SMALL Publications Completed during 2020-2023
(Asterisks denote current or former students — see below for publications based on work before SMALL 2020)
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- Colin Adam’s Group: 2022:
- “Hyperbolic Knotoids”, C. Adams, A. Bonat*, M. Chande*, J. Chen*, M. Jiang*, Z. Romrell*, D. Santiago*, B. Shapiro*, D. Woodruff*, ArXiv 2209.04566 (2022). (not published so not added to NSF)
- “Generalized Knotoids”, C. Adams, A. Bonat*, M. Chande*, J. Chen*, M. Jiang*, Z. Romrell*, D. Santiago*, B. Shapiro*, D. Woodruff*, ArXiv 2209.01922 (2022), to appear in Mathematical Proceedings of the Cambridge Philosophical Society. (not published so not added to NSF)
- “Hyperbolicity of Alternating Links in Thickened Surfaces with Boundary”, C. Adams and J. Chen*, ArXiv 2309.04999, 2023. (not published so not added to NSF)
- “Composition Properties of Knots in Handlebodies”, C. Adams and D. Santiago*, New York Journal of Mathematics, Vol. 29 (2023) 1097-1116. https://arxiv.org/abs/2303.02477
- Joshua Carlson’s Group: 2021:
- Throttling for standard zero forcing on directed graphs (with Emily Cairncross, Peter Hollander, Benjamin Kitchen, Emily Lopez, Ashley Zhuang), Australian Journal of Combinatorics, Volume 84(1) (2022), Pages 1–27. https://arxiv.org/abs/2008.08646
- Susan Loepp’s Group: 2023:
- Completions of Quasi-excellent Domains (D. Baron*, A. Eltigani*, S. Loepp, A. Perez*, and M. Teplitskiy*), Beitr. Algebra Geom, to appear. https://arxiv.org/abs/2310.00479
- Controlling Formal Fibers of Countably Many Principal Prime Ideals (D. Baron*, A. Eltigani*, S. Loepp, A. Perez*, and M. Teplitskiy*), https://arxiv.org/abs/2311.15797
- Steven J. Miller’s Groups: 2020, 2021, 2022, 2023 (with Eyvi Palsson, Alex Iosevich):
- Extending the support of 1- and 2-level densities for cusp form $L$-functions under square-root cancellation
hypotheses (Annika Mauro, Jack Miller and Steven J. Miller) Acta Arithmetica, special volume dedicated to Henryk Iwaniec on the occasion of his 75th birthday, to appear. (Added 9/26/23, need to add to NSF webpage, online but not in print yet) - Distinct angle problems and variants (H. L. Fleischmann*, H. B. Hu*, F. Jackson*, S. J. Miller, E. A. Palsson, E. Pesikoff*, C. Wolf), Discrete & Computational Geometry, 70 (2023), 1715–1740. https://arxiv.org/abs/2108.12015
- Distinct angles in general position (H. L. Fleischmann*, S. V. Konyagin, S. J. Miller, E. A. Palsson, E. Pesikoff*, C. Wolf), Discrete Mathematics, 346 (2023), no. 4, Paper No. 113283, 4 pp. https://arxiv.org/abs/2206.04367
- Distinct angles and angle chains in three dimensions (R. Ascoli*, L. Betti*, J. L. Duke*, X. Liu*, W. Milgrim*, S. J. Miller, E. A. Palsson, F. Romero Acosta, S. Velazquez Iannuzzelli*), Discrete Mathematics & Theoretical Computer Science,
25 (2023), no. 1, Paper No. 2, 19 pp. https://arxiv.org/abs/2208.13284 - VC-Dimension and Distance Chains in ${\Bbb F}_q^d$ (Ruben Ascoli*, Livia Betti*, Justin Cheigh*, Alex Iosevich, Ryan Jeong*, Xuyan Liu*, Brian McDonald, Wyatt Milgrim*, Steven J. Miller, Francisco Romero Acosta, Santiago Velazquez Iannuzzelli*), Korean Journal of Mathematics 32 (2024), no. 1, 43–57. https://arxiv.org/abs/2210.03058
- Recurrence relations for S-legal index difference sequences (Guilherme Zeus Dantas E Moura*, Andrew Keisling*, Astrid Lilly*, Annika Mauro*, Steven J. Miller, Matthew Phang*, and Santiago Velazquez Iannuzzelli*), Fibonacci Quarterly. (61 (2023), no. 3, 257–274) https://www.fq.math.ca/Papers/61-3/miller01102023.pdf
- Lower-Order Biases in the Second Moments of Dirichlet Coefficients in Families of L-Functions (Megumi Asada, Ryan Chen, Eva Fourakis, Yujin Kim, Andrew Kwon, Jared Lichtman, Blake Mackall, Steven J. Miller, Eric Winsor, Karl Winsor, Jianing Yang, Kevin Yang, appendix with Roger Weng), Experimental Mathematic 32 (2023), no. 3, 431–456, https://doi.org/10.1080/10586458.2021.1980453
- Optimal point sets determining few distinct angles (Henry L. Fleischmann*, Steven J. Miller, Eyvindur A. Palsson, Ethan Pesikoff* and Charles Wolf), The Australasian Journal of Combinatorics, Volume 87(1) (2023), 165–181.
