Applications of the Renormalization group

In the last half century, Renormalization Group (RG) theory based on multiscale analysis has become a central topic both in theoretical and mathematical physics. Not only it has represented a powerful technical tool, but also it has changed deeply our view of many physical phenomena: it has provided a unifying language for many apparently unrelated fields, which were showed to exhibit unexpected similarities in their underlying mathematical structure.

Aim of this workshop is to group together several researchers with different interests and working in possibly different and apparently unrelated areas, but all using RG ideas and methods. The similarity of problems belonging to different areas will emerge and, hopefully, deep insigths and new points of view will be fruitfully obtained through this exchange, maybe leading to new solutions or deeper understanding of open problems.

The topics will include RG applications belonging to the following fields:

(1) Condensed Matter (Fermionic systems, Fermi or Luttinger liquids, superconductivity, quantum phase transitions).
(2) Dynamical systems (KAM theory, break-up of invariant tori, quasi-periodic cocycles, quasi-periodic solutions in nonlinear PDE systems, and other small divisor problems).
(3) Quantum Field Theory (Gauge theories, constructive QFT, noncommutative QFT, sigma models, mass generation).
(4) Quantum Mechanics (QED for nonrelativistic matter, spectral problems, diffusion, Schrödinger equation).
(5) Ricci Flows (Poincare' conjecture).
(6) Statistical mechanics (epsilon-expansion, universality versus nonuniversality, lattice spin models, self-avoiding walks).

Aim of the program is to bring together experts in Renormalization, and to give them the opportunity to communicate and discuss for some time at the Institute. We plan a series of talks and lectures. In addition three workshops will be organized during the program:

A: Renormalization Group Flow and Ricci Flow (October 22nd - 26th)
(Participants: Carfora, Chatzistavrakidis, Gentile, Grigor'yan, Hamilton, Huisken, Kopper, Mastropietro, McCann, Oliynyk, Salmhofer, Schomerus, Villani, Wilking, Zamolodchikov, Zoupanos)

B: Renormalization in Dynamical Systems (October 29th - November 3rd)

C: Renormalization in Quantum Field Theory, Statistical Mechanics and Condensed Matter (November 12th - 17th).

The program will be followed by an ESF-Workshop on Noncommutative Quantum Field Theory (November 26th to 30th; participants: Aschieri, Bahns, Balachandran, Barrett, Bietenholz, O'Connor, Dolan, Freidel, Gurau, Iochum, Lizzi, Madore, Presnajder, Rivasseau, Schupp, Szabo, Watamura, Wulkenhaar, Vitale). Some introductory courses to this subject will be given by R. Szabo and J. Barret in the last week of the program.

The following people people have already agreed to participate:

Volker Bach (Mainz)
Joao Carlos Alves Barata (Sao Paulo)
John Barrett (Nottingham)
Michele Bartucelli (Surrey)
Giosi Benfatto (Roma)
Henning Bostelmann (Göttingen)
Henk Broer (Groningen)
Mauro Carfora (Pavia)
Thanassis Chatzistavrakidis(Athens)
Claudio D'Antoni (Roma)
Walter De Siqueira Pedra (Leipzig)
Margherita Disertori (Rouen)
Hakan Eliasson (Paris)
Laszlo Erdoes (München)
Alvaro Ferraz (Brasilia)
Krzysztof Gawedzki (Lyon)
Guido Gentile (Roma)
Alessandro Giuliani (Princeton)
Alexander Grigor'yan(London)
Harald Grosse (Vienna)
Richard Hamilton (Ithaca)
Gerhard Huisken (Potsdam)
Yuji Igarashi (Niigata)
Hans Rudolph Jauslin (Dijon)
Horst Knoerrer (Zurich)
Peter Kopietz (Frankfurt)
Christoph Kopper (Palaiseau)
Dirk Kreimer (Boston)
Raphael Krikorian (Paris)
Joao Lopes Dias (Lisboa)
Joszef Loerinczi (München)
Jacques Magnen (Palaiseau)
Vieri Mastropietro (Roma)
Robert J. McCann (Toronto)
Moukadas Missarov (Kazan)
Pronob Mitter (Montpellier)
Gerardo Morsella (Pisa)
Pierre Moussa (Saclay)
Todd Oliynyk (Edmonton)
Alessandro Pizzo (Zürich)
Michela Procesi (Roma)
Vincent Rivasseau (Orsay)
Vered Rom-Kedar (Rehovot)
Manfred Salmhofer (Leipzig)
Volker Schomerus (Hamburg)
Erhard Seiler (München)
Thomas Spencer (Princeton)
Cedric Villani (Lyon)
Burkhard Wilking (Münster)
Yingfei Yi (Atlanta)
Jiangong You (Nanjing)
Alexander Zamolodchikov (Piscataway)
George Zoupanos (Athens)