Below are my publications. This site is currently under construction. I will have more downloadable documents available shortly.
Preprints and Publications
- The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology, (with M. Hedden, M. Hogancamp, and P. Kirk), to appear in Trans. Amer. Math. Soc. 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 clusterÐdilute 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. MoosmŸller, 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, 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.
This webpage is under construction. Please check back for updates. (In the meantime, many of the recent papers listed above are listed on the mathematics preprint arxiv.)
last updated 12/25/19 (still somewhat under construction)