Publications from SMALL 2017-2019

(Asterisks denote current or former students — see below for publications based on work before SMALL 2017)

- C. Adams, C. Albors Riera*, B. Haddock*, D. Nishida*, B. Reinoso*, L. Wang*, Alternating Links in Thickened Surfaces, ArXiv 1802.05770, to be submitted.
- Megumi Asada*, Eva Fourakis*, Sarah Manski*, Steven J. Miller, Gwyneth Moreland* and Nathan McNew, Subsets of $\mathbb{F}_q[x]$ free of 3-term geometric progressions, Finite Fields and their Applications \textbf{44} (2017), 135–147. [[uploaded to NSF]] https://arxiv.org/abs/1512.01932
- Owen Barrett*, Paula Burkhardt*, Jon DeWitt*, Robert Dorward* and Steven J. Miller, One-Level density for holomorphic cusp forms of arbitrary level, Research in Number Theory \textbf{3} (2017), no. 25, DOI 10.1007/s40993-017-0091-9. [[uploaded to NSF]] https://arxiv.org/abs/1604.03224
- Thealexa Becker*, David Burt*, Taylor C. Corcoran*, Alec Greaves-Tunnell*, Joseph R. Iafrate*, Joy Jing*, Steven J. Miller, Jaclyn D. Porfilio*, Ryan Ronan*, Jirapat Samranvedhya*, Frederick W. Strauch and Blaine Talbut, Benford’s Law and Continuous Dependent Random Variables, Annals of Physics \textbf{388} (2018), 350–381. DOI: 10.1016/j.aop.2017.11.013. [[uploaded to NSF]] https://arxiv.org/abs/1111.0568
- John Berry*, Eliot Bongiovanni*, Wyatt Boyer*, Bryan Brown*, Matthew Dannenberg*, Paul Gallagher*, David Hu*, Jason Liang*, Alyssa Loving*, Zane Martin*, Maggie Miller*, Byron Perpetua*, Sarah Tammen*, and Yingyi Zeng*, The convex body isoperimetric conjecture in
**R**^{2}, Rose-Hulman Und. Math. J., 2018. - John Berry*, Matthew Dannenberg*, Jason Liang*, Yingyi Zeng*, The isoperimetric problem for the sum of two Gaussian densities, Involve, 11:4 (2018), 549–567; [[uploaded to NSF]] https://msp.org/involve/2018/11-4/p02.xhtml

