

1987  Diploma, University of Mainz  1990  PhD, University of Heidelberg  1990  1993  Research Fellow, LMU and TU Munich  1993  1994  Research Fellow, Harvard University, Cambridge, MA, USA  1994  1996  Research Fellow, CERN THDivision, Geneva, Switzerland  1996  1998  Research Fellow, Enrico Fermi Institute, Chicago, IL, USA  1998  Habilitation, LMU Munich  1998  2000  Heisenberg Fellow, Institute for Advanced Study, Princeton, NJ, USA  2000  2003  Professor (C3), HU Berlin  2003  2006  Associate Professor, University of Madison, WI, USA  2006  2007  Professor, University of Madison, WI, USA  Since 2007  Professor (W3), University of Bonn 


Super String Theory is a mayor attempt to unify gauge theories with quantum gravity. Compactifications of string theory on varieties with special holonomy including calibrated submanifolds leads to quantum theories in various dimensions. Mathematical well defined subsectors of these theories are the topological string and field theories. Their correlators determine topological invariants of the geometric setting. Often are different physical formulations with different manifest symmetries and duality symmetries among them available. Based on these we extended the methods to calculate the correlators exactly, such as mirror symmetry, the string/gauge theory correspondence, the modular and the integrable system approach. In particular using the string/gauge theory correspondence we provided with the topological vertex and the topological recursions two major tools, which are widely in use. We used mirror symmetry and the modular approach to obtain high genus amplitudes on compact CalabiYau spaces and showed that the all genus topological string amplitudes on elliptically fibred CalabiYau spaces can be expressed in terms of meromorphic Jacobi forms.


DFG Project KL2271/11: “Exakte Methoden in Eich und StringTheorien”
Bethe Center for Theoretical Physics
Member
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal Investigator


Research Area C A relation between the modular anomaly of topological string theory on elliptic CalabiYau spaces and the chiral anomaly of certain six dimensional superconformal theories was discovered recently [1,2,3,4]. As was shown in the eighties, six is the maximal dimension in which these remarkable superconformal symmetries can be realized in quantum theories. The theories are self dual, couple to string degrees of freedom, do not admit a Langrangian description and stayed therefore elusive despite the potential to obtain a classification of lower dimensional theories by dimensional reduction. With the new techniques in topological string theory one can obtain information of their spectrum of BPS states [5]. Another application of the refined topological string that we pursue is the study of nonperturbative effects in quantum systems using resurgence. On the geometrical side our group investigates more generally the effective action of four dimensional field theories obtained by dimensional reduction of maximal supersymmetric theories on special holonomy manifolds or manifolds with Gstructures. Currently under investigation is a promising class of manifolds with G2 holonomy obtained using the twisted gluing construction proposed by Kovalev. 


