Research Publications

 Publications from SMALL 2014-2016

(Asterisks denote current or former students — see below for publications based on work before SMALL 2014)

  • Owen Barrett*, Brian McDonald*, Ryan Patrick*, Caroline Turnage-Butterbaugh and Karl Winsor*, Gaps between zeros of GL(2) L-functions, to appear in the Journal of Mathematical Analysis and Applications, Updated April 2015.  http://arxiv.org/pdf/1410.7765v2
  • A. Best*, P. Dynes*, X. Edelsbrunner*, B. McDonald*, S. J. Miller, C. Turnage-Butterbaugh* and M. Weinstein*), Benford Behavior of Zeckendorf Decompositions, to appear in the Fibonacci Quarterly. Updated March 2015.  http://arxiv.org/pdf/1409.0482v1
  • A. Best*, P. Dynes*, X. Edelsbrunner*, B. McDonald*, S. J. Miller, C. Turnage-Butterbaugh* and M. Weinstein*), Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals, to appear in the Fibonacci Quarterly. Updated March 2015.  http://arxiv.org/pdf/1409.0483v1
  • Andrew Best*, Patrick Dynes*, Xixi Edelsbrunner*, Brian McDonald*, Kimsy Tor*, Caroline Turnage-Butterbaugh and Madeleine Weinstein*, Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals, submitted. Updated March 2015.  http://arxiv.org/pdf/1501.06833v2
  • Andrew Best*, Karen Huan*, Steven J. Miller, Nathan McNew, Jasmine Powell*, Kimsy Tor* and Madeleine Weinstein*, Geometric-Progression-Free Sets over Quadratic Number Fields, Geometric-Progression-Free Sets over Quadratic Number Fields, submitted. Updated March 2015.  http://arxiv.org/pdf/1412.0999v1
  • Wyatt Boyer*, Bryan Brown*, Gregory Chambers, Alyssa Loving*, and Sarah Tammen*, Isoperimetric regions in Rn with density rp, arxiv.org/abs/1504.01720 (2015). Updated April 2015.
  • Wyatt Boyer*, Bryan Brown*, Paul Gallagher*, David Hu*, Alyssa Loving*, Zane Martin*, Maggie Miller*, Byron Perpetua*, and Sarah Tammen*. The convex body isoperimetric conjecture in R2, in preparation. Updated March 2015.
  • Wyatt Boyer*, Bryan Brown*, Alyssa Loving*, and Sarah Tammen*, Double bubbles in hyperbolic surfaces, work in progress. Continued by Alyssa Loving as undergraduate research at the University of Hawaii. Updated March 2015.
  • Wyatt Boyer*, Bryan Brown*, Alyssa Loving*, and Sarah Tammen*, Optimal transportation with constant constraint, submitted. Updated March 2015.
  • Alan Chang*, David Mehrle*, Steven J. Miller, Tomer Reiter*, Joseph Stahl* and Dylan Yott*, Newman’s Conjecture in Function Fields, submitted.  Updated March 2015.  http://arxiv.org/pdf/1310.3477v1 
  • Julien Clancy*, Rina Friedberg*, Indraneel Kasmalkar*, Isaac Loh*, Tudor Padurariu*, Cesar E. Silva, Sahana Vasudevan*, Ergodicity and Conservativity of products of infinite transformations and their inverses, preprint. Updated March 2015.
  • Xixi Edelsbrunner*, Karen Huan*, Blake Mackall*, Steven J. Miller, Jasmine Powell*, Caroline Turnage-Butterbaugh and Madeleine Weinstein*, Benfordness of Cauchy Distributions, part of Chapter 3: Fourier Analysis and Benford’s Law, in the book Benford’s Law: Theory and Applications, Steven J. Miller, editor. Updated March 2015. http://web.williams.edu/Mathematics/sjmiller/public_html/benford/
  • Feixue Gong*, Olivia Meyerson*, Jeremy Meza*, Mihai Stoiciu, Abigail Ward*, Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators’, preprint. Updated March 2015.
  • Blake Mackall*, Steven J. Miller, Christina Rapti* and Karl Winsor*, Lower-Order Biases in Elliptic Curve Fourier Coefficients in Families, to appear in the Conference Proceedings of the Workshop on Frobenius distributions of curves at CIRM in February 2014. Updated March 2015.  http://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/BiasCIRM30.pdf
  • Steven J. Miller, Kirk Swanson*, Kimsy Tor* and Karl Winsor*, Limiting Spectral Measures for Random Matrix Ensembles with a Polynomial Link Function, submitted. Updated March 2015.  http://arxiv.org/pdf/1411.3442v1

 

Publications from SMALL 2009 – 2013

(Asterisks denote current or former students — see below for publications based on work before SMALL 2009)

