Antti Kupiainen

Antti Kupiainen (born 23 June 1954, Varkaus, Finland) is a Finnish mathematical physicist.

Education and career

Kupiainen completed his undergraduate education in 1976 at the Technical University of Helsinki and received his Ph.D. in 1979 from Princeton University under Thomas C. Spencer (and Barry Simon) with thesis Some rigorous results on the 1/n expansion.[1] As a postdoc he spent the academic year 1979/80 at Harvard University and then did research at the University of Helsinki. He became a professor of mathematics in 1989 at Rutgers University and in 1991 at the University of Helsinki.

In 1984/85 he was the Loeb Lecturer at Harvard. He was several times a visiting scholar at the Institute for Advanced Study.[2] He was a visiting professor at a number of institutions, including IHES, University of California, Santa Barbara, MSRI, École normale supérieure, and Institut Henri Poincaré. He was twice an invited speaker at the International Congress of Mathematicians; his ICM talks were in 1990 at Kyoto on Renormalization group and random systems and in 2010 at Hyderabad on Origins of Diffusion.

From 2012 to 2014 he was the president of the International Association of Mathematical Physics. From 1997 to 2010 he was on the editorial board of Communications in Mathematical Physics. In 2010 he received the Science Award of the city of Helsinki. He received an Advanced Grant from the European Research Council (ERC) for 2009–2014.

Research

Kupiainen works on constructive quantum field theory and statistical mechanics. In the 1980s he developed, with Krzysztof Gawedzki, a renormalization group method (RG) for mathematical analysis of field theories and phase transitions for spin systems on lattices.[3][4][5][6][7] In addition in the 1980s he and Gawedzki did research on conformal field theories, in particular the WZW (Wess-Zumino-Witten) model. Then he was involved in applications of the RG method to other problems in probability theory, the theory of partial differential equations (for example, pattern formation, blow up, and moving fronts in asymptotic solutions of nonlinear parabolic differential equations),[8][9] and dynamical systems (e.g. KAM theory[10]).

As an application of RG in probability theory, Kupiainen and Jean Bricmont showed that the random walk with asymmetric random transition probabilities in three or more spatial dimensions leads to diffusion (and therefore time-irreversible behavior).[11] Kupiainen continued his investigations into the origins of diffusion and time-irreversibility in various model systems (such as coupled chaotic mappings and weakly coupled anharmonic oscillations).[12]

He also did research on the turbulent flow problem in hydrodynamic models.[13] With Gawedzki, he established "anomalous inertial range scaling of the structure functions for a model of homogeneous, isotropic advection of a passive scalar by a random vector field." (Kolmogorov's theory of homogeneous turbulence breaks down for a particular model.)[14][15]

In 1996 Kupianien and Bricmont applied high temperature methods from statistical mechanics to chaotic dynamical systems.[16]

References

  1. ↑ Antti Kupiainen at the Mathematics Genealogy Project
  2. ↑ Kupiainen, Antti | Institute for Advanced Study
  3. ↑ K. Gawedzki, Kupiainen Massless Lattice Theory: Rigorous Control of a Renormalizable Asymptotically Free Model, Commun. Math. Phys., vol. 99, 1985, pp. 197–252 doi:10.1007/BF01212281
  4. ↑ Gawedzki, Kupiainen Gross-Neveu Model Through Convergent Perturbation Expansions, Commun. Math. Phys., vol. 102, 1985, pp. 1–30 doi:10.1007/BF01208817
  5. ↑ Gawedzki, Kupiainen Renormalization of a Non-Renormalizable Quantum Field Theory, Nuclear Physics B, vol. 262, 1985, pp. 33–48 doi:10.1016/0550-3213(85)90062-8
  6. ↑ Gawedzki, Kupiainen Renormalizing the nonrenormalizable, Phys. Rev. Lett., vol. 55, 1985, pp. 363–365 doi:10.1103/PhysRevLett.55.363
  7. ↑ J. Bricmont, Kupiainen Phase Transition in the 3d Random Field Ising model, Commun. Math. Phys., vol. 116, 1987, pp. 539-572 doi:10.1007/BF01224901
  8. ↑ J. Bricmont, G. Lin, Kupiainen Renormalization group and asymptotics of solutions of nonlinear parabolic equations, Comm. Pure Applied Math., vol. 47, 1994, pp. 893-922 arxiv.org preprint
  9. ↑ Renormalization of Partial Differential Equations, in Vincent Rivasseau (ed.) Constructive Physics, Springer Verlag 1995, pp. 83-117
  10. ↑ J. Bricmont, K. Gawedzki, Kupiainen KAM theorem and quantum field theory, Comm. Math. Phys., Band 201, 1999, pp. 699- 727, arxiv.org preprint
  11. ↑ Bricmont, Kupiainen Random Walks in Asymmetric Random Environments, Commun. Math. Phys., vol. 142, 1991, pp. 345-420 doi:10.1007/BF02102067
  12. ↑ See Kupiainen's lecture at the ICM 2010 in Hyderabad.
  13. ↑ Kupiainen Lessons for Turbulence, Geometric and Functional Analysis, 2000, pp. 316-333 doi:10.1007/978-3-0346-0422-2_11
  14. ↑ Gawedzki, Kupiainen Anomalous Scaling for Passive Scalar, Phys. Rev. Lett., vol. 75, 1995, p. 3834. Kupiainen Some mathematical problems of passive advection, Contemporary Mathematics, vol. 217, 1998, pp. 83-99, Arxiv
  15. ↑ Gawedzki, Kupiainen Universality in turbulence: an exactly soluble model, Lecture 1995
  16. ↑ Bricmont, Kupiainen High temperature expansions and dynamical systems, Comm. Math. Phys., vol. 178, 1996, pp. 703-732 doi:10.1007/BF02108821

External links

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