The NNGT seminar meets on Wednesdays at Lecture room B, 4F, the 3rd General Building, NTHU, from 15:10 am to 16:30 pm this semester.
Nearby seminars and conferences.
Abstracts
October 14, 2015
Chi-Kwong Fok, "Twisted Poisson manifolds and their almost symplectically complete isotropic realizations I"
Abstract: Let B be a twisted Poisson manifold with a fixed tropical affine structure. In this talk, we will discuss the classification of almost symplectically complete isotropic realizations (ASCIRs) over B in the spirit of Dazord-Delzant. We will construct a product among ASCIRs in analogy with tensor product of line bundles, thereby introducing the notion of the Picard group of B. We will give descriptions of the Picard group and the corresponding 'Neron-Severi group' using certain sheaf cohomology groups.
October 28, 2015
Chi-Kwong Fok, "Twisted Poisson manifolds and their almost symplectically complete isotropic realizations II "
Abstract: Let B be a twisted Poisson manifold with a fixed tropical affine structure. In this talk, we will discuss the classification of almost symplectically complete isotropic realizations (ASCIRs) over B in the spirit of Dazord-Delzant. We will construct a product among ASCIRs in analogy with tensor product of line bundles, thereby introducing the notion of the Picard group of B. We will give descriptions of the Picard group and the corresponding 'Neron-Severi group' using certain sheaf cohomology groups.
November 25, 2015
Nan-Kuo Ho, "Quasi-Hamiltonian system and the moduli space of flat connections I "
Abstract: We will continue the theme of looking at generalizations of symplectic manifolds/hamiltonian system. Quasi-Hamiltonian system is a generalization of hamiltonian system where the symplectic form is no longer closed nor non-degenerate, and the moment map image is not in the dual of the Lie algebra but in the Lie group. This system arises naturally from the study of moduli space of flat connections. It can also be used to study Higss bundles and meromorphic connections. The main reference is "Lie group valued moment map" by Alekseev, Malkin, and Meinrenken.
December 9, 2015
Nan-Kuo Ho, "Quasi-Hamiltonian system and the moduli space of flat connections II"
Abstract: We will continue the theme of looking at generalizations of symplectic manifolds/hamiltonian system. Quasi-Hamiltonian system is a generalization of hamiltonian system where the symplectic form is no longer closed nor non-degenerate, and the moment map image is not in the dual of the Lie algebra but in the Lie group. This system arises naturally from the study of moduli space of flat connections. It can also be used to study Higss bundles and meromorphic connections. The main reference is "Lie group valued moment map" by Alekseev, Malkin, and Meinrenken.
December 23, 2015
Chi-Kwong Fok, " Equivariant formality of homogeneous spaces"
Abstract: In equivariant topology, equivariant formality is a desirable property of spaces with group actions. In this talk we will present our recent progress of characterizing equivariant formality of compact homogeneous spaces G/K with isotropy action of K. This is joint work with Jeffrey Carlson.
Previous years
October 1, 2014
Chi-Kwong Fok, "The Real K-theory of compact Lie groups I"
Abstract: In this talk I will first review topological K-theory, its Real variant in the sense of Atiyah, and Brylinski-Zhang's result on the equivariant K-theory of a compact Lie group G equipped with the conjugation action by itself. Then I will present a description of the ring structure of the equivariant Real K-theory ring of G and show how the built-in Real structure gives extra information about the K-theory of G.
October 8, 2014
Chi-Kwong Fok, "The Real K-theory of compact Lie groups II"
Abstract: Let G be a compact Lie group viewed as a G-space via the conjugation action. A recent deep theorem by Freed-Hopkins-Teleman (FHT) asserts a canonical ring isomorphism between the twisted equivariant K-homology of G and its Verlinde algebra. In this talk I will review the background of FHT, including K-homology and its local coefficient systems, and then present a generalization of FHT in the context of Real K-theory.
October 22, 2014
Chi-Kwong Fok, "An introduction to topological K-theory"
Abstract: In this talk I will introduce with topological K-theory with emphasis on its cohomological properties. Examples and computational machineries will be given
October 29, 2014
Chi-Kwong Fok, "An introduction to topological K-theory"
Abstract: In this talk I will introduce with topological K-theory with emphasis on its cohomological properties. Examples and computational machineries will be given
November 5, 2014
Nan-Kuo Ho, "Introduction to the Hitchin moduli space"
Abstract: In this talk, I will give the definition of the Hitchin moduli space over a Riemann surface and explain the other two descriptions of the moduli space : the de Rham moduli space and the Betti moduli space.
November 26, 2014
Chi-Kwong Fok, "An introduction to topological K-theory"
Abstract: In this talk I will introduce with topological K-theory with emphasis on its cohomological properties. Examples and computational machineries will be given
December 10, 2014
Nan-Kuo Ho, "Introduction to the moduli space of Yang-Mills connections I (Atiyah-Bott)"
Abstract: This is an introductory talk on the moduli space of Yang-Mills connections over a Riemann surface. The reference is "The Yang-Mills equations over Riemann surfaces" by Atiyah-Bott.
December 17, 2014
Nan-Kuo Ho, "Introduction to the moduli space of Yang-Mills connections II (Atiyah-Bott)"
Abstract: This is an introductory talk on the moduli space of Yang-Mills connections over a Riemann surface. The reference is "The Yang-Mills equations over Riemann surfaces" by Atiyah-Bott.
December 31, 2014
Chi-Kwong Fok, " Equivariant Cohomology and the Localization Theorem"
Abstract: Equivariant cohomology, first constructed by A. Borel, is a generalized cohomology theory for topological spaces with group actions. In this talk, I will give an introduction to the subject. I will also show how the enlarged coefficient ring enables one to localize the equivariant cohomology suitably so that some information about the latter can be captured by the information of the fixed point set.