  • C. Adams, D. Collins*, K. Hawkins*, C. Sia*, R. Silversmith*, B. Tshishiku*, Planar and Spherical Stick Indices of Knots, Journal of Knot Theory and Its Ramifications, Vol. 20, No. 5 (2011), 721-739.
  • C. Adams, D. Collins*, K. Hawkins*, C. Sia*, R. Silversmith*, B. Tshishiku*, Duality Properties of Indicatrices of Knots, Geometriae Dedicata, 159 (2012), 185-206.
  • C. Adams, M. Chu*, T. Crawford*, S. Jensen*, K. Siegel*, L. Zhang*, Stick Index of Knots and Links in the Cubic Lattice, Journal of Knot Theory and its Ramifications, Vol. 21, No. 5 (2012), 1250041(16 pages).
  • C. Adams, N. MacNaughton*, C. Sia*, From Doodles to Diagrams to Knots, Mathematics Magazine, Vol. 86, No. 2, April, 2013, 83-96.
  • J. Ahn*, E. Ferme*, F. Jiang*, S. Loepp, G. Tran*, Completions of Hypersurface Domains, Communications in Algebra, (2013), no. 1, 29-56.
  • O. Aichholzer, H. Cheng*, S. Devadoss, T. Hackl, S. Huber, B. Li*, A. Risteski*, What Makes a Tree a Straight Skeleton?, Proceedings of the Canadian Conference on Computational Geometry (2012).
  • O. Aichholzer, H. Cheng*, S. Devadoss, T. Hackl, S. Huber, B. Li*, A. Risteski*, What Makes a Tree a Straight Skeleton?, Proceedings of the European Conference on Computational Geometry (2012).
  • Levent Alpoge* and Steven J. Miller, The low-lying zeros of level 1 Maass forms, Int Math Res Notices (2014), 24 pages, doi:10.1093/imrn/rnu012.  http://arxiv.org/pdf/1301.5702v2
  • N. Amersi*, O. Beckwith* S. J. Miller, R. Ronan*, J. Sondow, Generalized Ramanujan Primes, Combinatorial and Additive Number Theory, CANT 2011 and 2012 (Melvyn B. Nathanson, editor), Springer Proceedings in Mathematics \& Statistics (2014), 1–13.  http://arxiv.org/pdf/1108.0475v4
  • Julio Andrade, Alan Chang* and Steven J. Miller, Newman’s conjecture in various settings, Journal of Number Theory 144 (2014), 70–91. http://arxiv.org/pdf/1310.3477v1
  • Julio Andrade, Steven J. Miller, Kyle Pratt* and Minh-Tam Trinh*, Sets of Special Primes in Function Fields, INTEGERS 14 (2014), #A18. http://arxiv.org/pdf/1309.5597v1
  • Julio Andrade, Kyle Pratt*, Steven J. Miller and Minh-Tam Trinh*, The n-Level Density of Dirichlet L-Functions over F_q[T]$, Communications in Number Theory and Physics 8 (2014), no. 3, 1–29.  http://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/ampt_dirichlet_62rCNTP.pdf
  • N. Arnosti*, R. Karpman*, C. Leverson*, J. Levinson*, S. Loepp, Semi-Local Formal Fibers of Minimal Prime Ideals of Excellent Reduced Local Rings, Journal of Commutative Algebra, (2012), no. 1, 29-56.
  • T. Becker*, A Greaves-Tunnell*, L. Kontorovich*, S. J. Miller, K Shen*, Virus Dynamics on Spoke and Star Graphs, Journal of Nonlinear Systems and Applications, 4 (2013), no. 1, 53–63.  http://arxiv.org/pdf/1111.0531v2
  • O. Beckwith*, A. Bower*, L. Gaudet, R. Insoft*, S. Li*, S. J. Miller and P. Tosteson*, The Average Gap Distribution for Generalized Zeckendorf Decompositions, Fibonacci Quarterly, 51 (2013), 13–27.  http://arxiv.org/pdf/1208.5820v3
  • Olivia Beckwith*, Victor Luo*, S. J. Miller, Karen Shen* and Nicholas Triantafillou*, Distribution of eigenvalues of weighted, structured matrix ensembles, to appear in Integers: Electronic Journal Of Combinatorial Number Theory. http://arxiv.org/pdf/1112.3719v2
  • Amanda Bower*, Rachel Insoft*, Steven J. Miller, Shiyu Li* and Philip Tosteson*, Distribution of gaps in generalized Zeckendorf decompositions, Journal of Combinatorial Theory, Series A 135 (2015), 130–160.  http://arxiv.org/pdf/1402.3912v2
  • A. Bower*, R. Evans, V. Luo* and S. J. Miller, Generalized sum and difference sets of d-dimensional modular hyperbolas, Integers, INTEGERS #A31, 2013, 16 pages.  http://arxiv.org/pdf/1212.2930.pdf