- Determining optimal test functions for $2$-level densities (Elzbieta Boldyriew, Fangu Chen, Charles Devlin VI, Steven J. Miller, Jason Zhao), Research in Number Theory 9 (2023), no. 32, https://doi.org/10.1007/s40993-022-00367-0.
- A Refined Conjecture for the Variance of Gaussian Primes Across Sectors) (Ryan C. Chen*, Yujin H. Kim*, Jared D. Lichtman*, Steven J. Miller, Alina Shubina*, Shannon Sweitzer*, Ezra Waxman, Eric Winsor*, Jianing Yang*). Experimental Mathematics. (published online May 2020; volume 32 (2023), no. 1, 33-53). Added 4-12-23: https://doi.org/10.1080/10586458.2020.1753598
- The Fibonacci Quilt Game (with Alexandra Newlon), Fibonacci Quarterly 58 (2020), no. 2, 157–168. https://arxiv.org/pdf/1909.01938
- On Near Perfect Numbers (with Peter Cohen, Katherine Cordwell, Alyssa Epstein, Chung-Hang Kwan and Adam Lott), Acta Arithmetica 194 (2020), no. 4, 341–366. https://arxiv.org/pdf/1610.04253
- A Refined Conjecture for the Variance of Gaussian Primes Across Sectors (with Ryan C. Chen, Yujin H. Kim, Jared D. Lichtman, Alina Shubina, Shannon Sweitzer, Ezra Waxman, Eric Winsor, Jianing Yang), Experimental Mathematics. Published online May 2020: https://doi.org/10.1080/10586458.2020.1753598.
- Rank and Bias in Families of Hyperelliptic Curves via Nagao’s Conjecture (with Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon, \’Alvaro Lozano-Robledo), to appear in the Journal of Number Theory. https://arxiv.org/pdf/1906.09407
- The Inverse Gamma Distribution and Benford’s Law (with Rebecca F. Durst, Chi Huynh, Adam Lott, Eyvindur A. Palsson, Wouter Touw, and Gert Vriend), The PUMP Journal of Undergraduate Research 3 (2020), 95–109. https://arxiv.org/pdf/1609.04106
- Higher Order Fibonacci Sequences from Generalized Schreier sets (with Hung Viet Chu, Zimu Xiang), Fibonacci Quarterly 3 (2020), 249–253. https://arxiv.org/pdf/1909.03465
- Deterministic Zeckendorf Games (with Ruoci Li, Xiaonan Li, Clay Mizgerd, Chenyang Sun, Dong Xia, And Zhyi Zhou), Fibonacci Quarterly 58 (2020), no. 5, 152–160. https://arxiv.org/pdf/2006.16457
- Crescent Configurations in Normed Spaces (with Sara Fish, Dylan King, Eyvi Palsson and Catherine Wahlenmayer), Integers 20 (2020), \#A96. https://arxiv.org/pdf/1909.08769
- Completeness of Positive Linear Recurrence Sequences (with Ela Boldyriew, John Havilan, Phuc Lam, John Lentfer, Fernando Trejos Suarez), to appear in the Fibonacci Quarterly. https://arxiv.org/pdf/2010.01655
- Extending Zeckendorf’s Theorem to a Non-constant Recurrence and the Zeckendorf Game on this Non-constant Recurrence Relation (with Ela Boldyriew, Anna Cusenza, Linglong Dai, Pei Ding, Aidan Dunkelberg, John Haviland, Kate Huffman, Dianhui Ke, Daniel Kleber, Jason Kuretski, John Lentfer, Tianhao Luo, Clayton Mizgerd, Vashisth Tiwari, Jingkai Ye, Yunhao Zhang, Xiaoyan Zheng, and Weiduo Zhu), Fibonacci Quarterly 58 (2020), no. 5, 55–76. https://arxiv.org/pdf/2009.12475
- An Introduction to Completeness of Positive Linear Recurrence Sequences (with Ela Boldyriew, John Havilan, Phuc Lam, John Lentfer, Fernando Trejos Suarez), Fibonacci Quarterly 58 (2020), no. 5, 77–90. https://arxiv.org/pdf/2010.04071
