 Date : 20220124 10:00 ~ 17:00
 Place : 129309 (SNU)

Speaker : 김경모 (SNU)

Title : Toric varieties

Abstract :
In this talk, basic definitions and properties about toric varieties are introduced. A toric variety is an algebraic variety in which an algebraic torus is embedded such that the action extends to the whole variety. We'll study how toric varieties are constructed from combinatorial data called a fan.
 Date : 20220523 10:00 ~ 17:00
 Place : 129309 (SNU)

Speaker : 노경민 (SNU)

Title : SYZ Mirror symmetry for toric CalabiYau mainfolds

Abstract :
In this seminar, we discuss mirror symmetry for toric CalabiYau manifolds from the perspective of the SYZ conjecture. For a nontoric special Lagrangian torus fibration on a toric CalabiYau manifold, its mirror can be constructed as a complex manifold using Tduality modified by quantum corrections. We also investigate the relation between those corrections and Fourier transforms of generating functions of certain open GromovWitten invariants.
 Date : 20220613 10:00 ~ 17:00
 Place : 129104 (SNU)

Speaker : 손범준 (SNU)

Title : Lefschetz fibrations and symplectic homology

Abstract :
In this talk, we briefly introduce the how M. Mclean proved the existence of infinitely many exotic Stein manifolds diffeomorphic to Euclidean space with dimension at least 8. Then, we will define variant version of symplectic homologies related to lefschetzfibration and prove the relations between them. Our main reference is Mark McLean's "Lefschetz fibrations and symplectic homology."
 Date : 20220627 10:00 ~ 18:00
 Place : 129104 (SNU)

Speaker : 김용환 (SNU)

Title : Theta functions and mirror symmetry

Abstract :
In this talk, we introduce the ongoing programme of GrossSiebert and GrossHackingKeel to expand the ideas of SYZ mirror symmetry to a broader class of symplectic manifolds. We first recall the SYZ mirror symmetry construction, and its limitations. To analyze how the mirror should behave near critical torus fibers, we introduce the language of tropical geometry and explain SYZ mirror symmetry for CalabiYau manifolds in this context. We end by giving some recent developments in this direction. The talk will be mostly based on two expository papers of Mark Gross  "Theta Functions and Mirror Symmetry", and "The StromingerYauZaslow conjecture: From torus fibrations to degenerations".
 Date : 20220711 14:30 ~ 16:30
 Place : 129309 (SNU)

Speaker : 김용환 (SNU)

Title : Lefschetz bifibrations and matching cycles

Abstract :
We first give some methods to compute the symplectic homology of a complement of a Milnor fiber, and show that it is nonvanishing in many cases. Then, we introduce how to interpret a Milnor fiber as a Lefschetz fibration over a disc, and briefly look at McLean's spectral sequence. Then we move on to the general theory of Lefschetz fibrations, and introduce the concept of Lefschetz bifibrations and matching cycles  these will appear later in the construction of Seidel.
 Date : 20220801 10:00 ~ 18:00
 Place : 129406 (SNU)

Speaker : 김도형 (SNU)

Title : Dehn twist along an exact Lagrangian sphere

Abstract :
Before we actually construct the long exact sequence of Lagrangian Floer homology groups, we will talk about its main ingredient : a Dehn twist along an Exact Lagrangian sphere L. We will use a notion of "exact Lefschetz fibration" to depict it and if time permits, we will also talk about vanishing cycle in the exact Lefschetz fibration. (lunch: 12:00  14:00, break: 15:20  15:40)