  • E. Burger, D. Clyde*, C. Colbert*, G. Shin*, Z. Wang*, A Generalization of a Theorem of Lekkerkerker to Ostrowski’s Decomposition of Natural Numbers, Acta Arithmetica, 153 (2012), 217-249.
  • E. Burger, D. Clyde*, C. Colbert*, G. Shin*, Z. Wang*, Canonical Diophantine representations of natural numbers with respect to quadratic “bases,” Journal of Number Theory, 133 (2013), 1372-1388.
  • Francesco Cellarosi, Doug Hensley, Steven J. Miller and Jake Wellens*, Continued Fraction Digit Averages and Maclaurin’s Inequalities, Experimental Mathematics 24 (2015), no. 1, 23–44.  http://arxiv.org/pdf/1402.0208v3
  • H. Cheng*, S. Devadoss, B. Li*, A. Risteski*, Skeletal Configurations of Ribbon Trees, Discrete Applied Mathematics, 170 (2014) 46-54.
  • P. Chung*, M. Fernandez*, Y. Li*, M. Mara*, F. Morgan, I Plata*, N. Shah*, L. Vieira*, E. Wikner*, Isoperimetric pentagonal tilings, Notices Amer. Math. Soc., 59 (May, 2012), 632-640.
  • P. Chung*, M. Fernandez*, N. Shah*, L. Vieira*, E. Wikner*, Perimeter-minimizing pentagonal tilings, Involve, to appear (2012).
  • Z. Chonoles*, J. Cullinan, H. Hausman*, A. Pacelli, S. Pegado*, F. Wei*, Arithmetic Properties of Generalized Rikuna Polynomials, Publications Mathematiques de Besancon, to appear.
  • Taylor Corcoran*, Victor Luo*, Steven J. Miller and Jaclyn Porfilio*, Pythagoras at the Bat, book chapter in Social Networks and the Economics of Sports (organized by Victor Zamaraev), Springer-Verlag, 2014.. http://arxiv.org/pdf/1406.0758v1
  • V. Cuff*, A. Lewis*  and S. J. Miller, The Weibull distribution and Benford’s law, to appear in Involve. http://arxiv.org/pdf/1402.5854v1
  • I. Dai*, X. Garcia*, T. Padurariu*, C. Silva, On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations, Ergodic Theory and Dynamical Systems, to appear.
  • Philippe Demontigny*, Thao Do*, Archit Kulkarni*, Steven J. Miller and Umang Varma*, A Generalization of Fibonacci Far-Difference Representations and Gaussian Behavior, Fibonacci Quarterly 52 (2014), no. 3, 247–273.. http://arxiv.org/pdf/1309.5600v3
  • Philippe Demontigny*, Thao Do*, Archit Kulkarni*, Steven J. Miller and Umang Varma, Generalizing Zeckendorf’s Theorem to f-decompositions, Journal of Number Theory 141 (2014), 136–158. http://arxiv.org/pdf/1309.5599v1
  • S. Devadoss, D. Huang*, D. Spadacene*, Polyhedral covers of tree space, SIAM Journal of Discrete Mathematics, 28 (2014) 1508-1514.
  • A. Díaz*, N. Harman*, S. Howe*, D. Thompson*, Isoperimetric problems in sectors with density, Advances in Geometry, 12 (2012) 589-619.
  • Thao Do*, Archit Kulkarni*, Steven J.  Miller*, David Moon* and Jake Wellens*, Sums and Differences of Correlated Random Sets, to appear in the Journal of Number Theory.  http://arxiv.org/pdf/1401.2588v1
  • C. Dominguez*, S. J. Miller, S. Wong, Quadratic Fields with Cyclic 2-class Groups, Journal of Number Theory, 133 (2013), no. 3, 926-939. http://arxiv.org/pdf/1211.2605v1
  • P. Gallagher*, W. Ghang*, D. Hu*, Z. Martin*, M. Miller*, B. Perpetua*, S. Waruhiu*, Surface-area-minimizing n-hedrals, Rose-Hulman Und. Math. J. 15(1) (2015). http://www.rose-hulman.edu/mathjournal/v15n1.php
  • Paul Gallagher, David Hu, Zane Martin, Maggie Miller, Byron Perpetua, Isoperimetric problem on the plane with density e^-1/r, Rose-Hulman Und. Math. J. 15(2) (2015). http://www.rose-hulman.edu/mathjournal/v15n2.php
  • W. Ghang*, Z. Martin*, S. Waruhui*, The sharp log-Sobolev inequality on a compact interval, Involve, 7-2 (2014), 181-186.
  • J. Goes*, S. Jackson*, S. J. Miller, D. Montague*, K. Ninsuwan*, R. Peckner*, T. Pham*, A Unitary Test of the L-functions Ratios Conjecture, the Journal of Number Theory 130 (2010), no. 10, 2238–2258. http://arxiv.org/pdf/0909.4916v3
