Workshop in Analytic and Probabilistic Combinatorics (16w5048)

Arriving in Banff, Alberta Sunday, October 23 and departing Friday October 28, 2016

Organizers

(University of Florida)

(Purdue University)

(Universidad Nacional Autonoma de Mexico)

Objectives

The workshop will bring two well-established, but mostly separate groups of researchers together. Each of these groups have their own annual workshops and conferences, which are usually not attended by many members of the other group. There is a substantial potential to increase collaboration between these two circles of researchers, and our workshop aims to initiate such synergy. ​

One of the two groups in question is that of Analytic Combinatorialists. Researchers working in this field often attend conferences like the International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA; held since 1993), the Meeting on Analytic Algorithmics and Combinatorics (ANALCO; held since 2004; now held as a special session within the ACM-SIAM Symposium on Discrete Algorithms (SODA)), and the Latin American Theoretical Informatics Symposium (LATIN; held since 1992). The methods include analytic (complex-valued) approaches, such as analyzing the singularities of the relevant generating functions; symbolic computation (e.g., in Maple, Mathematica, or Sage); multivariate methods; mathematical transforms (Fourier, Laplace, Mellin); etc. One of the main goals of analytic combinatorics is the precise characterization of exact or asymptotic information about enumerating combinatorial objects or about the mean, variance, distribution, etc., of randomly distributed objects. Since modern-day computing platforms allow researchers throughout the sciences to routinely study very large objects, the study of asymptotic properties of objects is more relevant today than ever before.

The other group is that of Probabilistic Combinatorialists. Regularly scheduled conferences attended by this group include the Southeastern International Conference on Combinatorics, Probability and Computing, the Cumberland Combinatorics Conference, the Polish Combinatorics Conference, and the Atlanta Lecture Series in Combinatorics and Graph Theory. Here the objects of study often come from Extremal Combinatorics or Graph Theory, or Computational Complexity Theory. The methods used can come from classic or modern probability theory, including the classic "Probabilistic Method" introduced by Paul Erdös in the 1930s. Existence proofs are a common feature in the work of this group, and so are constructive proofs and efficient algorithms. As the well consolidated connection between combinatorics and ergodic theory, i.e. the study of dynamics systems together with invariant probability measures, keeps on growing, we expect a representation of people working in the intersection of these two fields.