The aim of this workshop is be to bring together a small group of experts from the general areas of harmonic analysis and rigorous renormalization group (RG) theory in statistical mechanics and quantum field theory in order to share ideas and hopefully make progress on some key questions in the RG program where input from harmonic analysis may prove to be critical.
As explained in the recent expository article "QFT, RG, and all that, for mathematicians, in eleven pages"
by the organizer, a bottleneck towards further progress in the area is to devise an RG framework which can handle small spatial inhomogeneities (spacedependent coupling "constants") and this may need refined tools from harmonic analysis. The goal is to understand statistical mechanics systems or random fields such as the phifour model which arises as an invariant measure for PDEs or SPDEs as recently considered by Hairer in his article on regularity structures.
One way to approach the problem is to decompose the random field in a wavelet basis. The RG amounts to the transformation from the joint probability measure for all the wavelet coefficients to the marginal one for the low frequency coefficients only. The new problem here is to understand the effect of small spatial inhomogeneities which break translation invariance, and to find the right kind of "wavelet decomposition" or timefrequency analysis one needs to use in order to have good analytic control on these inhomogeneities. In the language of the above expository article by the organizer, this is the problem of "control of deviations" over real spacetimes.
For totally disconnected spacetimes (padics), this problem has been solved recently.
Going from that simplified setting to that of real spacetimes is thematically similar to the passage from Walsh series to Fourier series, a common strategy used in harmonic analysis.
Some funding is available in order to cover travel and living expenses during the workshop, for a limited number of participants. First priority will be given to junior researchers and members of underrepresented groups.
People interested in participating in the workshop should contact the organizer at hargconf @virginia.edu.