[ 1] Minxin Huang, Sheldon Katz, Albrecht Klemm
Topological string on elliptic CY 3folds and the ring of Jacobi forms J. High Energy Phys. (10): 125, front matter+78 2015[2] Babak Haghighat, Albrecht Klemm, Guglielmo Lockhart, Cumrun Vafa
Strings of minimal 6d SCFTs Fortschr. Phys. , 63: (5): 294322 2015 [ 3] Minxin Huang, Sheldon Katz, Albrecht Klemm
Elliptically fibered CalabiYau manifolds and the ring of Jacobi forms Nuclear Phys. B , 898: : 681692 2015[ 4] Jie Gu, Minxin Huang, AmirKian KashaniPoor, Albrecht Klemm
Refined BPS invariants of 6d SCFTs from anomalies and modularity J. High Energy Phys. (5): 130, front matter+61 2017[5] Jie Gu, Albrecht Klemm, Marcos Mariño, Jonas Reuter
Exact solutions to quantum spectral curves by topological string theory J. High Energy Phys. (10): 025, front matter+68 2015 [6] A. Klemm, D. Maulik, R. Pandharipande, E. Scheidegger
NoetherLefschetz theory and the YauZaslow conjecture J. Amer. Math. Soc. , 23: (4): 10131040 2010 [ 7] Mina Aganagic, Albrecht Klemm, Marcos Mariño, Cumrun Vafa
The topological vertex Comm. Math. Phys. , 254: (2): 425478 2005[ 8] Vincent Bouchard, Albrecht Klemm, Marcos Mariño, Sara Pasquetti
Topological open strings on orbifolds Comm. Math. Phys. , 296: (3): 589623 2010[ 9] M.x. Huang, A. Klemm, S. Quackenbush
Topological string theory on compact CalabiYau: modularity and boundary conditions Homological mirror symmetry of Lecture Notes in Phys. : 45102 Publisher: Springer, Berlin 2009[ 10] Jie Gu, Hans Jockers, Albrecht Klemm, Masoud Soroush
Knot invariants from topological recursion on augmentation varieties Comm. Math. Phys. , 336: (2): 9871051 2015[ 11] Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil, Eric Zaslow
Mirror symmetry With a preface by Vafa of Clay Mathematics Monographs : xx+929 Publisher: American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA 2003 ISBN: 0821829556[ 12] S. Katz, A. Klemm, R. Pandharipande
On the motivic stable pairs invariants of K3 surfaces K3 surfaces and their moduli With an appendix by R. P. Thomas of Progr. Math. : 111146 Publisher: Birkhäuser/Springer, [Cham] 2016 DOI: 10.1007/9783319299594_6




• Zeitschrift für Naturforschung A


1998  2001  Heisenberg Fellow, IAS, Princeton, NJ, USA  2006  Andrejewski Lecturer, Berlin and Potsdam  2006  Simons Professor, Berkeley, CA, USA  2011  Guest Professor, École Normale Supérieure, Paris, France  2014  Frederick W. and Lois B. Gehring Visiting Professor, LSA Mathematics, University of Michigan, Ann Arbor, MI, USA  2017  Visiting Professor, École Normale Supérieure, Paris, France  2018  Visiting Professor, MSRI, Berkeley, CA, USA 


2009  Minicourse “The Topological Vertex and its Applications”, Instituto Superior Técnico, Lisbon, Portugal  2009  Minicourse “Direct Integration in Topological String Theory”, Workshop on “Geometry and Physics”, Chendgu, China  2010  Minicourse “Topological Strings, Modularity and nonperturbative Physics”, Erwin Schroedinger Institute, Vienna, Austria  2011  Minicourse “Topological Gauge and String theories”, ENS Paris, France  2011  “Direct integration in General Omega Backgrounds”, Banff, AB, Canada  2011  StringMath, Philadelphia, PA, USA  2014  StringMath, Edmonton, AB, Canada  2015  “Topological string on elliptic CY 3folds and the ring of weak Jacobi forms”, in “Motivic invariants related to K3 and abelian geometries”, Berlin  2015  “Elliptically fibred CalabiYau and the ring of weak Jacobi Forms”, in Workshop of “Moduli Spaces in algebraic Geometry and Physics”, Tianjin, China  2016  “Ftheory at 20”, California Institute of Technology, CA, USA  2016  “Jacobi Forms and Curve Counting”, at the Workshop “Curves on surfaces and 3folds”, Centre Interfacultaire Bernoulli CIB Lausanne, Switzerland  2016  “Topological String and Jacobi Forms”, Workshop on “Geometric Correspondence of Gauge Theories”, Trieste, Italy 


2003  University of Colorado, Boulder, CO, USA 


Ralph Blumenhagen (2002), now Permanent Staff Member, Max Planck Institute for Physics, Munich


Babak Haghighat (2009): “On Topological String Theory with CalabiYau Backgrounds”,
now Postdoc, Harvard University, MA, USA
Denis Klevers (2011): “Holomorphic Couplings In NonPerturbative String Compactifications”,
now Fellow, CERN, Theoretical Physics Department, Switzerland
Jie Gu (2014): “Braiding knots with topological Strings”,
now Postdoc, LPTHE ENS Paris, France


 Master theses: 5, currently 2
 Diplom theses: 4
 PhD theses: 12, currently 8


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