Department of Mathematics

Details

Compatible Poisson structures in cluster algebras

by Michael Gekhtman  (www) | University of Notre Dame
Time: 14:10  (Monday, Oct. 17, 2011)
Location: BA6183, Bahen Center, 40 St George St
Abstract:
I will discuss the notion of Poisson brackets compatible with the structure of a cluster algebra. Examples will include Grassmannians and Teichmueller spaces. Time permitting, a conjecture on an interplay between cluster algebras and Poisson-Lie structures associated with Belavin-Drinfeld classification of solutions of the Classical Yang-Baxter Equation will be formulated along with some supporting evidence.

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)