• Date :  2022-01-24  10:00 ~ 17:00  
• Place :  129-309 (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 :  2022-05-23  10:00 ~ 17:00  
• Place :  129-309 (SNU)

• Speaker :  노경민 (SNU)

• Title :   SYZ Mirror symmetry for toric Calabi-Yau mainfolds

• Abstract : 

In this seminar, we discuss mirror symmetry for toric Calabi-Yau manifolds from the perspective of the SYZ conjecture. For a non-toric special Lagrangian torus fibration on a toric Calabi-Yau manifold, its mirror can be constructed as a complex manifold using T-duality modified by quantum corrections. We also investigate the relation between those corrections and Fourier transforms of generating functions of certain open Gromov-Witten invariants.

 

 

• Date :  2022-06-13  10:00 ~ 17:00  
• Place :  129-104 (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 lefschetz-fibration and prove the relations between them. Our main reference is Mark McLean's "Lefschetz fibrations and symplectic homology."

 

 

• Date :  2022-06-27  10:00 ~ 18:00  
• Place :  129-104 (SNU)

• Speaker :  김용환 (SNU)

• Title :  Theta functions and mirror symmetry

• Abstract : 

In this talk, we introduce the ongoing programme of Gross-Siebert and Gross-Hacking-Keel 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 Calabi-Yau 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 Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations".

 

 

• Date :  2022-07-11  14:30 ~ 16:30  
• Place :  129-309 (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 :  2022-08-01  10:00 ~ 18:00  
• Place :  129-406 (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)