Text Box: We are pleased to welcome Michael Freedman to the Theory Group at Microsoft Research. Before joining us here, Mike was Charles Lee Powell Professor of Mathematics at UCSD. Mike is an incredible mathematician. The work for which he is best known is the solution of the long-standing Poincare conjecture in four dimensions, for which he received the Fields Medal, the highest honor in mathematics. Mike has received numerous other awards and honors including Sloan and Guggenheim Fellowships, a MacArthur Fellowship and the National Medal of Science. He is an elected member of the National Academy of Sciences, the American Academy of Arts and Sciences, and the New York Academy of Sciences. Mike has recently begun to work on fundamental problems in the theoretical computer science, in particular on the P/NP question and on non-standard models of computation.  

 

 

 

   Michael H. Freedman

    Researchers:

      Chetan Nayak

      Kevin Walker   

    Postdoc 2004

      Joost Slingerland

    Publications

  • An extended Hubbard model with ring exchange: a route to a non-abelian topological phase. Phys. Rev. Lett. 94, 066401 Feb 2005.
     149KB  

  • On the Asymtotics of Quantum SU(2) Representations of Mapping Class Groups. Forum Mathematicum. pp.1-12 3.05.05  To be published:  218KB

  • Approximate Counting and Quantum Computation. Combinatorics, Probability, and Computing (2005) 000,000. To be published. 252KB  

  • Universal Manifold Pairings and Positivity. arXiv: math.GT/0503054  146KB  

  • Reflection positivity, rank connectivity, and homomorphism of graphs. arXiv: math.CO/0404468  197KB  

  • Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State. arXiv: cond-mat/0412343 202KB  
  • A Line of Critical Points in 2+1 Dimensions: Quantum Critical Loop Gases and Non-Abelian Gauge Theory.  arXiv: cond-mat/0408257 113KB  
  • Non-abelian topological phases in an extended Hubbard model.  arXiv:cond-mat/0309120 v2 5 Sep 2003. 234KB  
  • Covering a nontaming knot by the unlink. 401KB  
  • A Class of P, T-Invariant Topological Phases of Interacting Electrons. Annals of Physics. Vol 310, Issue 2, April 2004, pg 428-492. 850KB  
  • A magnetic model with a possible Chern-Simons phase.   With an appendix by F. Goodman and H. Wenzl. Comm. Math. Phys. 234 (2003), no. 1, 129—183. 704KB
  • Diameters of Homogeneous Spaces. Math. Res. Lett. 10 (2003), no. 1, 11--20.
  • Topological quantum computation. Mathematical challenges of the 21st century (Los Angeles, CA, 2000). Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 1, 31--38. 329KB
  • Quantum SU(2) faithfully detects mapping class groups modulo center.  Geom. Topol. 6 (2002), 523--539.180KB
  • Z 2 -Systolic Freedom and Quantum Codes. Mathematics of Quantum Computation. , 287--320, Comput. Math. Ser., Chapman & Hall/CRC, Boca Raton, FL, 2002.
  • The two-eigenvalue problem and density of Jones representation of braid groups. Comm. Math. Phys.228 (2002),no.1,177 –199. 183KB
  • A modular functor which is universal for quantum computation.Comm.Math.Phys.227 (2002),no.3,605 –622. 148KB
  • Simulation of topological field theories by quantum computers.Comm.Math.Phys.227 (2002), no.3, 587 –603. 281KB
  • Poly-locality in quantum computing.Found.Comput.Math.2 (2002), no.2 ,145 –154. 94KB
  • Projective plane and planar quantum codes. Found. Comput.Math.1 (2001),no.3,325 – 332.
  • Quantum computation and the localization of modular functors. Found. Comput.Math.1 (2001),no.2,183 –204.
  • Extension of incompressible surfaces on the boundaries of 3-manifolds.Pacific J. Math. 194 (2000), no.2, 335 –348. 165KB
  • Z 2 -systolic-freedom. Proceedings of the Kirbyfest (Berkeley,CA,1998),113 –123 (electronic), Geom. Topol. Monogr., 2, Geom.Topol.Publ.,Coventry,1999.270KB
  • Zeldovich’s neutron star and the prediction of magnetic froth. The Arnoldfest (Toronto,ON,1997),165 –172,Fields Inst.Commun.,24,Amer.Math.Soc., Providence, RI, 1999. 174KB
  • K -sat on groups and undecidability. STOC ’98 (Dallas,TX), 572 –576, ACM, New York,1999.
  • Topological views on computational complexity. Proceedings of the International Congress of Mathematicians, Vol.II (Berlin,1998).Doc.Math.1998 ,Extra Vol. II, 453 –464. 219KB
  • Elder siblings and the taming of hyperbolic 3 – manifolds. Ann. Acad. Sci. Fenn. Math. 23 (1998),no.2,415 – 428. 193KB
  • P/NP, and the quantum field computer. Proc. Natl. Acad. Sci. USA 95 (1998), no. 1, 98—101. 243KB  
  • Limit, logic, and computation. Proc. Natl. Acad. Sci. USA 95 (1998), no. 1, 95—97. 208KB  
  • Kneser-Haken finiteness for bounded 3 – manifolds locally free groups, and cyclic covers. Topology 37 (1998),no.1,133 –147.
  • Betti number estimates for nilpotent groups. Fields Medallists ’lectures,413 –434,World Sci.Ser.20th Century Math.,5,World Sci. Publishing, River Edge,NJ,1997.
  • Percolation on the projective plane.Math.Res.Lett.4 (1997),no.6,889 –894.

     To search for other publications, please go to: http://research.microsoft.com/pubs/ or to request copies contact Rosa Teorell.

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