  • J. Goes* and S. J. Miller, Towards an `average’ version of the Birch and Swinnerton-Dyer Conjecture, the Journal of Number Theory 130 (2010), no. 10, 2341–2358.  http://arxiv.org/pdf/0911.2871v2
  • Leo Goldmakher, Cap Khoury, Steven J. Miller and Kesinee Ninsuwan*, The expected eigenvalue distribution of large, weighted d-regular graphs. Random Matrices: Theory and Applications 3 (2014), no. 4, 1450015.   http://arxiv.org/pdf/1306.6714.pdf
  • A. Henrich, N. MacNaughton*, S. Narayan*, O. Pechenik*, J. Townsend*, Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus, Journal of Knot Theory and Its Ramifications, Vol. 20, No. 4 (2011), 625-650.
  • A. Henrich, N. MacNaughton*, S. Narayan*, O. Pechenik*, R. Silversmith*, J. Townsend*, A Midsummer Knot’s Dream, The College Math Journal, Vol. 42, No. 2, March 2011, 126-134.
  • G. Iyer*, O. Lazarev*, S. J. Miller, L. Zhang*, Finding and Counting MSTD Sets, Combinatorial and Additive Number Theory, CANT 2011 and 2012 (Melvyn B. Nathanson, editor), Springer Proceedings in Mathematics & Statistics (2014), 79–98. http://arxiv.org/pdf/1107.2719v1
  • G. Iyer*, O. Lazarev*, S. J. Miller, L. Zhang*, Generalized More Sums Than Difference Sets, Journal of Number Theory, 132 (2012), no. 5, 1054-1073. http://arxiv.org/pdf/1108.4500.pdf
  • S. Jackson*, T. Pham* and S. J. Miller, Distribution of eigenvalues for highly palindromic real symmetric Toeplitz matrices, Journal of Theoretical Probability, 25 (2012), 464–495.  http://arxiv.org/pdf/1003.2010v2
  • M. Kologlu*, G. Kopp*, S. J. Miller, F. W. Strauch, W. Xiong, The Limiting Spectral Measure for Ensembles of Symmetric Block Circulant Matrices, Journal of Theoretical Probability, 26 (2013), no. 4, 1020–1060. http://arxiv.org/pdf/1008.4812v5
  • M. Kologlu*, G. Kopp*, S. J. Miller, Y. Wang*, On the number of summands in Zechendorf decompositions, Fibonacci Quarterly, 49 (2011), no. 2, 116-130.  http://arxiv.org/pdf/1008.3204.pdf
  • O. Lazarev*, S. J. Miller and K. O’Bryant, Distribution of Missing Sums in Sumsets, Experimental Mathematics, 22 (2013), no. 2, 132–156. http://arxiv.org/pdf/1109.4700v3
  • Y. Li*, M. Mara*, I. Plata*, E. Wikner*, Tiling with penalties and isoperimetry with density, Rose-Hulman Und. Math. J. 13 (1), 2012.
  • L. Manuelli*, J. Hallett*, C. Silva, On Li-Yorke Measurable Sensitivity, Proceedings Amer. Math. Soc., to appear.
  • S. J. Miller and D. Montague*, An Orthogonal Test of the L-functions Ratios Conjecture, II, Acta Arithmetica, 146 (2010), 53-90. http://arxiv.org/pdf/0911.1830.pdf
  • S. J. Miller and D. Montague*, Rational irrationality proofs, Mathematics Magazine, 85 (2012) no.2, 110-114. http://arxiv.org/pdf/0909.4913v2
  • S. J. Miller and R. Peckner*, Low-lying zeros of number field L-functions, Journal of Number Theory 132 (2012), 2866–2891. http://arxiv.org/pdf/1003.5336v1
  • S. J. Miller and K. Vissuet, Most Subsets are Balanced in Finite Groups, Combinatorial and Additive Number Theory, CANT 2011 and 2012 (Melvyn B. Nathanson, editor), Springer Proceedings in Mathematics \& Statistics (2014), 147–157. http://arxiv.org/pdf/1308.2344v2
  • S. J. Miller and Y. Wang*, From Fibonacci numbers to Central Limit Type Theorems, Journal of Combinatorial Theory, Series A 119 (2012), no. 7, 1398–1413. http://arxiv.org/pdf/1008.3202v3
  • S. J. Miller and Y. Wang*, Gaussian Behavior in Generalized Zeckendorf Decompositions, CANT 2011 and 2012 (Melvyn B. Nathanson, editor), Springer Proceedings in Mathematics & Statistics (2014), 159–173. http://arxiv.org/pdf/1107.2718v1
  • F. Morgan, S. Howe*, N. Harman*, Steiner and Schwarz symmetrization in warped products and fiber bundles with density, Revista Mat. Iberoamericana, 27 (2011), 909-918. http://arxiv.org/abs/0911.1938.

