Symplectic and Algebraic Geometry in the Statistical Physics of Polymers: October 12-16, 2015

Symplectic and Algebraic Geometry in the Statistical Physics of Polymers

Organized by Jason Cantarella, University of Georgia, Tetsuo Deguchi, Ochanomizu University, Elizabeth Denne, Washington and Lee University, Alexander Grosberg, NYU, Clayton Shonkwiler, Colorado State University.

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October 12-16, 2015

Polymer physics has a number of deep unanswered questions about ring polymers such as DNA minicircles and polymers which form more general graphs or networks. These situations have been analyzed by traditional methods in statistical physics such as scaling arguments, but there is still much to do.A ring polymer can be modeled by a random walk with equal edge lengths which returns to its start point. This is an equilateral polygon in Euclidean 3-space with a fixed number of edges. Random polygons have proved rather challenging, both computationally and theoretically, due to a lack of mathematical understanding of how the closure constraint affects the probability distribution.Independently, the algebraic and symplectic geometry communities have, over the last twenty years, developed a deep and comprehensive theory of these spaces of polygons. Their key idea is an identification of moduli spaces of polygons with Grassmannian and Stiefel manifolds, and with other toric symplectic manifolds.

This fundamentally geometric approach to studying random polygons has already lead to some significant advances, and provides a coherent theoretical and computational framework with the potential to revolutionize the field. This workshop will bring together statistical physicists and geometers to explore these new tools for analyzing random polygons and to work on extensions to more general polymer networks.

Workshop Application is now closed.

Talk Schedule


Time Title Presenter Location
9:00am Grassmannians and Random Walks Jason Cantarella SCGP 102
10:30am Coffee Break N/A SCGP Lobby
11:00am The Symplectic Geometry of Polygon Space and How to Use It Clayton Shonkwiler SCGP 102
12:15pm Lunch N/A SCGP Cafe
2:00pm Topological problems in polymer physics Alexander Grosberg SCGP 102
3:15pm Tea Time N/A SCGP Lobby
3:45pm Topological problems in polymer physics Alexander Grosberg SCGP 102


Time Title Presenter Location
9:00am The Symplectic Geometry of Polygon Spaces Rebecca Goldin SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Knots and links in the simple cubic lattice Koya Shimokawa SCGP 102
12:15pm Lunch N/A SCGP Cafe
1:00pm SCGP Weekly Talk: Zohar Komargodski (Weizmann) SCGP 102
2:00pm Invariant Theory of Spatial Polygons Dr. Ben Howard SCGP 102
3:15pm Tea Time N/A SCGP Lobby
3:45pm Sampling the Space Thick Polygons Ken Millett SCGP 102


Time Title Presenter Location
9:00am Algebraic Geometry and Combinatorics of polygon spaces Chris Manon SCGP 102
10:30am Coffee Break N/A SCGP Lobby
11:00am Statistical physics of topological polymers studied through quaternions Tetsuo Deguchi SCGP 102
12:15pm Lunch N/A SCGP Cafe
2:00pm The Geometry of Framed Path and Loop Spaces Tom Needham SCGP 102
3:15pm Tea Time N/A  SCGP Lobby
3:45pm Protein and RNA geometry. Joanna Sulkowska SCGP 102


Time Title Presenter Location
9:00am Self-Avoiding Walks: Problems and Progress Neal Madras SCGP 102
10:30am Coffee Break N/A SCGP Lobby
11:00am Pattern Theorems, Entanglement Complexity and Confinement Effects for Lattice Polymer Models Chris Soteros SCGP 102
12:15pm Lunch N/A SCGP Cafe
2:15pm Generalized Euclidean distance to understand polymer uncrossing and polymer knotting: Problems, solutions, and more problems. Steve Plotkin SCGP 102
3:15pm Tea Time N/A  SCGP Lobby
3:45pm Random Knots from Petal Diagrams, and their Invariants Chaim Even-Zohar SCGP 102


Time Title Presenter Location
9:00am Statistical Mechanics of Anchored Polymer Chains Bertrand Duplantier  SCGP 102
10:30am Coffee Break N/A SCGP Lobby
11:00am Open Problems Session N/A SCGP 102
12:15pm Lunch N/A SCGP Cafe

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