Knots, Strings, Symplectic Geometry and Dualities
September 1 - December 11, 2020
Very fruitful interactions between geometry and physics has had large impact on mathematics over the last 35 years. Exceptionally symmetric theories in physics become topologically invariant and have found their mathematical counterparts. These physical theories are typically part of a larger framework that is often hard to capture mathematically but nevertheless very useful and effective for finding dualities between different theories.
For a brief description of how such dualities arise consider some intrinsically quantum theory. The classical limit of such a theory is not unique but any two of its classical limits are naturally related. This leads to dualities between distinct limits, and these can even interchange small fluctuations near one limit with large fluctuations near another.
A well-known example of a duality is mirror symmetry where certain twists in topological string theory gives rise to connections between symplectic (A-model topological string) and complex (B-model topological string) geometry. Another key example from the interface between geometry, topology, and physics that is central to this proposal is the connection between knot invariants and holomorphic curve counting that arise from a chain of dualities connecting Chern-Simons gauge theory to open strings and then through a geometric transition to closed string.
Interactions between geometry, topology and physics continue to pose and solve central mathematical problems and it is to this framework the proposed program belongs.
Participation in the program is by invitation only.
Seminars
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Augmentations, Annuli, and Alexander polynomials September 03 14:00 - 15:00 -
Secondary coproducts in Morse and Floer homology September 08 14:00 - 15:00 Secondary coproducts in Morse and Floer homology
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Floer homotopy without spectra September 15 14:00 - 15:00 Floer homotopy without spectra
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Skeins on branes September 24 14:00 - 15:00 Skeins on branes
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Fiber Floer cohomology and conormal stops October 01 14:00 - 15:00 Fiber Floer cohomology and conormal stops
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On the spatial restricted three-body problem October 08 14:00 - 15:00 On the spatial restricted three-body problem
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A symplectic look at the Fargues-Fontaine curve October 15 14:00 - 15:00 A symplectic look at the Fargues-Fontaine curve
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Infinitely many fillings through augmentations October 22 14:00 - 15:00 Infinitely many fillings through augmentations
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Knot Floer homology and monodromy October 29 14:00 - 15:00 Knot Floer homology and monodromy
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Displacement energy of Lagrangian 3-spheres November 05 14:00 - 15:00 Displacement energy of Lagrangian 3-spheres
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Perturbations for bare curve counts November 12 14:00 - 15:00 Perturbations for bare curve counts
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Legendrian lifts of montone tori November 17 14:00 - 15:00 Legendrian lifts of montone tori
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Contact geometry in the restricted three-body problem (part I) November 23 17:00 - 19:30 Contact geometry in the restricted three-body problem (part I)
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Contact geometry in the restricted three-body problem (part II) November 25 17:00 - 19:30 Contact geometry in the restricted three-body problem (part II)
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Contact geometry in the restricted three-body problem (part III) November 26 17:00 - 19:30 Contact geometry in the restricted three-body problem (part III)
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Small energy isotopies of loose Legendrians December 03 14:00 - 15:00 Small energy isotopies of loose Legendrians