Publications from SMALL 2004 – 2008

(Asterisks denote current or former students — see below for publications based on work before SMALL 2009)

  • C. Adams, H. Bennett*, C. Davis*, M. Jennings*, J. Novak*, N. Perry* and E. Schoenfeld*, Totally Geodesic Surfaces in Hyperbolic Knot and Link Complements II, Journal of Differential Geometry, Vol. 79, No. 3, May, 2008, 1-23.
  • C. Adams, W. George*, R.  Hudson*, R. Morrison*,  L. Starkston*, S. Taylor*, O. Turanova*, The Spiral Index on Knots, The Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 149, Issue 2, (2010), 297-315.
  • C. Adams, T. Kindred*, Spanning Surfaces in Alternating Knot Complements, Algebraic and Geometric Topology 13, (2013) 2967-3007.
  • Elizabeth Adams*, Ivan Corwin*, Diana Davis*, Michelle Lee*, Regina Visocchi*, Isoperimetric regions in Gauss sectors, Rose-Hulman Und. Math. J. 8 no. 1 (2007). http://www.rose-hulman.edu/mathjournal/v8n1.php.
  • D. Aiello*, H. Diao*, Z. Fan*, D. King*, J. Lin*, C. Silva, Measurable Time-Restricted Sensitivity, Nonlinearity 25 (2012) 3313-3325.
  • A. Boocher*, M. Daub*, R. Johnson*, H. Lindo*, S. Loepp, and P. Woodard*,  Formal Fibers of Unique Factorization Domains, Canadian Journal of Mathematics, 62, (2010), 721-736.
  • A. Boocher*, M. Daub*, S. Loepp, Dimensions of Formal Fibers of Height one Prime Ideals, Communications in Algebra, (2010), no. 1, 233-253.
  • Nathan Brown*, Rachel Fink*, Matthew Spencer*, Kristopher Tapp, Zhongtao Wu*, Invariant metrics with nonnegative curvature on compact Lie groups, Canad. Math. Bull. 50 (2007), no. 1, 24-34.
  • E.B. Burger, J. Gell-Redman*, R. Kravitz*, D. Walton*, N. Yates*), Shrinking the period lengths of continued fractions while still capturing convergents, Journal of Number Theory, 128 (2008) 144-153.
  • Colin Carroll*, Adam Jacob*, Conor Quinn*, Robin Walters*, The isoperimetric problem on planes with density, Bull. Austral. Math. Soc. 78 (2008) 177-197.
  • J. Chatlos*, B. Simanek*, N. Watson*, S. Wu*, Semilocal Formal Fibers of Principal Prime Ideals, Journal of Commutative Algebra, to appear.
  • Joe Corneli*, Ivan Corwin*, Stephanie Hurder*, Vojislav Sesum*, Ya Xu*, Elizabeth Adams*, Diana Davis*, Michelle Lee, Regina Visocchi, Double bubbles in Gauss space and spheres, Houston J. Math. 34  (2008) 181-204.
  • Ivan Corwin*, Neil Hoffman*, Stephanie Hurder*, Vojislav Sesum*, Ya Xu*, Differential geometry of manifolds with density, Rose-Hulman Und. Math. J. 7 no. 1 (2006). http://www.rose-hulman.edu/mathjournal/v7n1.php.
  • D. Creutz*, C. Silva, Mixing on Rank-One Transformations, Studia Mathematica, 199 (2010), no. 1, 43-72.
  • J. Dahlberg*, A. Dubbs*, E. Newkirk*, H. Tran*, Isoperimetric regions in the plane with density rp  , New York J. Math. 16 (2010), 31-51. http://nyjm.albany.edu/j/2010/16-4.html.
  • J. Danciger*, S. Devadoss, J. Mugno*, D. Sheehy* and R. Ward*, Shape Deformation in Continuous Map Generalization”, GeoInformatica 13 (2009) 203- 221.
  • M. Daub*, J. Lang*, M. Merling*, A. Pacelli, N. Pitiwan*, and M. Rosen, Function Fields with Class Number Indivisible by a Prime p, Acta Arithmetica, 150 (2011), 339-359.
  • S. Devadoss, J. Danciger*, and D. Sheehy*, Compatible triangulations and series-triangular graphs, Computational Geometry: Theory and Applications 34 (2006) 195-202.
  • S. Devadoss, B. Fehrman*, T. Heath*, A. Vashist*, Moduli Spaces of Punctured Poincare Disks, Tamari Memorial Festschrift:  Progress in Mathematics, Volume 299 (2012).