- Winning Strategy for the Multiplayer and Multialliance Zeckendorf Games (with Anna Cusenza, Aiden Dunkelberg, Kate Huffman, Dianhui Ke, Daniel Kleber, Clayton Mizgerd, Vashisth Tiwari, Jingkai Ye, Xiaoyan Zheng), to appear in the Fibonacci Quarterly. https://arxiv.org/pdf/2009.03708
- Lower-Order Biases Second Moments of Dirichlet Coefficients in Families of $L$-Functions (with Megumi Asada, Ryan Chen, Eva Fourakis, Yujin Kim, Andrew Kwon, Jared Lichtman, Blake Mackall, Eric Winsor, Karl Winsor, Jianing Yang, Kevin Yang, appendices with Roger Weng and Michelle Wu), to appear in Experimental Mathematics. https://arxiv.org/pdf/2103.03942
- On Zeckendorf related partitions using the Lucas sequence (with Hung Viet Chu and David Luo), to appear in the Fibonacci Quarterly. https://arxiv.org/pdf/2004.08316
- An Introduction to Completeness of Positive Linear Recurrence Sequences (with Ela Boldyriew, John Haviland, Phuc Lam, John Lentfer, Fernando Trejos Suarez). Fibonacci Quarterly (5 (2020), 77–90) pdf
- Constructions of Generalized MSTD Sets in Higher Dimensions (with Elena Kim), to appear in the Journal of Number Theory pdf
- Generalizing Zeckendorf’s Theorem to Homogeneous Linear Recurrences, I (with Thomas Martinez, Clay Mizgerd and Chenyang Sun), to appear in the Fibonacci Quarterly. pdf
- Generalizing Zeckendorf’s Theorem to Homogeneous Linear Recurrences, II (with Thomas Martinez, Clay Mizgerd, Jack Murphy and Chenyang Sun), to appear in the Fibonacci Quarterly. pdf
- The limiting spectral measure for an ensemble of generalized checkerboard matrices (with Fangu Chen, Yuxin Lin and Jiahui Yu). The PUMP Journal of Undergraduate Research (4 (2021), 202–221). pdf
- Papers added 2023:
- The Bergman Game (Benjamin Baily, Justine Dell, Irfan Durmic, Henry Fleischmann, Faye Jackson, Isaac Mijares, Steven J. Miller, Ethan Pesikoff, Luke Reifenberg, Alicia Smith Reina, Yingzi Yang), the Fibonacci Quarterly (Proceedings of the 20th International Conference on Fibonacci Numbers and Their Applications) (2022) \textbf{60}, no. 5, 18–38. https://arxiv.org/pdf/2109.00117
- Sums of Reciprocals of Recurrence Relations (Hao Cui, Xiaoyu Cui, Sophia C. Davis, Irfan Durmic, Qingcheng Hu, Lisa Liu, Steven J. Miller, Fengping Ren, Alicia Smith Reina, and Eliel Sosis), the Fibonacci Quarterly (Proceedings of the 20th International Conference on Fibonacci Numbers and Their Applications) (2022) \textbf{60}, no. 5, 111–142. https://arxiv.org/pdf/2212.02639
- Generalizing Zeckendorf’s Theorem to Homogeneous Linear Recurrences, I (Thomas Martinez, Steven J. Miller, Clay Mizgerd and Chenyang Sun), the Fibonacci Quarterly (Proceedings of the 20th International Conference on Fibonacci Numbers and Their Applications) (2022) \textbf{60}, no. 5, 222–230. https://arxiv.org/pdf/2001.08455
- Generalizing Zeckendorf’s Theorem to Homogeneous Linear Recurrences, II (Thomas Martinez, Steven J. Miller, Clay Mizgerd, Jack Murphy and Chenyang Sun), the Fibonacci Quarterly (Proceedings of the 20th International Conference on Fibonacci Numbers and Their Applications) (2022) \textbf{60}, no. 5, 231–254. https://arxiv.org/pdf/2009.07891
- Completeness of Positive Linear Recurrence Sequences (with Ela Boldyriew, John Haviland, Phuc Lam, John Lentfer, Fernando Trejos Suarez), Combinatorial and Additive Number Theory V, Springer Proceedings in Mathematics \& Statistics \textbf{395} (2023), 21–78. https://arxiv.org/pdf/2010.01655
