Exactly solvable and integrable models make pronounced appearance in mathematical physics with applications ranging from strongly correlated condensed-matter systems to holographic duality and string theory. Quasi-1D systems observed in condensed-matter and cold-atom experiments are often described by quantum integrable models.
As an example, the first picture (taken from the talk by J.-S. Caux) shows exact dynamical formfactor of 1d quantum antiferromagnet. Similar models reappear in an entirely different field of 4d gauge theories, elucidating their celebrated holographic duality. Among many uses of integrability in this context, its application to Feynman diagrams was widely discussed during the program.
The second picture (taken from the talk by F. Levkovich-Maslyuk) shows the spectrum of anomalous dimensions arising from summing up ladder diagrams for a cusped Wilson loop. Quantum integrability has inspired new developments in pure mathematics especially in algebra, representation theory and combinatorics. The dialogue between mathematics and physics was another key aspect of the program.
The conference took place between May 28th and June 1st 2018. This was the second Nordita Conference with the same concept and title. Most presenters had a strong theoretical background in physics, math or other natural sciences. Some use theory as a means to design and analyse their own experiments whereas others rely on experimental or clinical data gathered by collaborators.
During the meeting, we discussed areas where a quantitative, theoretical approach can be useful - and what are their limitations. Some of the topics that were discussed included oscillations and DNA damage, heterogeneity at the cell and patient level, understanding of drug resistance, landscapes in disease, and theoretical methods for the analysis of clinical data, which is far less homogeneous than data from natural science experiments. One noted limitation, of experimental and computational studies alike, is the inability to deal with metastasis. On the other hand, we have seen an improvement in the approaches to deal with clinical data. One example is shown in the figure above, where replicates from the same experiments appear dissimilar due to irrelevant instrument-related factors (left), but calibration with the help of Distribution-Matching Residual Networks removes this artefact (right). The figure is from Removal of batch effects using distribution-matching residual networks.
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This page was printed on 2018-07-18 from www.nordita.org
19 Jun 2018