  • S. Devadoss, T. Heath*, C. Vipismakul*, Deformations of Bordered Riemann Surfaces and Associahedral Polytopes, Notices of the American Mathematical Society, 58 (2011) 530-541.
  • S. Devadoss, R. Shah*, X. Shao*, E. Winston*, Visibility Graphs and Deformations of Associahedra, Contributions to Discrete Mathematics 7 (2012) 68-81.
  • H. Diao*, and C. Silva, Digraph Representations of Rational Functions over the p-adic Numbers, with P-adic Numbers, Ultrametric Analysis, and Applications, Vol. 3, no. 1 (2011), 23-38.
  • Chris Dodd*, Phakawa Jeasakul*, Anne Jirapattanakul*, Daniel M. Kane*, Becky Robinson*, Noah D. Stein*, Cesar E.  Silva. Ergodic Properties of a Class of Discrete Abelian Group Extensions of Rank-One Transformations, Colloquium Mathematicum, 119 (2010), 1-22.
  • Alexander Dubbs*, Jonathan Dahlberg*, Edward Newkirk*, Hung Tran*, Isoperimetric regions in the plane with density r^p, New York J. Math., to appear.
  • Max Engelstein*, The least-perimeter partition of a sphere into four equal areas, Disc. Comp. Geom., 44 (2010), 645-653.
  • Max Engelstein*, Anthony Marcuccio*, Quinn Maurmann*, and Taryn Pritchard*, Isoperimetric problems on the sphere and on surfaces with density, New York J. Math. 15 (2009), 97-123. http://www.emis.de/journals/NYJM/j/2009/Vol15.html.
  • C. Erickson*, N. Kaplan*, N. Mendoza*, A. Pacelli, T. Shayler*, Parametrized Families of Quadratic Number Fields with 3-Rank at Least 2  Acta Arithmetica, 130 (2007) 141 – 147.
  • I. Grigoriev*, N. Ince*, C. Iordan*, A. Lubin*, C. Silva, On mu-Compatible Metrics and Measurable Sensitivity, Colloquium Math., 126 (2012), 53-72.
  • Huizenga, Jack*; Tapp, Kristopher Invariant metrics with nonnegative curvature on $\rm SO(4)$ and other Lie groups. Michigan Math. J. 55, no. 3 (2007) 609–630.
  • James, Jennifer*; Koberda, Thomas*; Lindsey, Kathryn*; Silva, Cesar E.; Speh, Peter*,  Measurable sensitivity. Proc. Amer. Math. Soc. 136, no. 10 (2008) 3549–3559.
  • James, Jennifer*; Koberda, Thomas*; Lindsey, Kathryn*; Silva, Cesar E.; Speh, Peter*; On ergodic transformations that are both weakly mixing and uniformly rigid. New York Journal of Mathematics, no. 15 (2009) 393-403.
  • Daniel Kane*, Weak mixing of a transformation similar to Pascal, Colloq. Math. 108, no. 1 (2007) 135-140.
  • Kingsbery, James*; Levin, Alex*; Preygel, Anatoly*; Silva, Cesar E. Dynamics of the p-adic shift and applications, Discrete and Continuous Dynamical Systems, 30, (2011), no. 1, 209-218.
  • Kingsbery, James*; Levin, Alex*; Preygel, Anatoly*; Silva, Cesar E. Measurable dynamics of maps on profinite groups. Indag. Math. (N.S.) 18, no. 4, (2007) 561–581.
  • Kingsbery, James*; Levin, Alex*; Preygel, Anatoly*; Silva, Cesar E. On measure-preserving $C\sp 1$ transformations of compact-open subsets of non-Archimedean local fields. Trans. Amer. Math. Soc. 361, no. 1 (2009) 61–85.
  • Michelle Lee*, Isoperimetric regions in surfaces and in surfaces with density, Rose-Hulman Und. Math. J. 7, no. 2 (2006). http://www.rose-hulman.edu/mathjournal/v7n2.php.
  • Quinn Maurmann*, Max Engelstein*, Anthony Marcuccio*, and Taryn Pritchard*, Asymptotics of perimeter-minimizing partitions, Canadian Math. Bull., 53 (2010), 516-525.
  • Quinn Maurmann* and Frank Morgan, Isoperimetric comparison theorems for manifolds with density, Calc. Var. PDE 36 (2009) 1-5.
  • Conor Quinn*, Area-minimizing partitions of the sphere, Rose-Hulman Und. Math. J. 8, no. 2 (2007). http://www.rose-hulman.edu/mathjournal/v8n2.php.

