Analytic Low-Dimensional Dynamics:
a Celebration of Misha Lyubich's
60th Birthday
May 27 - June 7, 2019 • Fields Institute
Organizers: Anna Benini (Universitat de Barcelona), Tanya Firsova (Kansas State University),
Petr Makienko (Instituto de Matemáticas, Unidad Cuernavaca), Scott Sutherland (Stony Brook University),
Michael Yampolsky (University of Toronto)
Analytic dynamics, a subject that has experienced
explosive growth over the last few decades,
studies the iteration of analytic maps, either real
or complex, and the flows of systems of analytic
differential equations, a closely related area. In this
setting, many function-theoretic, geometric, and
number-theoretic methods come into play. This
conference took stock of the current activity in the
field and charted new directions, and offered the
chance to celebrate the 60th birthday of Misha
Lyubich, one of the foremost experts in the field,
whose vision has led to much of its development.
The massive scale of the conference was a
tribute to the major impact that complex-
analytic methods have had on the study of
low-dimensional dynamics over the last few
decades. The two-week conference featured 40
invited speakers and attracted more than 150
visitors from over 20 countries. The conference
structure featured talks by senior researchers,
shorter talks from emerging researchers, poster
sessions and unstructured time to foster informal
mathematical exchange between participants.
A beautiful synthesis of techniques has emerged,
highlighting the interconnections between seemingly
disjointed topics: the structure of the Mandelbrot
set, the stochastic properties of a typical interval
map, Feigenbaum-Coullet-Tresser universality
and renormalization, among many others.
It is difficult to overstate the relevance of
Lyubich’s contribution to the field, both as a
brilliant mathematician and as a charismatic
leader who formed and influenced several of the
most successful young researchers in the current
generation, including his students and the many
postdoctoral fellows who worked with him. At the
Fields Institute in 2005-2006, Lyubich organized
two notable semester-long programs which
helped to launch many careers. Several conference
participants engaged in those programs as postdocs
or graduate students. Many of those he influenced
spoke at the conference, and their talks spanned
a wide range of topics inspired by Lyubich’s work:
complex dynamics in one and several variables,
Ising models, and holomorphic foliations.
A significant group of the conference’s participants
represent the new crop of young mathematicians,
current postdocs and graduate students who will
similarly benefit in their research progress from
seeing the field through the eyes of the experts,
and the wealth of
Pictured: Participants in the Analytic
open questions
Dynamics
and problems that Low-Dimensional
Conference, including Misha
were discussed.
Lyubich (front row, 9th from right).
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