DOI: 10.2140/involve.2018.11.549. arXiv.org - Andrew Best*, Patrick Dynes*, Xixi Edelsbrunner*, Brian McDonald*, Steven J. Miller, Kimsy Tor*, Caroline Turnage-Butterbaugh and Madeleine Weinstein*, Benford Behavior of Generalized Zeckendorf Decompositions, Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer, New York, 2017. https://arxiv.org/abs/1412.6839
- Andrew Best*, Karen Huan*, Nathan McNew, Steven J. Miller, Jasmine Powell*, Kimsy Tor* and Madeleine Weinstein*, Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions, Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer, New York, 2017. https://arxiv.org/abs/1508.02907
- [[–]] Eliot Bongiovanni*, Alejandro Diaz*, Leonardo Di Giosia*, Jay Habib*, Arjun Kakkar*, Lea Kenigsberg*, Dustin Ping*, Dylanger Pittman*, Nat Sothanaphan*, Weitao Zhu*, Double bubbles on the line with log-convex density, Anal. Geom. Metr. Spaces 6 (2018), 64-88. [[—–NEED TO ADD TO THE NSF SITE—–]] https://www.degruyter.com/downloadpdf/j/agms.2018.6.issue-1/agms-2018-0004/agms-2018-0004.pdf
- Wyatt Boyer*, Bryan Brown*, Alyssa Loving*, Frank Morgan, and Sarah Tammen*, Double bubbles in hyperbolic surfaces, Involve 11 (2018), 207-217. DOI 10.2140/involve.2018.11.207. https://msp.org/involve/2018/11-2/p03.xhtml
- Wyatt Boyer*, Bryan Brown*, Alyssa Loving*, and Sarah Tammen*, Optimal transportation with constant constraint,
*Involve*, to appear. - [[—–]] Paula Burkhardt*, Peter Cohen*, Jonathan Dewitt*, Max Hlavacek*, Steven J. Miller, Carsten Sprunger*, Yen Nhi Truong Vu*, Roger Van Peski*, and Kevin Yang*, and an appendix joint with Manuel Fernandez and Nicholas Sieger, Random Matrix Ensembles with Split Limiting Behavior, Random Matrices: Theory and Applications 7 (2018), no. 3, 39 pages, DOI: 10.1142/S2010326318500065. https://arxiv.org/abs/1609.03120 [[—–NEED TO ADD TO THE NSF SITE—–]]
- David Burt, Sam Donow, Steven J. Miller, Matthew Schiffman and Ben Wieland, Irrationality measure and lower bounds for $\pi(x), Pi Mu Epsilon Journal \textbf{14} (2017), no. 7, 421–429. https://arxiv.org/abs/0709.2184
- Jonathan DeWitt*, Kevin Ford*, Eli Goldstein*, Steven J. Miller, Gwyneth Moreland*, Eyvindur A. Palsson, Steven Senger, Dimensional lower bounds for Falconer type incidence and point configuration theorems, to appear in the Journal d’Analyse Math\’ematique. https://arxiv.org/abs/1612.00539
- Leonardo Di Giosia, Jay Habib, Lea Kenigsberg, Dylanger Pittman, Weitao Zhu, The log convex density conjecture in hyperbolic space, Rose-Hulman Und. Math. J. 18 (2017), http://scholar.rose-hulman.edu/rhumj/vol18/iss1/9/.
- Alyssa Epstein*, Adam Lott*, Steven J. Miller, and Eyvindur Palsson, Optimal point sets determining few distinct triangles, Integers \textbf{18} (2018), \#A16 (17 pages). http://math.colgate.edu/~integers/cgi-bin/get.cgi
- Oscar Gonzalez*, Chung Hang Kwan*, Steven J. Miller, Roger Van Peski* and Tian An Wong, On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy, Journal of Number Theory \textbf{183} (2018), 407–427. https://arxiv.org/abs/1608.05938
- Sarah Manski*, Steven J. Miller, Hong Suh*, Fringe pairs in generalized MSTD sets, International Journal of Number Theory \textbf{13} (2017), no. 10, 2653–2675. https://arxiv.org/abs/1509.01657
- Anand Hemmady*, Adam Lott* and Steven J. Miller, When almost all sets are difference dominated in $\mathbb{Z}/n\mathbb{Z}$, Integers \textbf{17} (2017), Paper No. A54, 15 pp. https://arxiv.org/abs/1608.03209

Publications from SMALL 2014-2016

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

- Colin Adams, Rose Kaplan-Kelly*, Michael Moore*, Brandon Shapiro*, Shruthi Sridhar*, Joshua Wakefield*, Densities of hyperbolic cusp invariants, ArXiv 1701.03479, to appear in Proceedings of the American Mathematical Society, 2018.
- Colin Adams, Aaron Calderon*, Nathaniel Mayer*, Generalized bipyramids and hyperbolic volumes of alternating k-uniform tiling links”,ArXiv 1603.03715, 2016, submitted for publication.
- Colin Adams, Aaron Calderon*, Xinyi Jiang*, Alexander Kastner*, Gregory Kehne*, Nathaniel Mayer*, Mia Smith*, Volume and Determinant Densities of Hyperbolic Rational Links, Journal of Knot Theory and Its Ramifications Vol. 26, No. 1 (2017) 1750002(13pages) http://arxiv.org/abs/1510.06050
- Owen Barrett*, Frank W. K. Firk, Steven J. Miller and Caroline Turnage-Butterbaugh, From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, Open Problems in Mathematics (editors John Nash Jr. and Michael