Publications from SMALL 1999 – 2003

(Asterisks denote current or former students — see below for publications based on work before SMALL 1999)

  • C. Adams, A. Colestock*, J. Fowler*, W.D. Gillam*, E. Katerman*, Cusp Size Bounds from Surfaces in Hyperbolic 3-Manifolds, Trans. Amer. Math. Soc. 358 (2005), No. 2, 727-741.
  • C. Adams, A. Colestock*, J. Fowler*, W.D. Gillam*, E. Katerman*, Cleanliness of Geodesics in Hyperbolic 3-Manifolds, Pacific Journal of Mathematics 213 (2004), 201-211.
  • C. Adams, T. Fleming*, M. Levin*, A. Turner*, Alternating Knots in S x I, Pacific Journal of Mathematics 203 (2002), no. 1, 1-22.
  • C. Adams, C. Lefever*, J. Othmer*, S. Pahk*, A. Stier* and J. Tripp*, An Introduction to the Supercrossing Index of Knots and the Crossing Map, Journal of Knot Theory and its Ramifications 11 (2002), no. 3, 445-459.
  • S. Armstrong*, M. Carr*, S. Devadoss, E. Engler*, A. Leininger*, M. Manapat*, Particle Configurations and Coxeter Operads, Homotopy and Related Structures, 4 (2009) 83-109.
  • Sami Assaf*, Li-Chung Chen*, Tegan Cheslack-Postava*, Benjamin Cooper*, Alexander Diesl*, Thomas Garrity, Matthew Lepinski* and Adam Schuyler*, A Dual Approach to Triangle Sequences: A Multidimensional Continued Fraction Algorithm, Integers: Electronic Journal of Combinatorial Number Theory 5 (2005).
  • Tracy Borawski Baker* amnd Robert Lopez*, The Double Bubble Problem on the cone, NY J. Math. 12 (2006) 157-167. Preprint available at http://nyjm.albany.edu:8000/j/2006/12-9.html.
  • A. Bowels*, L. Fidkowski*, A. Marinello*, and C.E. Silva, Double ergodicity of nonsingular transformations and infinite measure-preserving staircase transformations, Illinois J. Math. 45 (2001) 999-1019.
  • J. Bryk* and C.E. Silva, Measurable dynamics of simple p-adic polynomials, American Math. Monthly 112 (2005) no. 3, 212-232.
  • J. Bryk*, S. Mapes*, C. Samuels*, and G. Wang*, Constructing Almost Excellent Unique Factorization Domains, Communications in Algebra 33 (2005) 1321-1336.
  • E. Burger, A. Folsom*, A. Pekker*, R. Roengpitya*, J. Snyder*, On a quantitative refinement of the Lagrange spectrum, Acta Arithmetica 102 (2002) 55-82. This paper answers a long-standing open question of Davenport from 1947.
  • M. Carr* and S. Devadoss, Coxeter complexes and graph-associahedra, Topology and its Applications 153 (2006) 2155-2168.
  • Miguel Carrin, Joseph Corneli*, Genevieve Walsh, and Shabnam Beheshti, Double bubbles in the three-torus, Exp. Math. 12 (2003) 79-89.
  • Joseph Corneli*, Neil Hoffman*, Paul Holt*, George Lee*, Nicholas Leger*, Stephen Moseley*, Eric Schoenfeld*, Double bubbles in S3 and H3, J. Geom. Anal. 17 (2007) 189-212.
  • Joseph Corneli*, Paul Holt*, George Lee*, Nicholas Legher*, Eric Schoenfeld*, and Benjamin Steinhurst*, The double bubble problem on the flat two-torus, Trans. Amer. Math. Soc. 356 (2004) 3769-3820.
  • Joseph Corneli*, Paul Holt*, Nicholas Leger*, and Eric Schoenfeld*, Student Chapter Members at Board of Governors Meeting, MAA FOCUS (November, 2001).
  • Joseph Corneli*, Paul Holt*, Nicholas Leger*, Frank Morgan, and Eric Schoenfeld*, Mathematicians on Michael Feldman’s ‘Whad’Ya Know?’, MAA FOCUS (November, 2001).
  • Andrew Cotton* and David Freeman*, The double bubble problem in spherical and hyperbolic space, Intern. J. Math. Math. Sci. 32 (2002) 641-699.
  • Andrew Cotton*, David Freeman*, Andrew Gnepp*, Ting Fai Ng*, John Spivack*, and Cara Yoder* (Geometry Groups 1998 and 2000). The isoperimetric problem on some singular surfaces, J. Austral. Math. Soc. 78 (2005) 167-197.
  • D. Creutz* and C.E. Silva, Mixing on a class of rank one transformations, Ergodic Theory and Dynamical Systems 24 (2004) no. 2, 407-440.
  • A. Dundon*, D. Jensen*, S. Loepp, J. Provine*, and J. Rodu*, Controlling Formal Fibers of Principal Prime Ideals, Rocky Mountain Journal of Mathematics, 37 (2007) 1871-1892.
  • K. Gruher*, F. Hines*, D. Patel*, C.E. Silva, and R. Waelder*, Power Weak Mixing does not imply Multiple Recurrence in Infinite Measure and other Counterexamples, New York J. Math. 9 (2003) 1-22.
  • Cory Heilmann*, Yuan Lay*, Ben Reichardt*, and Anita Spielman*, Proof of the Double Bubble Conjecture in R4 and certain higher dimensional cases, Pacific J. Math. 208 (2003) 347-366.
  • Michael Hutchings*, Frank Morgan, Manuel Ritor, and Antonio Ros, Proof of the double bubble conjecture, Ann. Math. 155 (March, 2002) 459-489. Using work begun by Hutchings as an undergraduate during and after SMALL.
  • S. Iams*, B. Katz*, C.E. Silva, B. Street*, and K. Wickelgren*, Weakly mixing and doubly ergodic infinite measure-preserving Rd actions, Colloq. Math. 103 (2005) 247-264.
  • D. Lee*, L. Leer*, S. Pilch*, and Y. Yasufuku*, Characterizations of Completions of Reduced Local Rings, Proc. Amer. Math. Soc. 129 (2001) 3193-3200.
  • D. Lee*, L. Leer*, S. Pilch*, and Y. Yasufuku*, Excellent Rings with Singleton Formal Fibers, Furman University Electronic Journal of Undergraduate Mathematics (1999).

Publications 1988 – 2002, based on work through 1998

(Asterisks denote current or former students)

