Rigidity, Flexibility and Complexity of Geometric Constraint Systems (26w5578)

The Chennai Mathematical Institute will host the "Rigidity, Flexibility and Complexity of Geometric Constraint Systems" workshop in Chennai, India from January 18 to January 23, 2026. Participants will check in at the hotel starting on the evening of the Sunday prior to the start of the workshop, and check out before noon of the following Friday.

Take a triangle and a square. The triangle is rigid: its angles are determined by the lengths of its edges. The square is flexible in the plane or higher dimensional spaces: you can deform it into a diamond-shape without changing the lengths of its edges. But both are rigid in 1 dimensional space, if forced to lie on a line. How do you determine the rigidity or flexibility of more complicated structures in different, or all, dimensions?

In a related problem, one is given a subset of entries from a rectangular array and would like to infer the remaining values, given some constraints on the array. For example, assuming that the array, as a matrix, has some specific low rank, makes this problem tractable even when only surprisingly few entries are known. Such matrix completion problems are at the heart of recommendation system algorithms used by Netflix, Amazon and others.

Geometric constraint systems in general encompass these and many other problems. This workshop will focus on emerging trends in the theory of geometric constraint systems with particular focus not only on graph rigidity, but also complexity, algorithms, and topology of flexible linkage configurations. In particular the workshop will be an important opportunity to synergise the various sub-topics (graphs and matroids, algorithms and complexity theory, discrete geometry and topology) and for early career researchers to engage in the latest developments.

The Chennai Mathematical Institute (CMI) in Chennai, India, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide 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 in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta's Advanced Education