Th. Rassias, Springer-Verlag), 2016. https://arxiv.org/pdf/1505.07481 - Owen Barrett*, Brian McDonald*, Ryan Patrick*, Caroline Turnage-Butterbaugh and Karl Winsor*, Gaps between zeros of GL(2) L-functions, Journal of Mathematical Analysis and Applications, 429 (2015), 204–232. http://arxiv.org/pdf/1410.7765v2
- John Berry*, Wyatt Boyer*, Bryan Brown*, Matthew Dannenberg*, Paul Gallagher*, David Hu*, Jason Liang*, Alyssa Loving*, Zane Martin*, Maggie Miller*, Byron Perpetua*, Sarah Tammen*, and Yingyi Zeng*, The convex body isoperimetric conjecture in
**R**^{2}, preprint (2015). - John Berry*, Matthew Dannenberg*, Jason Liang*, Yingyi Zeng*, The isoperimetric problem for the sum of two Gaussian densities, Involve, to appear; arXiv.org (2016). Updated June 2017.
- John Berry*, Matthew Dannenberg*, Jason Liang*, Yingyi Zeng*, Optimal pentagonal tilings, preprint (2015).
- John Berry*, Matthew Dannenberg*, Jason Liang*, Yingyi Zeng*, Relaxed disc packings, http://sites.williams.edu/Morgan/2015/08/14/relaxed-disk-packings/ preprint (2016)
- John Berry*, Matthew Dannenberg*, Jason Liang*, Yingyi Zeng*, Symmetries of Cairo-Prismatic tilings, Rose-Hulman Und. Math. J. 17 (2016), http://scholar.rose-hulman.edu/rhumj/vol17/iss2/3. Updated June 2017.
- A. Best*, P. Dynes*, X. Edelsbrunner*, B. McDonald*, S. J. Miller, C. Turnage-Butterbaugh and M. Weinstein*), Benford Behavior of Zeckendorf Decompositions, Fibonacci Quarterly. 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, 16 (2016), #A6. Updated March 2016. 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, to appear in the Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. Updated March 2015. http://arxiv.org/pdf/1412.0999v1
- Andrew Best*, Patrick Dynes*, Steven J. Miller, Jasmine Powell* and Benjamin Weiss, The Emergence of 4-Cycles in

Polynomial Maps over the Extended Integers, the Minnesota Journal of Undergraduate Mathematics, 2 (2016–2017), no. 1,

15 pages. https://arxiv.org/pdf/1507.03597 - A. Bower*, R. Insoft*, S. Li*, S. J. Miller and P* Tosteson, Distribution of gaps in generalized Zeckendorf decompositions (and an appendix on Extensions to Initial Segments with Iddo Ben-Ari), Journal of Combinatorial Theory, Series A 135 (2015), 130–160. Updated Feb 2016. http://arxiv.org/pdf/1402.3912v2
- Wyatt Boyer*, Bryan Brown*, Gregory Chambers, Alyssa Loving*, and Sarah Tammen*, Isoperimetric regions in R
with density r^{n}, Anal. Geom. Metr. Spaces 4 (2016), 236–265. Updated June 2017.^{p} - Wyatt Boyer*, Bryan Brown*, Alyssa Loving*, Frank Morgan, and Sarah Tammen*, Double bubbles in hyperbolic surfaces, work in progress. Continued by Alyssa Loving as undergraduate research at the University of Hawaii. Preprint (2015). Updated June 2015.
- Wyatt Boyer*, Bryan Brown*, Alyssa Loving*, and Sarah Tammen*, Optimal transportation with constant constraint, submitted. Updated March 2015.
- David Burt*, Eli Goldstein*, Sarah Manski*, Steven J. Miller, Eyvindur A. Palsson and Hong Suh*, Crescent

