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

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.

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 Kupiainen and Bricmont applied high temperature methods from statistical mechanics to chaotic dynamical systems.^{[16]}

**^**Antti Kupiainen at the Mathematics Genealogy Project**^**Kupiainen, Antti | Institute for Advanced Study**^**Gawedzki, K; Kupiainen, A (1985). "Massless lattice φ_{4}^{4}theory: Rigorous control of a renormalizable asymptotically free model".*Communications in Mathematical Physics*.**99**(2): 197–252. Bibcode:1985CMaPh..99..197G. doi:10.1007/BF01212281. S2CID 121722023.**^**Gawȩdzki, K; Kupiainen, A (1985). "Gross-Neveu model through convergent perturbation expansions".*Communications in Mathematical Physics*.**102**(1): 1–30. Bibcode:1985CMaPh.102....1G. doi:10.1007/BF01208817. S2CID 122720270.**^**Gawȩdski, K; Kupiainen, A (1985). "Renormalization of a non-renormalizable quantum field theory".*Nuclear Physics B*.**262**(1): 33–48. Bibcode:1985NuPhB.262...33G. doi:10.1016/0550-3213(85)90062-8.**^**Gawedzki, K; Kupiainen, A (1985). "Renormalizing the nonrenormalizable".*Physical Review Letters*.**55**(4): 363–365. Bibcode:1985PhRvL..55..363G. doi:10.1103/PhysRevLett.55.363. PMID 10032331.**^**Bricmont, J; Kupiainen, A (1988). "Phase transition in the 3d random field Ising model".*Communications in Mathematical Physics*.**116**(4): 539–572. Bibcode:1988CMaPh.116..539B. doi:10.1007/BF01224901. S2CID 117021659.**^**Bricmont, J; Kupiainen, A; Lin, G (1993). "Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations". arXiv:chao-dyn/9306008. Bibcode:1993chao.dyn..6008B.`{{cite journal}}`

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(help)**^**Rivasseau, Vincent, ed. (1995). "Renormalization of Partial Differential Equations".*Constructive Physics*. Springer Verlag. pp. 83–117. ISBN 9783662140611.**^**Bricmont, J; Kupiainen, A; Lin, G (1999). "KAM Theorem and Quantum Field Theory".*Communications in Mathematical Physics*.**201**(3): 699–727. arXiv:chao-dyn/9807029. Bibcode:1999CMaPh.201..699B. CiteSeerX 10.1.1.139.8766. doi:10.1007/s002200050573. S2CID 15995164.**^**Bricmont, J; Kupiainen, A (1991). "Random walks in asymmetric random environments".*Communications in Mathematical Physics*.**142**(2): 345–420. Bibcode:1991CMaPh.142..345B. doi:10.1007/BF02102067. S2CID 121487464.**^**See Kupiainen's lecture at the ICM 2010 in Hyderabad.**^**Kupiainen, Antti (2010). "Lessons for Turbulence".*Visions in Mathematics*. pp. 316–333. doi:10.1007/978-3-0346-0422-2_11. ISBN 978-3-0346-0421-5.**^**Bricmont, J; Kupiainen, A; Lin, G (1995). "Anomalous Scaling of the Passive Scalar".*Physical Review Letters*.**75**(21): 3834–3837. arXiv:chao-dyn/9506010. Bibcode:1995PhRvL..75.3834G. doi:10.1103/PhysRevLett.75.3834. PMID 10059743. S2CID 14446225.**^**Gawedzki, K; Kupiainen, A; Lin, G (1996). "University in turbulence: An exactly solvable model".*Low-Dimensional Models in Statistical Physics and Quantum Field Theory*. Lecture Notes in Physics. Vol. 469. pp. 71–105. arXiv:chao-dyn/9504002. doi:10.1007/BFb0102553. ISBN 978-3-540-60990-2. S2CID 18589775.**^**Bricmont, J; Kupiainen, A (1996). "High temperature expansions and dynamical systems".*Communications in Mathematical Physics*.**178**(3): 703–732. arXiv:chao-dyn/9504015. Bibcode:1996CMaPh.178..703B. doi:10.1007/BF02108821. S2CID 8167255.

- Kupiainen's homepage at the University of Helsinki
- Kupiainen's alternate homepage at the U. of Helsinki, dealing with his research
- An Introduction to Liouville Theory, Talk at Institute for Advanced Study, may 2018