- Extending the support of 1- and 2-level densities for cusp form $L$-functions under square-root cancellation
- Colin Adam’s Group: 2022:
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- Ralph Morrison’s Group: 2020, 2021, 2023:
- Liza Jacoby*, Ralph Morrison, and Ben Weber*: Prism graphs in tropical plane curves. Involve 14 (2021), no. 3, 495-510. https://arxiv.org/abs/2009.08570
- Marino Echavarria*, Max Everett*, Robin Huang*, Liza Jacoby*, Ralph Morrison, and Ben Weber*: On the scramble number of graphs. Discrete Applied Mathematics 310 (2022), 43-59. https://arxiv.org/pdf/2103.15253.pdf
- Marino Echavarria*, Max Everett*, Robin Huang*, Liza Jacoby*, Ralph Morrison, Ayush K. Tewari, Raluca Vlad*, and Ben Weber*: Moduli dimensions of lattice polygons. Journal of Algebraic Combinatorics 55 (2022), no. 2, 559-589. https://arxiv.org/pdf/2010.13135.pdf
- Lisa Cenek*, Lizzie Ferguson*, Eyobel Gebre*, Cassandra Marcussen*, Jason Meintjes*, Ralph Morrison, Liz Ostermeyer*, and Shefali Ramakrishna*: Uniform scrambles on graphs. Australasian Journal of Combinatroics 87 (2023), 129–147. https://arxiv.org/abs/2108.09821
- Lisa Cenek*, Lizzie Ferguson*, Eyobel Gebre*, Cassandra Marcussen*, Jason Meintjes*, Ralph Morrison, Liz Ostermeyer*, and Shefali Ramakrishna*: Bounds on higher graph gonality. Under review. https://arxiv.org/abs/2206.06907 (not published, not added to NSF)
- Lisa Cenek*, Lizzie Ferguson*, Eyobel Gebre*, Cassandra Marcussen*, Jason Meintjes*, Ralph Morrison, Liz Ostermeyer*, Shefali Ramakrishna*, and Ben Weber*: Scramble number and tree-cut decompositions. Under review. https://arxiv.org/abs/2209.01459 (not published, not added to NSF)
- Seamus Connor*, Steven DiSilvio*, Sasha Kononova*, Ralph Morrison, Krish Singal*: On the size and complexity of scrambles. Under review. https://arxiv.org/abs/2311.17342 (not published, not added to NSF)
- Nila Cibu*, Kexin Ding*, Steven DiSilvio*, Sasha Kononova*, Chan Lee*, Ralph Morrison, Krish Singal*: The gonality of chess graphs. Under review. https://arxiv.org/abs/2403.03907 (not published, not added to NSF)
- Ralph Morrison’s Group: 2020, 2021, 2023:
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- Jenna Zomback and Austyn Simpson’s Groups: 2022, 2023:
- Clay Adams*, Francesca Cantor*, Anese Gashi*, Semir Mujevic*, Sejin Park*, Austyn Simpson and Jenna Zomback, Uniform arithmetic in local rings via ultraproducts [pdf, arXiv] (2023) (not published, not added to NSF)
- Levi Borevitz*, Naima Nader*, Theodore Sandstrom*, Amelia Shapiro*, Austyn Simpson and Jenna Zomback, On localization of tight closure in Line-S_4 Quartics [pdf, arXiv] (2022)(not published, not added to NSF)
- Jenna Zomback and Austyn Simpson’s Groups: 2022, 2023:
Publications from SMALL 2017-2019
(Asterisks denote current or former students — see below for publications based on work before SMALL 2017)
- E. Barrett*, E. Graf*, S. Loepp, K. Strong*, and S. Zhang*, Cardinalities of Prime Spectra of Precompletions, in Commutative Algebra, Contemporary Mathematics., vol.773, Amer. Math. Soc., Providence, RI, 2021, pp. 133-152.