configurations, Integers (electronic journal of combinatorial number theory) 16 (2016), #A38. http://arxiv.org/abs/1509.07220 - Alan Chang*, David Mehrle*, Steven J. Miller, Tomer Reiter*, Joseph Stahl* and Dylan Yott*, Newman’s Conjecture in Function Fields, Journal of Number Theory157 (2015), 154–169.. Updated Mar 2016. 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, Colloq. Math. 143 (2016), 271 – 291. http://arxiv.org/abs/1408.2445.
- Leo Di Giosia*, Jay Habib*, Lea Kenigsberg*, Dylanger Pittman*, Weitao Zhu*, Balls isoperimetric in
**R**with volume and perimeter densities r^{n}^{m}and r^{k}, arxiv.org (2016), submitted J. Geom. Anal. Updated June 2017. - Leo Di Giosia*, Jay Habib*, Lea Kenigsberg*, Dylanger Pittman*, Weitao Zhu*, The log convex density conjecture in hyperbolic space, Rose-Hulman Und. Math. J., to appear; arxiv.org (2016). Updated June 2017.
- Thao Do*, Archit Kulkarni*, Steven J. Miller*, David Moon* and Jake Wellens*, Sums and Differences of Correlated Random Sets, Journal of Number Theory 147 (2015), 44–68. http://arxiv.org/pdf/1401.2588v1 Updated Feb 2016.
- Thao Do*, Archit Kulkarni*, Steven J. Miller*, David Moon*, Jake Wellens* and James Wilcox, Sets Characterized by Missing Sums and Differences in Dilating Polytopes, Journal of Number Theory 157 (2015), 123–153. http://arxiv.org/pdf/1406.2052v2 Updated Feb 2016.
- Robert Dorward*, Pari L. Ford*, Eva Fourakis*, Pamela E. Harris, Steven J. Miller, Eyvindur A. Palsson and Hannah Paugh*, Individual Gap Measures from Generalized Zeckendorf Decompositions, Uniform Distribution Theory 12 (2017), no.

1, 27–36. https://arxiv.org/pdf/1509.03029 - Robert Dorward*, Pari L. Ford*, Eva Fourakis*, Pamela E. Harris, Steven J. Miller, Eyvindur A. Palsson and Hannah Paugh*, A Generalization of Zeckendorf’s Theorem via Circumscribed m-gons, Involve, a Journal of Mathematics 10-1

(2017), 125–150. https://arxiv.org/pdf/1508.07531 - 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/
- Madeleine Elyze, Alexander Kastner,Juan Ortiz Rhoton, Vadim Semenov,Cesar E. Silva,On conservative sequences and

their application to ergodic multiplier problems, Colloquium Mathematicum, to appear. - S. Fleming, L. Ji, S. Loepp, P. McDonald, N. Pande and D. Schwein, Controlling the Dimensions of Formal Fibers of a Unique Factorization Domain at the Height One Prime Ideals, Journal of Commutative Algebra, to appear.
- S. Fleming, L. Ji, S. Loepp, P. McDonald, N. Pande and D. Schwein, Completely Controlling the Dimensions of Formal Fiber Rings at Prime Ideals of Small Height, Journal of Commutative Algebra, to appear.
- Johann Gaebler, Alexander Kastner, Cesar E. Silva, Xiaoyu Xu, Zirui Zhou, Partially Bounded Transformations have

Trivial Centralizer. https://arxiv.org/abs/1609.04758. - Feixue Gong*, Olivia Meyerson*, Jeremy Meza*, Mihai Stoiciu, Abigail Ward*, Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators’, Involve, a Journal of Mathematics Vol. 9 (2016), No. 3, 517-540. http://msp.org/involve/2016/9-3/p13.xhtml
- Isaac Loh and Cesar E. Silva (2017), Strict doubly ergodic infinite transformations, Dynamical Systems, DOI:

10.1080/14689367.2017.1280665. - Isaac Loh, Cesar Silva,Ben Athiwaratkun, Infinite symmetric ergodic index and related examples in infinite

measure,https://arxiv.org/abs/1702.0145. - Blake Mackall*, Steven J. Miller, Christina Rapti* and Karl Winsor*, Some Results in the Theory of Low-lying Zeros (with an appendix with Megumi Asada*, Eva Fourakis*, Kevin Yang*), in Families of automorphic forms and the trace formula (editors), Simons Symposia series, Springer-Verlag. http://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/BiasCIRM30.pdf
- O Maxian, A Neufeld, EJ Talis, LM Childs, and JC Blackwood (2017). Zika virus dynamics: When does sexual transmission matter? Epidemics, [In press] Available online: http://www.sciencedirect.com/science/article/pii/S1755436517301093
- Steven J. Miller, Kirk Swanson*, Kimsy Tor* and Karl Winsor*, Limiting Spectral Measures for Random Matrix Ensembles with a Polynomial Link Function, Random Matrices: Theory and Applications 4 (2015), no. 2, 1550004 (28 pages) Updated Feb 2016. 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, O. Capovilla-Searle*, J. Freeman*, D. Irvine*, S. Petti*, D. Vitek*, A. Weber*, S. Zhang*, Bounds on Ubercrossing and Petal Number for Knots, Journal of Knot Theory and its Ramifications, Vol. 24, No. 2 (2015) 1550012 (16 pages). https://arxiv.org/abs/1311.0526
- Colin Adams, Orsola Capovilla-Searle*, Jesse Freeman*, Daniel Irvine*, Samantha Petti*, Daniel Vitek*, Ashley Weber*, Sicong Zhang*, Multi-crossing Number for Knots and the Kauffman

