Instanton Counting and Wall-Crossing for Orbifold Quivers

Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative {Mathematical expression} gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated with the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge theory variables and orbifold data. We introduce the notion of virtual instanton quiver associated with the natural symplectic charge lattice which governs the quantum wall-crossing behaviour of BPS states in this context. The McKay correspondence naturally connects our formalism with other approaches to wall-crossing based on quantum monodromy operators and cluster algebras

Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group

Network and Seiberg Duality

We define and study a new class of 4d N=1 superconformal quiver gauge theories associated with a planar bipartite network. While UV description is not unique due to Seiberg duality, we can classify the IR fixed points of the theory by a permutation, or equivalently a cell of the totally non-negative Grassmannian. The story is similar to a bipartite network on the torus classified by a Newton polygon. We then generalize the network to a general bordered Riemann surface and define IR SCFT from the geometric data of a Riemann surface. We also comment on IR R-charges and superconformal indices of our theories.Comment: 28 pages, 28 figures; v2: minor correction

Quiver Structure of Heterotic Moduli

We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.Comment: 38 pages, 5 figures, 1 tabl

Hilbert Series for Moduli Spaces of Two Instantons

The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where G is a simple gauge group, is studied in detail. For a given G, the moduli space is a singular hyperKahler cone with a symmetry group U(2) \times G, where U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli space transform in irreducible representations of the symmetry group and hence the Hilbert series admits a character expansion. For cases that G is a classical group (of type A, B, C, or D), there is an ADHM construction which allows us to compute the HS explicitly using a contour integral. For cases that G is of E-type, recent index results allow for an explicit computation of the HS. The character expansion can be expressed as an infinite sum which lives on a Cartesian lattice that is generated by a small number of representations. This structure persists for all G and allows for an explicit expressions of the HS to all simple groups. For cases that G is of type G_2 or F_4, discrete symmetries are enough to evaluate the HS exactly, even though neither ADHM construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure

On Arnold's 14 `exceptional' N=2 superconformal gauge theories

We study the four-dimensional superconformal N=2 gauge theories engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities (a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435 to singularities which are not the direct sum of minimal ones. In particular, we compute their BPS spectra in several `strongly coupled' chambers. From the TBA side, we construct ten new periodic Y-systems, providing additional evidence for the existence of a periodic Y-system for each isolated quasi-homogeneous singularity with $\hat c<2$ (more generally, for each N=2 superconformal theory with a finite BPS chamber whose chiral primaries have dimensions of the form N/l).Comment: 73 pages, 7 figure

Ornamental plants: annual reports and research reviews, 2002

Ohio State University Extension Nursery, Landscape, and Turf Team directory: 2003 / Jack Kerrigan -- Floriculture Industry Roundtable of Ohio: 2003 / Charles Behnke -- Ohio State University Extension 2002 Buckeye Yard and Garden Line evaluation survey / Amy K. Stone and James A. Chatfield -- Weather, environmental, and cultural problems of ornamental plants in Ohio: 2002 / Pamela J. Bennett -- Infectious disease problems of ornamental plants in Ohio: 2002 / James A. Chatfield, Nancy A. Taylor, Erik A. Draper, and Joseph F. Boggs -- A biological calendar for predicting pest activity: six years of plant and insect phenology in Secrest Arboretum / Daniel A. Herms -- Biological suppression of foliar diseases of ornamental plants with composted manures, biosolids, and Trichoderma hamatum 382 / Harry A. J. Hoitink, Carol A. Musselman, Terry L. Moore, Leona E. Horst, Charles R. Krause, Randy A. Zondag, and Hannah Mathers -- Growth and water use by four leguminous tree species in containers on a gravel surface or embedded in mulch / Michael Knee, Daniel K. Struve, Michael H. Bridgewater, and Joseph W. Phillips -- The effects of sprayer configuration on efficacy for the control of scab on crabapple / Charles R. Krause, Richard C. Derksen, Leona E. Horst, Randall Zondag, Ross D. Brazee, Michael G. Klein, and Michael E. Reding -- Update on honeylocust knot / Pierluigi Bonello, Maria Bellizzi, and Harry A. J. Hoitink -- Control of phytophthora and other major diseases of Ericaceous plants / Harry A. J. Hoitink, Steven T. Nameth, and James C. Locke -- Is your landscape mulch going up in smoke? / Larry G. Steward, T. Davis Sydnor, and Bert Bishop -- IR-4 ornamental trials conducted by USDA-ARS in Ohio: 2002 / Betsy A. Anderson, Michael E. Reding, Michael G. Klein, and Charles R. Krause -- Research on black vine weevil and white grubs in ornamental nurseries-in Ohio by USDA-ARS / Michael E. Reding, Michael G. Klein, Ross D. Brazee, and Charles R. Krause -- Herbaceous ornamental field trial results in Clark County, Ohio – 2002 / Pamela J. Bennett -- Results of annual trial gardens at the Cincinnati Zoo and Botanical Garden for 2002 / Dave Dyke -- Ohio State University Learning Garden annual cultivar trials / Monica M. Kmetz-Gonzalez and Claudio C. Pasian -- A collection of crabapple knowledge from Secrest Arboretum: 1993-2002 / Erik A. Draper, James A. Chatfield, and Kenneth D. Cochran -- Key results of the 2001 Ohio Green Industry Survey / Gary Y. Gao, John J. Smith, James A. Chatfield, Joseph F. Boggs, Erik A. Draper, and Hannah Mathers -- The USDA/Agricultural Research Service research weather network in Lake County, Ohio - 2002 update / R. D. Brazee, R. C. Derksen, C. R. Krause, K. A. Williams, D. Lohnes, M. G. Klein, M. Reding, R. Lyons, W. Hendricks, R. Zondag, R. D. Fox, and D. Herms -- The OSU Chadwick Arboretum Learning Gardens / Dr. Steven Still and Annette Duetz -- Choosing soil testing labs / Gary Y, Gao, Maurice E. Watson, Joseph F. Boggs, and James A. Chatfield -- Top horticultural references for a green industry professional's library / Gary Y. Gao and Pamela J. Bennett -- The maples of Secrest Arboretum / Gary W. Graham, James A. Chatfield, and Kenneth D. Cochran -- Deck the halls with boughs from Ollie! / Kenneth D. Cochran and James A. Chatfiel