research Area G
My main interest in Research Area G is the study of random matrices, and in particular, of the spectrum of Wigner matrices, whose entries are independent random variables. In [1], we establish the validity of the semicircle law on the smallest possible scales, and we prove a Wegner type estimate. Later, in [2], the semicircle law on short scales was used to show the universality of the local eigenvalue correlation for hermitian Wigner matrices. In [3], a new approach towards universality was developed and applied to Wigner matrices with arbitrary symmetry. | Research Area J
An important goal of my research is the derivation of effective evolution equations from microscopic many-body quantum dynamics. In a series of paper, we obtained a rigorous derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates; see [4,5,6]. In [7], we applied methods from quantum field theory to show that the nonlinear Hartree equation can be used to approximate the many-body evolution in the mean-field regime. More recently, in [8], I have been interested in the microscopic description of the phenomenon of stellar collapse. |
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