Lefschetz fibrations on adjoint orbits - PMA

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Constructing Letschetz <strong>fibrations</strong> via Lie theory This is a report of joint work with Lino Grama and Luiz A. B. San Martin. We show that adjoint orbits have the structure of <strong>Lefschetz</strong> <strong>fibrations</strong>. Elizabeth Gasparim <strong>Lefschetz</strong> <strong>fibrations</strong> on adjoint orbits
Motivation I want to explain the motivation carefully, and this will take a little detour away from Lie theory. Our main motivations is the Mirror Symmetry Conjecture which proposes that every object has a mirror. This leaves us with the obvious question: Elizabeth Gasparim <strong>Lefschetz</strong> <strong>fibrations</strong> on adjoint orbits
Page 1: Lefschetz
Page 5 and 6: Motivation I want to explain the mo
Page 7 and 8: Mirror Symmetry for Calabi-Yaus To
Page 9 and 10: This is NOT the Hodge diamond Toric
Page 11 and 12: Basic Hodge Theory Theorem (Hodge D
Page 17 and 18: The Hodge Diamond h n,n h n,n−1 h
Page 19 and 20: Amusing consequence of the classica
Page 21 and 22: Example 1: Smooth Elliptic Curve h
Page 23 and 24: Example 3: Hodge Diamond of a CY th
Page 25 and 26: Hodge Diamonds of Mirror Pairs h n,
Page 27 and 28: Mirror Symmetry is a duality For ou
Page 29 and 30: Known cases of the HMS conjecture T
Page 31 and 32: AKO Mirror of a Del Pezzo Surface T
Page 33 and 34: Vanishing cycle - mathematician’s
Page 35 and 36: Fukaya category A category whose ob
Page 37 and 38: Fukaya-Seidel category Definition T
Page 39 and 40: Monodromy representation Since X \
Page 41 and 42: Symplectic Lefschetz</stron
Page 43 and 44: Symplectic structure on the blow-up
Page 45 and 46: A flag Elizabeth Gasparim L
Page 47 and 48: Adjoint orbit The adjoint represent
Page 49 and 50: Lefschetz
Page 51 and 52: What I think we proved Theorem The

Lefschetz fibrations on adjoint orbits - PMA

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