- Adams, C. Albors Riera*, B. Haddock*, D. Nishida*, B. Reinoso*, L. Wang*, Hyperbolicity of Links in Thickened Surfaces,
Topology and its Applications, vol. 256, no. 1, 2019, 262-278. https://arxiv.org/pdf/1802.05770 - C. Adams, O. Eisenberg*, J. Greenberg*, K. Kapoor*, Z. Liang*, K. O’Connor*, N. Pacheco-Tallaj*, Y. Wang*, TG-Hyperbolicity of Virtual Links, Journal of Knot Theory and its Ramifications, 2019, 1950080 (26 pages). https://arxiv.org/pdf/1904.06385
- Ivan Aidun*, Frances Dean*, Ralph Morrison, Teresa Yu*, and Julie Yuan*, Gonality sequences of graphs, to appear in the SIAM Journal on Discrete Mathematics. https://arxiv.org/abs/2002.07753
- Ivan Aidun*, Frances Dean*, Ralph Morrison, Teresa Yu*, and Julie Yuan*, Graphs of gonality three, Algebraic Combinatorics, Volume 2 (2019) no. 6 p. 1197-1217, ArXiv 1810.08665.
- Ivan Aidun*, Frances Dean*, Ralph Morrison, Teresa Yu*, and Julie Yuan*, Treewidth and gonality of glued grid graphs, to appear in Discrete Applied Mathematics, ArXiv 1808.09475.
- Ivan Aidun* and Ralph Morrison, On the gonality of Cartesian products of graphs, The Electronic Journal of Combinatorics, Volume 27, Issue 4 (2020) https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i4p52
- 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. https://arxiv.org/abs/1512.01932
- C. Avery*, C. Booms*, T. Kostolansky*, S. Loepp, and A. Semendinger*, Characterization of Completions of Noncatenary Local Domains and Noncatenary Local UFDs, Journal of Algebra, 524, (2019), 1-18. https://arxiv.org/abs/1709.03825
- E. Barrett*, E. Graf*, S. Loepp, K. Strong*, and S. Zhang*, Structure of Spectra of Precompletions, Rocky Mountain Journal of
Mathematics 50 (2020), no. 6, 1965-1988. https://arxiv.org/pdf/1911.01394.pdf - 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. 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. 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 R2, 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. See blog post Bubbles inside bubbles. https://www.degruyter.com/downloadpdf/j/agms.2018.6.issue-1/agms-2018-0004/agms-2018-0004.pdf
- Eliot Bongiovanni*, Alejandro Diaz*, Arjun Kakkar*, Nat Sothanaphan*, Isoperimetry in surfaces of revolution with density, Missouri J. Math. 30 (2018), 150-165, https://arxiv.org/pdf/1709.06040.pdf
- Eliot Bongiovanni*, Alejandro Diaz*, Arjun Kakkar*, Nat Sothanaphan*, The least-area tetrahedral tile of space, Geometriae Dedicata, 2019, https://link.springer.com/epdf/10.1007/s10711-019-00465-x?author_access_token=Idawce5gmdqo2_s9NdbpiPe4RwlQNchNByi7wbcMAY7foNcrAGNktWWwKVWyYdbiXKn4U94PoPILjRMoJQP3pFFMw5NLH0uS2Ml4WbDIGArt7BImsvIosRHtzLRBSldPGzwmRsMSAej2SgTEvngtvQ%3D%3D
- 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
- 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
- Granger Carty*, Alex Gueganic*, Yujin H. Kim*, Steven J. Miller, Alina Shubina*, Shannon Sweitzer*, Eric Winsor* and Jianing Yang*, Limiting Distributions in Generalized Zeckendorf Decompositions, Fibonacci Quarterly 57 (2019), no. 2, 109–125. https://arxiv.org/pdf/1810.03053.pdf
- Ryan Chen*, Yujin Kim*, Jared Lichtman*, Steven J. Miller, Shannon Sweitzer*, and Eric Winsor*, Spectral Statistics of Non-Hermitian Random Matrix Ensembles, Random Matrices: Theory and Applications (8(2019), no. 1, 40 pages). https://arxiv.org/abs/1803.08127
