SMALL Publications

Publications 2004 - Present

(Asterisks denote current or former students -- see below for publications based on work before 2004)

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, to appear.

Elizabeth Adams*, Ivan Corwin*, Diana Davis*, Michelle Lee*, Regina Visocchi*, Isoperimetric Regions in Gauss Sectors, Rose-Hulman Und. Math. J. 8 (2007), no. 1.

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, The Journal of Number Theory, to appear.

Colin Carroll*, Adam Jacob*, Conor Quinn*, Robin Walters*, The Isoperimetric problem on planes with density, Bull. Austral. Math. Soc. to appear.

Joe Corneli*, Ivan Corwin*, Stephanie Hurder*, Vojislav Sesum*, Ya Xu*, Elizabeth Adams*, Diana Davis*, Michelle Lee*, Regina Viscocchi*, Double bubbles in Gauss space and spheres, Houston J. Math., to appear.

Ivan Corwin*, Neil Hoffman*, Stephanie Hurder*, Vojislav Sesum*, Ya Xu*, Differential geometry of manifolds with density, Rose-Hulman Und. Math. J. 7 (2006), no. 1.

S. Devadoss, J. Danciger*, and D. Sheehy*, Compatible triangulations and series-triangular graphs, "Computational Geometry: Theory and Applications 34 (2006), 195-202.

Carl Erickson*, Nathan Kaplan*, Neil Mendoza*, Allison M. Pacelli, and Todd Shayler*, Parameterized Families of Quadratic Number Fields with 3-Rank At Lest 2, Acta Arithmetica, to appear.

Jack Huizenga*, Kristopher Tapp, Invariant metrics with nonnegative curvature on SO(4) and other Lie groups, Michigan Math Journal, to appear.

Jennifer James*, Thomas Koberda*, Kathryn Lindsey*, Cesar E. Silva, Peter Speh*, Measurable Sensitivity, Proc. Amer. Math. Soc., to appear.

Daniel Kane*, Weak mixing of a transformation similar to Pascal, Colloq. Math. 108 (2007), no. 1, 135-140.

James Kingsbery*, Alex Levin*, Anatoly Preygel*, and Cesar E. Silva, Measurable dynamics of maps on profinite groups, Indag. Math., to appear.

James Kingsbery*, Alex Levin*, Anatoly Preygel*, and Cesar E. Silva, On measure-preserving C1 transformations of compact-open subsets of non-archimedean local fields, Tran. Amer. Math. Soc., to appear.

Michelle Lee*, Isoperimetric regions in surfaces and in surfaces with density, Rose-Hulman Und. Math. J. 7 (2006), no. 2.

Publications 1999 - 2003

(Asterisks denote current or former students -- see below for publications based on work before 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.

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, to appear.

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

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.

Thommas 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.

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 (Decmber 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.