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DTSTART;TZID=America/New_York:20251006T163000
DTEND;TZID=America/New_York:20251006T173000
DTSTAMP:20260513T130825
CREATED:20250914T165359Z
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UID:10003794-1759768200-1759771800@cmsa.fas.harvard.edu
SUMMARY:Geometry of dimer models
DESCRIPTION:Colloquium \nSpeaker: Alexei Borodin\, MIT \nTitle: Geometry of dimer models \nAbstract: Random dimer coverings of large planar graphs are known to exhibit unusual and visually apparent asymptotic phenomena that include formation of frozen regions and various phases in the unfrozen ones. For a specific family of subgraphs of the (periodically weighted) square lattice known as the Aztec diamonds\, the asymptotic behavior of dimers admits a precise description in terms of geometry of underlying Riemann surfaces. The goal of the talk is to explain how the surface structure manifests itself through the statistics of dimers. Based on joint works with T. Berggren and M. Duits. \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium_10625/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.6.2025.png
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DTSTART;TZID=America/New_York:20251027T163000
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CREATED:20250911T192619Z
LAST-MODIFIED:20250911T193132Z
UID:10003793-1761582600-1761586200@cmsa.fas.harvard.edu
SUMMARY:Rigidity\, expansion and polytopes
DESCRIPTION:Colloquium \nSpeaker: Eran Nevo (Hebrew University of Jerusalem) \nTitle: Rigidity\, expansion and polytopes \nAbstract: Given a graph G and an embedding of its vertices in R^d\, what continuous motions of the vertices preserve all edge lengths? Clearly all motions induced by an isometry of R^d do\, these are the trivial motions; are there any others? If the answer is NO for all (equivalently\, for one) generic embedding\, G is called d-rigid. \nWhat are the d-rigid graphs? \nThis problem has been extensively studied since the 70s\, and is still widely open for d≥3. It is studied mainly from algebraic geometry and combinatorial points of view. Variants of it\, especially in dimensions 2 and 3\, are of importance also beyond mathematics\, e.g. in structural engineering\, computational biology and more. \nI will focus on a quantitative version of rigidity via spectral analysis of the related stiffness matrix\, including the construction of “rigidity expanders”\, generalizing expander graphs. Higher dimensional notions of rigidity and of stiffness matrices\, and their relation to the study of polytopes\, will be addressed too.
URL:https://cmsa.fas.harvard.edu/event/colloquium_102725/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.27.2025.png
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