Prof. Dr. Benjamin Schlein

Former Hausdorff Chair
Subsequent position: Full Professor at the University of Zurich

E-mail: benjamin.schlein(at)hcm.uni-bonn.de
Fax: +49 228 73 7992
Homepage: http://www.hcm.uni-bonn.de/homepages/prof-dr-benjamin-schlein
Institute: Institute for Applied Mathematics
Research Areas: Research Area G
Research Area J
Birthdate: 28.May 1975
Mathscinet-Number: 688765

Publications

Academic Career

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--2014

Hausdorff Chair (W3), Bonn

2014--

Full Professor at the University of Zürich

Research profile

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].

Selected Publications

[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

Awards

2006

Sofja Kovalevskaja Award from the Alexander von Humboldt foundation

2009

ERC Starting Grant

2009

Young Scientist Prize in Mathematical Physics (IUPAP)

Invited Lectures

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

Research Projects and Activities

ERC Project ''Mathematical Aspects of Quantum Dynamics'' (2009--2014).

Contribution to Research Areas

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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