  • C. Adams, B. Brennan*, D. Greilsheimer*, A. Woo*, Stick Numbers and Composition of Knots and Links, Journal of Knot Theory and its Ramifications 6 (1997), no. 2, 149-161.
  • C. Adams, J. Brock*, J. Bugbee*, T. Comar*, K. Faigin*, A. Huston*, A. Joseph*, D. Pesikoff*, Almost Alternating Links, Topology and its Applications 46 (1992), 151-165.
  • C. Adams, K. Foley*, J. Kravis*, R. Dorman*, S. Payne*, Alternating Graphs, Journal of Combinatorial Theory, Series B 77 (1999), no. 1,, 96-120.
  • C. Adams, E. Furstenberg*, J. Li*, J. Schneider*, Exploring Knots, Mathematics Teacher 90 (1997), no. 8, 640-646, 652.
  • C. Adams and W. Sherman*, Minimum Ideals Triangulations of Hyperbolic 3-Manifolds, Journal of Discrete and Computational Geometry 6 (1991), 135-153.
  • Manual Alfaro*, Existence of shortest directed networks in R2, Pacific J. Math. 167 (1995), 201-214.
  • Manual Alfaro*, Jeff Brock*, Joel Foisy*, Nick Hodges*, Jason Zimba*, The standard double soap bubble in R2 uniquely minimizes perimeter, Pacific J. Math. 159 (1993), 47-59. Featured in 1994 What’s Happening in the Mathematical Sciences.
  • M. Alfaro*, T. Campbell*, J. Sher*, A. Soto*, Length Minimizing Directed Networks can Meet in Fours, J. Und. Math 22 (1990), 53-59.
  • M. Alfaro*, M. Conger*, K. Hodges*, R. Kochar*, L. Kuklinski*, A. Levy*, Z. Mahmood*, K. von Haam*, Segments Can Meet in Fours in Energy Minimizing Networks, J. Undergraduate Math 22 (1990), 9-20.
  • M. Alfaro*, M. Conger*, K. Hodges*, A. Levy*, R. Kochar*, L. Kuklinski*, Z. Mahmood*, K. von Haam*, The Structure of Singularities in Phi-Minimizing Networks in 2, Pacific Journal of Math. 149 (1991), 201-210.
  • Megan Barber*, Jennifer Tice*, and Brian Wecht*, Double salt crystals, Acta Crystallographica (Jan. 2000), Sect. A. 92-95.
  • D. Bergstrand, F. Harary, K. Hodges*, G. Jennings*, L. Kuklinsk*, J. Weiner*, Product Graphs are Sum Graphs, Math. Mag. 65 (1992), no. 4, 262-264.
  • D. Bergstrand, F. Harary, K. Hodges*, G. Jennings*, L. Kuklinski*, J. Weiner*, The Sum Number of a Complete Graph, Bull. Malaysian Math. Soc. (2) 12 (1989), no. 1, 25-28.
  • E. Burger, C. Kollett*, On the Structure of Quadratic Irrationals Associated with Generalized Fibonacci and Lucas Numbers, The Fibonacci Quarterly 34 (1996), 200-212.
  • E. Burger, J.M.Todd*, On diophantine approximation below the Lagrange constant, Fibonacci Quarterly 38 (2000), 136-144.
  • Thomas Colthurst*, Chris Cox*, Joel Foisy*, Hugh Howards*, Kathryn Kollett*, Holly Lowy*, Stephen Root*, Networks minimizing length plus the number of Steiner points, appeared in Ding-Zhu Du and Panos M. Pardalos, ed., Network Optimization Problems: Algorithms, Complexity and Applications, World Scientific, (1993), 23-36.
  • M. Conger*, Energy-Minimizing Networks in Rn, J. Und. Math. 22 (1990), 53-59.
  • Christopher Cox*, Flow-dependent networks: existence and behavior at Steiner points, Networks 31 (1998), 149-156.
  • Christopher Cox*, Lisa Harrison*, Meg Tilton*, The shortest enclosure of three connected areas in R2, Real Analysis Exchange 20 (1994/95), 313-335.
  • S.L. Day*, B.R. Grivna*, E.P. McCartney*, and C.E. Silva, Power weakly mixing infinite transformations, New York J. of Math. 5 (1999), 17-24.
  • R.D. De Veaux, J. Schumi*, J. Schweinsberg*, and L.H. Ungar, Predictions Intervals for Neural Networks via Nonlinear Regression, Technometrics 40 (1998), no. 4, 273-282.
  • M. Florenz*, D. Kunvipusilkul*, and J. Yang*, Constructing Chains of Excellent Rings with Local Generic Formal Fibersm Communications in Algebra 30 (2002), 3569-3587,
  • Christopher French*, Frank Morgan, and Scott Greenleaf*, Wulff clusters in R2, J. Geom. Anal., 8 (1998), 97-115.
  • Eric Furstenberg*, Jie Li*, Jodi Schneider*, Stick Knots, Chaos, Solitons and Fractals, special issue devoted to knots and their applications 9 (April/May 1998), no. 4/5, 561-568.
  • David Futer*, Andrew Gnepp*, David McMath*, Brian Munson*, Ting Fai Ng*, Sang Pahk*, and Cara Yoder*, (Geometry Groups 1997 and 1998), Cost-minimizing networks among immiscible fluids in R2, Pacific J. Math. 96 (2000), 295-414.
  • Hugh Howards*, Michael Hutchings*, and Frank Morgan. The isoperimetric problem on surfaces, Am. Math. Monthly 106 (1999), 430-439.
  • Hugh Howards*, Michael Hutchings*, and Frank Morgan, The isoperimetric Problem on Surfaces of Revolution of Decreasing Gauss Curvature, Trans. Amer. Math. Soc. 352 (2000), 4889-4909.
  • Michael Hutchings*, The structure of area-minimizing double bubbles, J. Geom. Anal. 7 (1997), 285-304.
  • G. Jennings*, and W. Lenhart, An Art Gallery Theorem for Line Segments in the Plane, Pattern Recognition Letters (1993) 727-732.
  • A. Levy*, Energy-Minimizing Networks Meet Only in Threes, J. Und. Math 22 (1990), 53-59.
  • Joseph Masters*, The perimeter-minimizing enclosure of two areas in S2, Real Analysis Exchange 22 (1995/96), 1-10.
  • Ted Melnick*, Frank Morgan, and Ramona Nicholson*, The Soap Bubble Geometry Contest, The Mathematics Teacher 90 (December 1997), 746-750.
  • E. Muehlegger*, B. Narasimhan*, A. Raich*, C.E. Silva, M. Touloumtzis*, amd W. Zhao*, Infinite ergodic index Zd actions in infinite measure, Colloquium Math. 82 (1999), no. 2, 167-190.
  • E. Muehlegger*, A. Raich*, C.E. Silva, and W. Zhao*, Lightly mixing on dense algebras, Real Analysis Exchange 23 (1998), no. 1, 259-266.