Antti Kupiainen

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

Life

Kupiainen graduated from Helsinki University of Technology in 1976 and received his PhD from Princeton University in 1979 with Thomas C. Spencer (and Barry Simon ) ( Some rigorous results on the 1 / n expansion ). As a post-doctoral student he was at Harvard University in 1979/80 and then researched at the University of Helsinki. In 1989 he became professor of mathematics at Rutgers University , which he remained until 1998 when he became a Visiting Distinguished Professor there. From 1991 he was a professor at the University of Helsinki , since 1999 as an academy professor.

In 1984/85 he was a Loeb Lecturer at Harvard. From 1987 he was a regular at the Institute for Advanced Study . Among other things, he was visiting scholar at IHES (from 1979 to 2000 regularly), at the University of California, Santa Barbara , at MSRI , the École normal supérieure and the Institut Henri Poincaré . He was invited speaker at the International Congress of Mathematicians in Kyoto in 1990 ( Renormalization group and random systems ) and in 2010 in Hyderabad (India) ( Origins of Diffusion ).

In 2011 he became 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 Helsinki City Science Prize. From 2009 to 2014 he received an Advanced Grant from the European Research Council (ERC). In 2016 he gave a plenary lecture at the European Congress of Mathematicians (ECM) in Berlin (Quantum fields and probability).

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He dealt with constructive quantum field theory and statistical mechanics and in the 1980s he developed a renormalization group method (RG) for the strict treatment of field theories and phase transitions for spin systems on the lattice. In addition, from the 1980s he dealt with conformal field theories , especially WZW models (Wess-Zumino-Witten), also with Gawedzki. He then applied the RG method to other problems in probability theory, with partial differential equations (e.g. pattern formation, blow up and moving fronts in asymptotic solutions of nonlinear parabolic differential equations ) and dynamic systems ( e.g. KAM theory ).

As an application of the RG in probability theory, he and Jean Bricmont showed that random movement (random walk) with asymmetrical random transition probabilities in three or more spatial dimensions leads to diffusion, i.e. irreversible behavior in time. He continued his research on the origins of diffusion and irreversibility in various model systems (such as coupled chaotic maps and weakly coupled anharmonic oscillators).

He also studied the turbulence problem in hydrodynamic models. For example, together with Krzysztof Gawedzki , he showed that the Kolmogorow theory of homogeneous turbulence collapses when advecting a passive scalar in an exactly solvable model (random vector fields) (anomalous scaling behavior).

In 1996, with Bricmont, he applied high-temperature developments from statistical mechanics to chaotic dynamic systems.

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ K. Gawedzki, Kupiainen Massless Lattice Theory: Rigorous Control of a Renormalizable Asymptotically Free Model , Commun. Math. Phys., Vol. 99, 1985, pp. 197-252
  3. ↑ Gawedzki, Kupiainen Gross-Neveu Model Through Convergent Perturbation Expansions , Commun. Math. Phys., Vol. 102, 1985, pp. 1-30
  4. ↑ Gawedzki, Kupiainen Renormalization of a Non-Renormalizable Quantum Field Theory , Nuclear Physics B, Volume 262, 1985, pp. 33-48
  5. ↑ Gawedzki, Kupiainen Renormalizing the nonrenormalizable , Phys. Rev. Lett., Vol. 55, 1985, pp. 363-365
  6. ^ J. Bricmont, Kupiainen Phase Transition in the 3d Random Field Ising model , Commun. Math. Phys., Vol. 116, 1987, pp. 539-572
  7. ↑ 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
  8. ↑ Renormalization of Partial Differential Equations , in Vincent Rivasseau (Ed.) Constructive Physics , Springer Verlag 1995, pp. 83-117
  9. ↑ J. Bricmont, K. Gawedzki, Kupiainen KAM theorem and quantum field theory , Comm. Math. Phys., Vol. 201, 1999, pp. 699-727, Arxiv
  10. ↑ Bricmont, Kupiainen Random Walks in Asymmetric Random Environments , Commun. Math. Phys., Vol. 142, 1991, pp. 345-420
  11. ↑ See his lecture at the ICM 2010 in Hyderabad
  12. ↑ Kupiainen Lessons for Turbulence , Geometric and Functional Analysis, 2000, pp. 316–333
  13. ↑ Gawedzki, Kupiainen Anomalous Scaling for Passive Scalar , Phys. Rev. Lett., Vol. 75, 1995, pp. 3834. Kupiainen Some mathematical problems of passive advection , Contemporary Mathematics, Vol. 217, 1998, pp. 83-99, Arxiv
  14. ^ Gawedzki, Kupiainen Universality in turbulence: an exactly soluble model , lecture 1995
  15. ↑ Bricmont, Kupiainen High temperature expansions and dynamical systems , Comm. Math. Phys., Vol. 178, 1996, pp. 703-732
personal data
SURNAME Kupiainen, Antti
BRIEF DESCRIPTION Finnish mathematical physicist
DATE OF BIRTH June 23, 1954
PLACE OF BIRTH Varkaus , Finland