Math Nuggets

Math nuggets are brief summaries describing all or some portion of the research accomplished during a specific ICERM program, usually written by one or more program organizer.


Polygon Iterations

Polygon Iterations

In the Fall of 2013, ICERM had a semester program on experiental geometry, topology, and dynamics. One of the many projects undertaken during this semester was the study of polygon iterations - geometrically defined maps on the space of polygons.

Fall 2013 Semester Program on "Low-dimensional Topology, Geometry, and Dynamics"

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From the Clinic to Partial Differential Equations and Back: Emerging challenges for Cardiovascular Mathematics

From the Clinic to Partial Differential Equations and Back: Emerging challenges for Cardiovascular Mathematics

In recent years, there have been great advances in mathematical and computational modeling of cardiovascular phenomena. The ultimate goal has been to develop predictive mathematical tools that can be used in medical decision-making and treatment. There have been notable successes in some areas; for example, extensive numerical simulation is used in some hospitals to plan pediatric heart surgery. However, further progress is needed for the use of mathematics-based clinical methods to become widespread and routine. Additional advances will require close communication and collaboration between mathematical scientists and physiologists in order to guide further developments most effectively.

Spring 2014 Topical Workshop - From the Clinic to Partial Differential Equations and Back: Emerging challenges for Cardiovascular Mathematics

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Limits of permutations

Limits of permutations

How many permutations on n elements have a relative fraction of some fixed pattern? The research spawned by this and related questions gave rise to some new variational principles and a new context for phase transitions, inspired by the ICERM Spring 2015 program, Emergent Phenomena and Phase Transitions.

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