Does natural selection act on preexisting mutations, or do mutations emerge as a response to selection pressure? Salvador Luria and Max Delbrück won the Noble Prize for answering this question in 1943. Their key insight was to use fluctuations between replicates of an experiment. Under the hypothesis of spontaneous mutations, the distribution of surviving mutants over a series of replicates of their experiment has a tremendous variance/mean ratio (consistent with the data). In contrast, if mutations emerge as a result of selection pressures one would expect a Poisson distribution with variance equal to mean.

Luria and Delbrück's work foreshadowed important aspects of 21st century quantitative biology, where the study of fluctuations have played a central role. In some cases, biological insight can be gained by working in a small noise regime where Gaussian approximations are sucient. However, for many problems, such as Luria and Delbrück's experiment, it is precisely the breakdown of these approximations which carries the signature of the underlying biological mechanisms. In these problems, it is the extremal statistics which dictate macroscopic behavior.

The mathematical tools for dealing with these problems range from Large deviation theory and stable distributions. Both theories generalize the central limit theorem (and its functional analogues for stochastic processes), with the former concerning deviations beyond the usual $\sqrt{n}$ and the latter concerning the situations where variances are infinite. Fundamental mathematical progress in these areas has historically been motivated by statistical physics. Here too, extremal statistics have long been appreciated.

Now it is biology's turn to benefit from the mathematical progress made on disordered systems. This is a timely endeavor, since recent experimental advances have allowed us to probe single-cells and molecules with high resolution and take measurements across many scales. However, In the biological world, systems are not in equilibrium and assumptions about symmetry can not always be made. It is therefore non-trivial to leverage the existing literature on extremal statistics for many complex biological problems. To make progress, and do so in a way that benefits both biology and mathematics, it is essential that there be widespread communications between researchers in mathematics (pure and applied), biology and physics.

The overall goal of this workshop is strengthen the ties between researches from different backgrounds interested in biological problems involving extremal events and the underlying mathematics that emerges from these problems. In particular, we hope to facilitate interactions that generate both novel solutions to biological problems and new mathematical questions.