January 12, 2015
Nan-Kuo Ho, "Introduction to the moduli space of Yang-Mills connections II (Atiyah-Bott)"
Abstract: This is an introductory talk on the moduli space of Yang-Mills connections over a Riemann surface. The reference is "The Yang-Mills equations over Riemann surfaces" by Atiyah-Bott.
January 12, 2015
Chi-Kwong Fok, " Equivariant Cohomology and the Localization Theorem II"
Abstract: Equivariant cohomology, first constructed by A. Borel, is a generalized cohomology theory for topological spaces with group actions. In this talk, I will give an introduction to the subject. I will also show how the enlarged coefficient ring enables one to localize the equivariant cohomology suitably so that some information about the latter can be captured by the information of the fixed point set.
March 25, 2015
Siye Wu, "Hitchin's equations and integrable system"
Abstract: We explain the origin of Hitchin's equations and relate the solution space to the moduli spaces of flat connections and of Higgs bundles. We also explain the appearance of integrable systems by Hitchin's fibration. The talk is accessible to graduate students in geometry.
April 1, 2015
Siye Wu, "Hitchin's equations and integrable system II"
Abstract: We explain the origin of Hitchin's equations and relate the solution space to the moduli spaces of flat connections and of Higgs bundles. We also explain the appearance of integrable systems by Hitchin's fibration. The talk is accessible to graduate students in geometry.
April 15, 2015
Chi-Kwong Fok, "Moduli spaces in the rank one case"
Abstract: In this talk I will focus on the toy example of moduli spaces of Riemann surfaces in the rank one case and introduce its three incarnations, namely, Betti, de Rham and Dolbeault moduli spaces. Ref: Goldman and Xia
April 22, 2015
Chi-Kwong Fok, "Moduli spaces in the rank one case II"
Abstract: In this talk I will focus on the toy example of moduli spaces of Riemann surfaces in the rank one case and introduce its three incarnations, namely, Betti, de Rham and Dolbeault moduli spaces. Ref: Goldman and Xia
September 26, 2012
Graeme Wilkin, "Moment map flows and the Hecke correspondence for quivers"
Abstract: In the 1990's, Nakajima gave a geometric construction of representations of affine Kac-Moody algebras. This construction uses a variety called the Hecke correspondence, which is analogous to the Hecke correspondence for holomorphic bundles over a compact Riemann surface. In this talk I will describe an interpretation of the Hecke correspondence in terms of moment map flow lines.
October 18, 2012
Chung-I Ho, "Geometric Invariant Theory I: Affine and projective quotients"
Abstract: We will be using Thomas's notes on GIT.
October 25, 2012
Chung-I Ho, "Geometric Invariant Theory II"
Abstract: We will be using Thomas's notes on GIT.
November 1, 2012
Chung-I Ho, "Geometric Invariant Theory III"
Abstract: We will be using Thomas's notes on GIT.
November 6, 2012
Chung-I Ho, "Geometric Invariant Theory IV: Hilbert-Mumford criterion"
Abstract: We will be using Thomas's notes on GIT.
December 6, 2012
Chung-I Ho, "Geometric Invariant Theory V: symplectic reduction and Kempf-Ness Theorem"
Abstract: We will be using Thomas's notes on GIT.
September 19, 2011
Graeme Wilkin, "Cohomology of Higgs bundle moduli spaces"
Abstract: In the early 80s, Atiyah and Bott developed a new method for computing the cohomology of moduli spaces of semistable bundles: the Morse theory of the Yang-Mills functional. In this talk I will describe some recent results extending their methods to moduli spaces of Higgs bundles in low rank. The emphasis will be on moduli spaces of U(2,1) Higgs bundles, which is joint work with Richard Wentworth.
October 3, 2011
Chung-I Ho, "Generalized complex geometry I"
Abstract: The generalized complex geometry is introduced by Hitchin and developed by Gualtieri as a generalization of complex and symplectic structures. In this talk, we will study the theory of generalized complex geometry and its application in decomposition of differential forms.
October 31, 2011
Chung-I Ho, "Generalized complex geometry II"
Abstract: The generalized complex geometry is introduced by Hitchin and developed by Gualtieri as a generalization of complex and symplectic structures. In this talk, we will study the theory of generalized complex geometry and its application in decomposition of differential forms.
November 14, 2011
Chung-I Ho, "Generalized complex geometry III"
Abstract: The generalized complex geometry is introduced by Hitchin and developed by Gualtieri as a generalization of complex and symplectic structures. In this talk, we will study the theory of generalized complex geometry and its application in decomposition of differential forms.
November 21, 2011
Chung-I Ho, "Generalized complex geometry IV"
Abstract: The generalized complex geometry is introduced by Hitchin and developed by Gualtieri as a generalization of complex and symplectic structures. In this talk, we will study the theory of generalized complex geometry and its application in decomposition of differential forms.
December 19, 2011
Siye Wu, "Index bundle gerbes and moduli spaces"
Abstract: We construct the index bundle gerbe associated to a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we also give a geometric description which agrees with the above analytic construction. Finally, we apply the result to certain moduli spaces associated to Riemann surfaces. This is a joint work with P.Bouwknegt and V.Mathai.
Other relevant information
Nearby conferences
- Chen - Jung Hsu Lecture series (this year is Prof. Nigel Hitchin) Academia Sinica
October 15, 16, 17, 2014
- Ninth Taiwan Geometry Symposium NCU
Nov 1, 2014
- Taiwan Mathematic Society Annual Meeting NCKU
December 6 – 7, 2014
Nearby seminars
- NCTS/TPE Activity Calendar
- TIMS Activity Calendar
- NTU String Group Seminar