

1999  Diploma in Theoretical Physics, ETH Zürich, Switzerland  1999  2002  Graduate studies in Mathematical Physics  2002  PhD from Institute of Theoretical Physics, ETH Zürich, Switzerland  2002  2003  Courant Instructor, Courant Institute, New York University, NY, USA  2003  2004  Instructor, Stanford University, CA, USA  2004  2005  NSF Postdoctoral Fellow, Stanford University, CA, USA  2005  2006  NSF Postdoctoral Fellow, Harvard University, Cambridge, MA, USA  2006  2007  Assistant Professor (tenuretrack), University of California, Davis, CA, USA  2007  2008  Research Fellow, supported by Kovalevskaja Award, LMU Munich  2007  2010  University Lecturer, Department of Pure Mathematics and Mathematical Statistics, Cambridge, England, UK  2010  2014  Hausdorff Chair (W3), University of Bonn  Since 2014  Professor, University of Zürich, Switzerland 


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 LiebRobinson 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 is related with scattering theory for models of nonrelativistic matter coupled to quantized radiation fields; see [10].


ERC Project “Mathematical Aspects of Quantum Dynamics”
2009  2014


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 manybody quantum dynamics. In a series of paper, we obtained a rigorous derivation of the GrossPitaevskii equation for the dynamics of BoseEinstein 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 manybody evolution in the meanfield regime. More recently, in [8], I have been interested in the microscopic description of the phenomenon of stellar collapse. 


[ 1] LÃ¡szlÃ³ Erdős, Benjamin Schlein, HorngTzer Yau
Wegner estimate and level repulsion for Wigner random matrices Int. Math. Res. Not. IMRN (3): 436479 2010 DOI: 10.1093/imrn/rnp136[2] LÃ¡szlÃ³ Erdős, JosÃ© RamÃrez, Benjamin Schlein, Terence Tao, Van Vu, HorngTzer Yau
Bulk universality for Wigner Hermitian matrices with subexponential decay Math. Res. Lett. , 17: (4): 667674 2010 DOI: 10.4310/MRL.2010.v17.n4.a7 [ 4] LÃ¡szlÃ³ Erdős, Benjamin Schlein, HorngTzer Yau
Derivation of the cubic nonlinear SchrÃ¶dinger equation from quantum dynamics of manybody systems Invent. Math. , 167: (3): 515614 2007 DOI: 10.1007/s0022200600221[ 5] LÃ¡szlÃ³ Erdős, Benjamin Schlein, HorngTzer Yau
Derivation of the GrossPitaevskii equation for the dynamics of BoseEinstein condensate Ann. of Math. (2) , 172: (1): 291370 2010 DOI: 10.4007/annals.2010.172.291[ 6] LÃ¡szlÃ³ Erdős, Benjamin Schlein, HorngTzer Yau
Rigorous derivation of the GrossPitaevskii equation with a large interaction potential J. Amer. Math. Soc. , 22: (4): 10991156 2009 DOI: 10.1090/S0894034709006353[ 7] Igor Rodnianski, Benjamin Schlein
Quantum fluctuations and rate of convergence towards mean field dynamics Comm. Math. Phys. , 291: (1): 3161 2009 DOI: 10.1007/s0022000908674[ 9] Bruno Nachtergaele, Hillel Raz, Benjamin Schlein, Robert Sims
LiebRobinson bounds for harmonic and anharmonic lattice systems Comm. Math. Phys. , 286: (3): 10731098 2009 DOI: 10.1007/s0022000806302[ 10] J. FrÃ¶hlich, M. Griesemer, B. Schlein
Asymptotic completeness for Compton scattering Comm. Math. Phys. , 252: (13): 415476 2004 DOI: 10.1007/s002200041180x




2006  Sofja Kovalevskaja Award from the Alexander von Humboldt Foundation  2009  ERC Starting Grant  2009  Young Scientist Prize in Mathematical Physics (IUPAP) 


2006  International Congress Mathematical Physics (ICMP), Rio de Janeiro, Brasil  2008  Annual meeting of DPG, Freiburg  2008  Annual meeting of DMV, Erlangen  2009  ICMP, Prague, Czech Republic  2010  Annual meeting DPG, Bonn  2010  QMath 11, Hradec Králové, Czech Republic  2011  ICIAM, Vancouver, BC, Canada  2011  Annual meeting DMV, Cologne 


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