Symplectic Seminar

The symplectic geometry seminars are held Mondays from 2:10--3:00 PM in BA 6183, unless otherwise indicated.  

If you would like more information, to join the mailing list, or if you would like to give a talk, please contact the organizer, Mehdi Mousavi

More information on these seminars can be found at the following link:


Toric degenerations and quantization of toric manifolds

by Mark Hamilton
Time: 14:10  (Monday, Mar. 15, 2010)
Location: BA6183, Bahen Center, 40 St George St
Quantization of flag manifolds was studied by Guillemin and Sternberg, who showed that the quantizations using real and Kahler polarizations are "the same." However, their proof is in terms of the equality of two numbers (the dimension of a representation space, and the number of Bohr-Sommerfeld fibres), and does not give any direct relationship between the two quantizations. We construct a family of complex structures on the flag manifold, depending on a real parameter s, so that elements of a canonical basis for the holomorphic sections (which are elements of the Kahler quantization) tend, in the limit as s goes to infinity, to distributional sections supported on the Bohr-Sommerfeld fibres (which can be seen as elements of the real quantization). We use two main techniques in the proof: the "toric degneration of integrable systems" of Nishinou, Nohara, and Ueda; and the deformation of complex structures constructed by Baier, Mourao, Florentino, and Nunes. This is joint work in progress with Hiroshi Konno.