Bracket Polynomial,Math. Proc. of Cambridge Phil. Soc., 164, Issue1, Jan. 2018, 147-178. http://arxiv.org/abs/1407.4485 - 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, T. Crawford*, B. DeMeo*, M. Landry*, M. Montee*, S. Park*, S. Venkatesh*, F. Yhee*, Knot Projections with a Single Multi-Crossing, Journal of Knot Theory and its Ramifications, Vol. 24, No. 3 (2015)1550011(30 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, Vol. 41, (2013), no. 12, 4491-4503.
- 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*, Nadine Amersi*, Geoffrey Iyer*, Oleg Lazarev*, Steven J. Miller and Liyang Zhang*, Maass waveforms and low-lying zeros, in “Analytic Number Theory: In honor of Helmut Maier’s 60th birthday,” Springer-Verlag, 2015. Updated Mar 2016
- 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.
- E. Beazley, M. Nichols*, M. Park*, X. Shi*, A. Youcis*, Bijective projections on parabolic quotients of affine Weyl groups, Journal of Algebraic Combinatorics, Vol. 41, Issue 4 (2015), p. 911-948.
- 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, Integers: Electronic Journal Of Combinatorial Number Theory, 15 (2015), paper A21, 28 pages. http://arxiv.org/pdf/1112.3719v2 Updated Mar 2016
- 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
- F. Bozgan*, A. Sanchez*, C.E. Silva, D. Stevens*, J. Wang*, Subsequence bounded rational ergodicity of rank-one transformations, Dyn. Syst. 30 (2015), no. 1, 70-84.
- 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*, N. Shah*, L. Vieira*, Are circles isoperimetric in the plane with density e
^{r}? Rose-Hulman Und. Math. J. 16(1) (2015). http://www.rose-hulman.edu/mathjournal/archives/2015/vol16-n1/paper12/v16n1-12pd.pdf Updated June, 2015. - 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, 7 (2014), 453-478.
- 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 Benfords law, Involve, a Journal of Mathematics 8-5

(2015), 859–874. DOI 10.2140/involve.2015.8.859. http://arxiv.org/pdf/1402.5854v1 - I. Dai*, X. Garcia*, T. Padurariu*, C.E. Silva, On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations, Ergodic Theory and Dynamical Systems, 35 (2015), no. 4, 1141-1164.
- 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.
- 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-hedral tiles, 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*, Perimeter-minimizing tilings by convex and nonconvex pentagons, Rose-Hulman Und. Math. J. 16(1) (2015). http://www.rose-hulman.edu/mathjournal/archives/2015/vol16-n1/paper2/v16n1-2pd.pdf Updated June, 2015.
- W. Ghang*, Z. Martin*, S. Waruhiu*, 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
- P. Jiang*, A. Kirkpatrick*, S. Loepp, S. Mack-Crane*, S. Tripp, Controlling the Generic Formal Fibers of Local Domains and Their Polynomial Rings, Journal of Commutative Algebra, Vol. 7 (2015), No. 2, 241-264.
- 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.E. Silva, On Li-Yorke Measurable Sensitivity, Proceedings Amer. Math. Soc., 143 (2015), no. 6, 2411-2426.
- 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.
- T. Padurariu*, C. Silva, E. Zachos*, On v-positive type transformations in infinite measure, Colloquium Mathematicum, to appear.

## 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.E. 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 r
^{p}, 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.