New Applications of Menger Curvature to Complex Analysis (16rit691)


Malabika Pramanik (UBC)

Loredana Lanzani (Syracuse University)


The Banff International Research Station will host the "New applications of Menger curvature to complex analysis" workshop in Banff from July 10, 2016 to July 17, 2016.

This Research in Team Mathematics research project will be focused on the area known
as ``Mathematical Analysis'', in particular on the problem of finding new applications
of the notion of Menger Curvature (that is, the reciprocal of the radius of the
circle joining any three given, distinct points A, B and C).

A leading theme in our team's work are the so-called ``integral formulas''. Integral
formulas are important tools for recovering information on large data sets that are located
in hard-to-reach places by collecting very small samples that are within easy reach. For
instance, integral formulas can be used to recover the temperature in the interior of a
solid body (say a tree, or even a planet) without having to probe holes in the body (that
is, in the tree example, without having to drill holes in the trunk). Instead, one measures
the temperature at surface level (say on the tree's bark) and plots these values in the
integral formula: the output will be the value of the temperature inside. One of the
novelties in our approach to these problems is that it allows to deal with objects whose
outer surface is very rough (as opposed to very smooth)

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).