Title    name   2012 SNU/KIAS Topology Winter School Cohomology of Toric Manifolds 5 Tomoo Matsumura (KAIST) 2012-02-24   In the first part, I will start with basic definitions and properties of equivalent cohomology and its relation to ordinary cohomology. I will also mention, in terms of equivariant cohomology, what we should calculate when we are dealing with orbifolds. In the second part, we will compute the equivariant cohomology and ordinary cohomology of toric manifolds and orbifolds. To compute the equivariant cohomology as the Stanley-Reisner ring, we will introduce ``moment angle complexes for simplicial complexes   2012 SNU/KIAS Topology Winter School Symplectic Toric Manifolds 5 Eugene Lerman (University of Illinois at Urbana-Champaign) 2012-02-24   Symplectic toric manifolds, old and new. I will define symplectic toric manifolds and explain the now classical theorem of Delzant classifying compact connected symplectic toric manifolds in terms of simple unimodular polytopes. I would also like to explain what happens to the classification when symplectic toric manifolds are not assumed to be compact.   2012 SNU/KIAS Topology Winter School Cohomology of Toric Manifolds 4 Tomoo Matsumura (KAIST) 2012-02-23   In the first part, I will start with basic definitions and properties of equivalent cohomology and its relation to ordinary cohomology. I will also mention, in terms of equivariant cohomology, what we should calculate when we are dealing with orbifolds. In the second part, we will compute the equivariant cohomology and ordinary cohomology of toric manifolds and orbifolds. To compute the equivariant cohomology as the Stanley-Reisner ring, we will introduce ``moment angle complexes for simplicial complexes   2012 SNU/KIAS Topology Winter School Symplectic Toric Manifolds 4 Eugene Lerman (University of Illinois at Urbana-Champaign) 2012-02-23   Symplectic toric manifolds, old and new. I will define symplectic toric manifolds and explain the now classical theorem of Delzant classifying compact connected symplectic toric manifolds in terms of simple unimodular polytopes. I would also like to explain what happens to the classification when symplectic toric manifolds are not assumed to be compact.   2012 SNU/KIAS Topology Winter School The quantum cohomology of toric orbifold Chung, Daewoong (KIAS) 2012-02-22   Recently, Gromov-Witten theory has been generalized to the category of orbifolds by W. Chen and Y. Ruan in symplectic geometry setting, and by D Abramovich, T. Graber and A. Vistoli in algebraic geometry setting, respectively. The so-called J-function encoding genus zero Gromov-Witten invariants for manifolds can be computed by using an auxilary moduli space to Kontsevich's moduli space of stable maps. Indeed, the Quot scheme and the`` toric compactification" were used to compute J-functions for Grassmannians and toric manifolds, respectively. A few years ago, I. Ciocan-Fontanine, B. Kim and D. Maulick constructed this type of moduli space for GIT quotients generalizing the Quot scheme and the toric compactification. Jointly with I. Ciocan-Fontanine and B. Kim, we generalized this compactification to the class of GIT stacks to which most of interesting orbifolds in Gromov-Witten theory belong. As an application, we compute J-function of compact toric orbifolds.   2012 SNU/KIAS Topology Winter School Symplectic Toric Manifolds 3 Eugene Lerman (University of Illinois at Urbana-Champaign) 2012-02-22   Symplectic toric manifolds, old and new. I will define symplectic toric manifolds and explain the now classical theorem of Delzant classifying compact connected symplectic toric manifolds in terms of simple unimodular polytopes. I would also like to explain what happens to the classification when symplectic toric manifolds are not assumed to be compact.   2012 SNU/KIAS Topology Winter School Cohomology of Toric Manifolds 2 Tomoo Matsumura (KAIST) 2012-02-22   In the first part, I will start with basic definitions and properties of equivalent cohomology and its relation to ordinary cohomology. I will also mention, in terms of equivariant cohomology, what we should calculate when we are dealing with orbifolds. In the second part, we will compute the equivariant cohomology and ordinary cohomology of toric manifolds and orbifolds. To compute the equivariant cohomology as the Stanley-Reisner ring, we will introduce ``moment angle complexes for simplicial complexes   2012 SNU/KIAS Topology Winter School Exercise in toric geometry Cho, Cheolhyun (Seoul National University) 2012-02-21     2012 SNU/KIAS Topology Winter School Cohomology of Toric Manifolds 1 Tomoo Matsumura (KAIST) 2012-02-21   In the first part, I will start with basic definitions and properties of equivalent cohomology and its relation to ordinary cohomology. I will also mention, in terms of equivariant cohomology, what we should calculate when we are dealing with orbifolds. In the second part, we will compute the equivariant cohomology and ordinary cohomology of toric manifolds and orbifolds. To compute the equivariant cohomology as the Stanley-Reisner ring, we will introduce ``moment angle complexes for simplicial complexes   2012 SNU/KIAS Topology Winter School Symplectic Toric Manifolds 1 Eugene Lerman (University of Illinois at Urbana-Champaign) 2012-02-21   Symplectic toric manifolds, old and new. I will define symplectic toric manifolds and explain the now classical theorem of Delzant classifying compact connected symplectic toric manifolds in terms of simple unimodular polytopes. I would also like to explain what happens to the classification when symplectic toric manifolds are not assumed to be compact.

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