# Publications

Below are my publications. This site is currently under construction. I will have more downloadable documents available shortly.

## Preprints and Publications

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)

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