Dates in this series

· Monday, Jan. 11, 2010: Construction of conformally compact Einstein manifolds (Dezhong Chen)
· Monday, Jan. 18, 2010: Homotopy Gerstenhaber algebras in toric topology (Matthias Franz)
· Monday, Jan. 25, 2010: Geography of symplectic 4-manifolds (Doug Park)
· Monday, Feb. 01, 2010: Lefschetz fibrations on cotagent bundles and Fukaya categories (Joseph Johns)
· Monday, Feb. 08, 2010: Varieties of complex Lie algebras (Tatyana Foth)
· Thursday, Mar. 04, 2010: A C*-algebraist looks at [Q,R]=0 (Nigel Higson)
· Monday, Mar. 15, 2010: Toric degenerations and quantization of toric manifolds (Mark Hamilton)
· Monday, Mar. 22, 2010: Eta-invariants and anomalies in U(1)-Chern-Simons theory (Brendan McLellan)
· Monday, Mar. 29, 2010: Ricci solitons (Andrew Dancer)
· Monday, Apr. 19, 2010: TBA (Octav Cornea)
· Monday, Apr. 26, 2010: B-fields, quantization and Morita equivalence (Henrique Bursztyn)
· Monday, Sep. 13, 2010: Remarks on symplectic realizations (Alejandro Cabrera)
· Monday, Sep. 20, 2010: On symplectic forms in the Soliton theory (Fedor Soloviev)
· Monday, Sep. 27, 2010: On the topology of fillings of contact manifolds (joint work with A. Oancea) (Claude Viterbo)
· Monday, Oct. 04, 2010: Generalized Euler-Poincar\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications (joint work with C. Vizman) (Feride Tiglay)
· Monday, Oct. 18, 2010: Embedded Lagrangian cobordism (Octav Cornea)
· Monday, Oct. 25, 2010: Hamiltonian Spaces with Group Valued Moment Maps (David Li-Bland)
· Monday, Nov. 01, 2010: Non-holonomic geometry and singularity theory (Alex Castro)
· Monday, Nov. 08, 2010: Homotopy Poisson actions (Rajan Mehta)
· Monday, Nov. 15, 2010: Kaehler metrics on spherical varieties (Victor Batyrev)
· Wednesday, Nov. 24, 2010: Geometric representation of closed 2-forms (Patrick Iglesias-Zemmour)
· Monday, Nov. 29, 2010: The graph complex and the Grothendieck-Teichmüller Lie algebra (Thomas Willwacher)
· Wednesday, Dec. 01, 2010: Steps towards the symplectization of Frölicher spaces (Augustin Batubenge)
· Wednesday, Dec. 08, 2010: Examples of co-Higgs bundles (Steven Rayan)
· Monday, Jan. 10, 2011: Braids and the Grothendieck-Teichmuller Group (Dror Bar-Natan)
· Monday, Jan. 17, 2011: Constructions of symplectic groupoids by blow-up's (Travis Li)
· Monday, Jan. 24, 2011: Abelian Chern-Simons theory: topological boundary conditions and surface operators (Natalia Saulina)
· Monday, Jan. 31, 2011: Variational Methods for the N-body problem (Richard Montgomery)
· Wednesday, Feb. 02, 2011: Rational Drinfeld associators and their denominators (Pavol Severa)
· Monday, Feb. 07, 2011: Quantization of manifolds with f-structure (Sean Fitzpatrick)
· Monday, Feb. 14, 2011: Geodesics on the group of symplectomorphisms (David Ebin)
· Monday, Feb. 28, 2011: Hamiltonian Torus Actions on Orbifolds (Tomoo Matsumura)
· Monday, Mar. 07, 2011: Infinitesimal Hilbert 16th problem (Dmitry Novikov)
· Monday, Mar. 14, 2011: The Modular Class of Poisson submersion (John Arlo Caine)
· Monday, Mar. 21, 2011: Poisson and Symplectic Geometry on b-manifolds (Ana Rita Pires)
· Monday, Mar. 28, 2011: Implosion constructions in hyperkahler geometry (Andrew Dancer)
· Monday, Apr. 04, 2011: Delocalized twisted equivariant cohomology (Ping Xu)
· Friday, May. 20, 2011: Toroidal orbifold compactifications of reductive groups and moduli of framed bundles (Johan Martens)
· Friday, Jul. 22, 2011: Lower bounds for Gromov width of coadjoint orbits in U(n). (Milena Pabiniak )
· Monday, Aug. 08, 2011: Real and Kaehler Quantization of Flag Manifolds (Mark Hamilton)
· Monday, Aug. 29, 2011: Local obstructions to approximating tropical curves in surfaces (Kristin Shaw)
· Monday, Sep. 12, 2011: Deforming Poisson varieties (Marco Gualtieri)
· Monday, Sep. 19, 2011: Degeneracy loci of Poisson varieties (Brent Pym)
· Monday, Sep. 26, 2011: Quantization and automorphic forms (Tatyana Barron)
· Monday, Oct. 03, 2011: Equivariant K-theory of the based loop group of SU(2) (Paul Selick)
· Wednesday, Oct. 12, 2011: Todd genera of complex torus manifolds (Hiroaki Ishida)
· Monday, Oct. 17, 2011: Compatible Poisson structures in cluster algebras (Michael Gekhtman)
· Wednesday, Oct. 19, 2011: Quantization and automorphic forms - 2 (Tatyana Barron)
· Wednesday, Oct. 19, 2011: The embedded contact homology of circle bundles over Riemann surfaces (David Farris)
· Monday, Oct. 24, 2011: Action homomorphisms, moment maps and quasimorphisms (Egor Shelukhin)
· Monday, Oct. 31, 2011: Betti numbers of twisted Higgs moduli spaces through quivers (Steven Rayan)
· Wednesday, Nov. 09, 2011: Toric Integrable Geodesic Flows (Susan Tolman)
· Monday, Nov. 14, 2011: $C^0$ limits of Hamiltonian paths and spectral invariants (Sobhan Seyfaddini)
· Monday, Nov. 21, 2011: Kirwan polyhedron of holomorphic coadjoint orbits (Guillaume Deltour)
· Monday, Dec. 05, 2011: Tau function on the spaces of admissible covers (Dmitry Korotkin)
· Wednesday, Jan. 18, 2012: Morse theory and invariants of (almost) symplectic manifolds, (Tara Holm)
· Monday, Jan. 23, 2012: Equivariant cohomology, syzygies, and orbit structure (Matthias Franz)
· Wednesday, Jan. 25, 2012: Kirwan polyhedron of holomorphic coadjoint orbits (Guillaume Deltour)
· Wednesday, Feb. 01, 2012: dg-Categories in Geometry (Jonathan Block)
· Monday, Feb. 06, 2012: A higher Riemann-Hilbert correspondence (Aaron Smith)
· Monday, Feb. 13, 2012: Quantum noise and symplectic rigidity (Leonid Polterovich)
· Wednesday, Feb. 22, 2012: Lower bounds for Gromov width of the unitary and special orthogonal coadjoint orbits (Milena Pabiniak)
· Wednesday, Mar. 07, 2012: The Kirwan method in hyperkahler geometry (Jonathan Fisher)
· Monday, Mar. 12, 2012: Positivity in the symplectic category (Rebecca Goldin)
· Monday, Mar. 19, 2012: Lagrangian Floer homology and toric oribfolds (Cheol-Hyun Cho)
· Monday, Mar. 26, 2012: On translated points of contactomorphisms (Sheila Margherita Sandon)
· Monday, Apr. 02, 2012: Foliated Groupoids and their infinitesimal data (Madeleine Jotz)
· Monday, Apr. 09, 2012: Unifying hypercomplex and holomorphic structures (Mathieu Stienon)
· Thursday, Apr. 12, 2012: Geometry of heterotic string compactifications (Xenia de la Ossa)
· Thursday, Apr. 12, 2012: Periods of Calabi-Yau manifolds in physics and number theory (Philip Candelas)
· Monday, Apr. 30, 2012: Combinatorics of polytopes and a model of nonrational toric varieties (Dan Zaffran)
· Wednesday, Jul. 18, 2012: Bohr-Sommerfeld-Heisenberg quantization (Richard Cushman)
· Friday, Jul. 20, 2012: Geometry of pseudodifferential algebra bundles (Mathai Varghese)
· Monday, Sep. 10, 2012: Generalizations of the Hunter-Saxton equation (Klas Modin)
· Monday, Sep. 24, 2012: Non-squeezing in $R^{2n}\times S^1$ (Maia Fraser)
· Monday, Oct. 01, 2012: Upper bound for the Gromov width of coadjoint orbits (Alexander Caviedes Castro)
· Monday, Oct. 15, 2012: Hydrodynamics and the skew-mean-curvature flow (Boris Khesin)
· Monday, Oct. 22, 2012: Root systems of torus graphs and characterization of extended actions of torus manifolds,  (Shintaro Kuroki)
· Wednesday, Oct. 24, 2012: Doing differential geometry on the irrational torus: a rush introduction to diffeology (Enxin Wu)
· Monday, Oct. 29, 2012: The discriminant metric on the contactomorphism group (Sheila Margherita Sandon)
· Monday, Nov. 12, 2012: Behavior of Welschinger invariants under Morse simplification (Erwan Brugallé)
· Monday, Nov. 19, 2012: On moduli spaces (David Li-Bland)
· Monday, Jan. 14, 2013: Compactness results for the quilted Atiyah-Floer conjecture (David Duncan)
· Monday, Jan. 21, 2013: Schubert calculus of weighted Grassmannians (Tomoo Matsumura)
· Monday, Jan. 28, 2013: A convexity theorem For symplectomorphism groups (Mehdi Mousavi)
· Monday, Feb. 04, 2013: On the Linearization of Poisson Lie group structures (Eckhard Meinrenken)