Preprints and Publications
The correspondence induced on the pillowcase by the earring tangle, (with G. Cazassus, P. Kirk, and A. Kotelskiy), J. Topol. 15 (2022), Issue 4, 2472-2543. Preprint at arXiv:2010.04320.
Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces, (with G. Cazassus and P. Kirk), Proceedings of Summer 2020 BIRS Workshop on “Interactions of gauge theory and symplectic geometry in dimensions 3 and 4,” Open Book Ser. 5 (2022), No. 1, Math. Sci. Publ., 95-121. Preprint at arXiv:2101.00901.
The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology, (with M. Hedden, M. Hogancamp, and P. Kirk), Trans. Amer. Math. Soc. 373 (2020), 8391-8437. Preprint at arXiv:1808.06957.
A note on orderability and Dehn filling (with X. Zhang), Proc. Amer. Math. Soc. 147 (2019), 2815-2819. Preprint at arXiv:1807.00742.
Holonomy perturbations and regularity for traceless SU(2) character varieties of tangles (with P. Kirk), Quantum Topology, 9 (2018), no. 2, 349-418. Preprint at arXiv:1511.00308.
The pillowcase and traceless representations of knot groups, II: A Lagrangian-Floer theory in the pillowcase (with M. Hedden and P. Kirk), J. Symplect. Geom. 16 (2018), no. 3, 721-815. Preprint at arXiv:1501.00028.
The SU(2) Casson-Lin invariant of the Hopf link, with H. Boden, Pacific J. Math. 285 (2016), no. 2, 283-288. Preprint (2016) arXiv:1601.06017.
The pillowcase and perturbations of traceless representations of knot groups, with P. Kirk and M. Hedden, Geom. Topol. 18 (2014), 211-287.
Simple Climate Models to Illustrate How Bifurcations Can Alter Equilibria and Stability, with S. Kurita and A. Telyakovskiy, J. Contemp. Water Res. Ed. 152 (2013), 14-21.
UNR Mathematics Dodges the Budget Axe For Now, Notices Amer. Math. Soc. 59 (2012), no. 02, 261.
Simulation of aggregates with point-contacting monomers in the cluster-dilute regime. Part 2: Comparison of two and three-dimensional structural properties as function of fractal dimension, with R. K. Chakrabarty, M. A. Garro, B.A. Garro, S. Chancellor, H. Moosmüller, Aerosol Sci. Technol. 45 (2011), no. 8, 893-898
Simulation of aggregates with point-contacting monomers in the cluster-dilute regime. Part 1: Determining the most reliable technique for obtaining three-dimensional fractal dimension from two-dimensional images dimension, with R. K. Chakrabarty, M. A. Garro, B.A. Garro, S. Chancellor, H. Moosmüller, Aerosol Sci. Technol. 45 (2011), no. 1, 75-80.
Extending the SU(3) Casson invariant to rational homology 3-spheres, AMS/IP Studies in Advanced Mathematics, Proceedings of Chern-Simons Theory: 20 Years After, edited by Andersen, Boden, Hahn, and Himpel 50 (2011), 115-130.
Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation (with P. Kirk and C. Livingston), Math. Z. 24 (2009) 925-949.
FracMAP: A User-Interactive Package for Performing Simulation and Orientation-Specific Morphology Analysis of Fractal-like Solid Agglomerates (with R. Chakrabarty, M. Garro, S. Chancellor, and H. Moosmüller), Comput. Phys. Commun. 180 (2009), 1376-1381.
Transversality for Equivariant Exact 1-Forms and Gauge Theory on 3-Manifolds, Adv. Math. 200 (2006), no.1, 245-302.
Thermal/Fluid Characteristics of Elliptic Cross Section Filament Box Lattice Matrices As Heat Exchanger Surfaces (with D. Sarde and R.A. Wirtz), Paper #3810, AIAA Thermophysics and Heat Transfer Conference, San Francisco, CA, June 6-8, 2006.
The SU(3) Casson Invariant for Brieskorn Homology 3-Spheres ( with H. Boden and P. Kirk), J. Differential Geom. 71 (2005), no. 1, 23-83.
Porosity, Specific Surface Area and Effective Thermal Conductivity of Anisotropic Open Cell Lattice Structures, (with K. Balantrapu, D. Sarde, and R.A. Wirtz), paper IPACK2005-73191, in Proceedings of ASME InterPack Conference 2005, July 17-22.
The Caldéron Projector for the Odd Signature Operator and Spectral Flow Calculations in 3-Dimensional Topology (with H. Boden and P. Kirk), in Spectral geometry of manifolds with boundary and decomposition of manifolds, 125-150, Contemporary Mathematics 366, Amer. Math. Soc., Providence, RI, 2005.
The integer valued SU(3) Casson invariant for Brieskorn spheres (with H. Boden and P. Kirk), J. Differential Geom. 71 (2005), no. 1, 23-83.
The SU(3) Casson invariant for 3-manifolds split along a 2-sphere or a 2-torus (with H. Boden), Proceedings of the 1999 Georgia Topology Conference (Athens, GA). Topology Appl. 124 (2004) no. 2, 187-204.
On the integer valued SU(3) Casson invariant (with H. Boden and P. Kirk), Topology and geometry of manifolds (Athens, GA, 2001), 209-236, Proc. Sympos. Pure Math., 71 , Amer. Math. Soc., Providence, RI, 2003.
SU(3) generalizations of the Casson invariant from gauge theory, Geometry, integrability, and quantization (Varna, 2001), 278-289, Coral Press Sci. Publ., Sofia, 2002.
An integer valued SU(3) Casson invariant (with H. Boden and P. Kirk), Math. Res. Lett. 8 (2001) no. 5-6, 589-603.
Gauge theoretic invariants of Dehn surgeries on knots (with H. Boden, P. Kirk and E. Klassen), Geom. Top. 5 (2001) 143-226.
A connected sum formula for the SU(3) Casson invariant (with H. Boden), J. Differential Geom. 53 (1999) no. 3, 443-464.
Chern-Simons gauge theory on 3-manifolds, The Proceedings of the Conference on Geometric Structures on Manifolds (Seoul 1997), Lecture Notes Ser. No. 46, Seoul Nat. Univ., Seoul 1999.
The SU(3) Casson invariant for integral homology 3-spheres (with H. Boden), J. Differential Geom. 50 (1998) no. 1 147--206.
Existence of irreducible representations for knot complements with nonconstant equivariant signature, Math. Ann. 309 (1997) 21—35.
Flat connections, the Alexander invariant, and Casson's invariant, Comm. Anal. Geom., 5 (1997) 93—120.
Legendrian cobordism and Chern-Simons theory on 3-manifolds with boundary, Comm. Anal. Geom., 2 (1994) 337—413.
last updated 1/2/23