Jaeyoo Choy

Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions

Abstract Let K be the compact Lie group USp ( N / 2 ) or SO ( N , R ) . Let M n K be the moduli space of framed K -instantons over S 4 with the instanton number n . By Donaldson (1984), M n K is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of μ − 1 ( 0 ) , where μ is a holomorphic moment map such that μ − 1 ( 0 ) consists of the ADHM data. The purpose of the paper is to study the geometric properties of μ − 1 ( 0 ) and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If K = USp ( N / 2 ) then μ is flat and μ − 1 ( 0 ) is an irreducible normal variety for any n and even N . If K = SO ( N , R ) the similar results are proven for low n and N . As an application one can obtain a mathematical interpretation of the K -theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).

VOLUME PRESERVING DYNAMICS WITHOUT GENERICITY AND RELATED TOPICS

In this article, we focus on certain dynamic phenomena in volume-preserving manifolds. Let be a compact manifold with a volume form and be a diffeomorphism of class that preserves . In this paper, we do not assume is -generic. We prove that satisfies the chain transitivity and we also show that, on , the -stable shadowability is equivalent to the hyperbolicity.

Dynamics of Riemannian

In this paper we study several dynamical properties of the riemannian

1

1

-foliations on

-dimensional foliation

3

\mathcal{L}

-manifolds

on an oriented closed 3-manifold

Chain Recurrences on Conservative Dynamics

M

Characterizations on Mazur-Ulam theorem

. Carri\`ere \cite{Ca} classified such pairs

On the Omega Limit Sets for Analytic Flows

(M,\mathcal{L})