- Hung Chu*, Noah Luntzlara*, Steven J. Miller, and Lily Shao*, Infinite Families of Partitions into MSTD Subsets, Integers 19 (2019), #A60, 20 pages. https://arxiv.org/abs/1808.05460
- Hung Chu*, Nathan McNew, Steven J. Miller, Victor Xu and Sean Zhang, When Sets Can and Cannot Have MSTD Subsets. Journal of Integer Sequences 21 (2018), Article 18.8.2: https://cs.uwaterloo.ca/journals/JIS/VOL21/Miller/miller8.pdf
- Desmond Coles, Neelav Dutta, Sifan Jiang, Ralph Morrison, Andrew Scharf, The Moduli Space of Tropical Curves with Fixed Newton Polygon, to appear in Advances in Geometry. https://arxiv.org/abs/2002.10874
- Desmond Coles, Neelav Dutta, Sifan Jiang, Ralph Morrison, and AAndrew Scharf: Tropically Planar Graphs. Collectanea Mathematica (2021). https://arxiv.org/abs/1908.04320
- Katherine Cordwell*, Alyssa Epstein*, Anand Hemmady*, Steven J. Miller, Eyvindur A. Palsson, Aaditya Sharma*, Stefan Steinerberger, Yen Nhi Truong Vu*, On algorithms to calculate integer complexity, Integers 19 (2019), A12, 13 pages. https://arxiv.org/pdf/1706.08424.pdf
- Katherine Cordwell*, Max Hlavacek*, Chi Huynh*, Steven J. Miller, Carsten Peterson*, and Yen Nhi Truong Vu*, On Summand Minimality of Generalized Zeckendorf Decompositions, Research in Number Theory (4(2018), no. 43, https://doi.org/10.1007/s40993-018-0137-7)
- 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/.
- Hindy Drillick*, Alonso Espinosa-Dominguez*, Jennifer Jones-Baro*, James Leng*, Yelena Mandelshtam*, Cesar E. Silva, Non-Rigid Rank-One Infinite Measures on the Circle, https://arxiv.org/abs/1810.11095
- 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
- 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
- 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
- Steven J. Miller and Carsten Peterson*, A geometric perspective on the MSTD question, Discrete and Computational Geometry 62 (2019), no. 4, 832–855. https://arxiv.org/pdf/1709.00606.pdf
- Steven J. Miller, Carsten Peterson*, Carsten Sprunger* and Roger Van Peski*, The bidirectional ballot polytope, Integers 18 (2018), #A81, 1–18. https://arxiv.org/pdf/1708.02399
- Nat Sothanaphan*, Double Bubbles on the Line with Log-convex density f with (log f)’ bounded, Missouri J. Math. 30 (2018), 166-175, https://projecteuclid.org/current/euclid.mjms; arxiv.org/abs/1807.02661.
Publications from SMALL 2014-2016
(Asterisks denote current or former students — see below for publications based on work before SMALL 2014)
- Colin Adams, Aaron Calderon*,Nathaniel Mayer*, “Generalized bipyramids and hyperbolic volumes of k-uniform tiling links”, Topology and its Applications. Vol. 271, February 2020.
- Colin Adams, Rose Kaplan-Kelly*, Michael Moore*, Brandon Shapiro*, Shruthi Sridhar*, Joshua Wakefield*, Densities of hyperbolic cusp invariants”, Proceedings of the American Mathematical Society, Vol. 146, No. 9, Sept. 2018 (4073-4089). ArXiv 1701.03479
- 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 R2, 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 Rn with density rp, Anal. Geom. Metr. Spaces 4 (2016), 236–265. Updated June 2017.
- 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 Rn with volume and perimeter densities rm and rk, 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, 10 (2018), no. 4, 475-498. https://arxiv.org/abs/1601.07136
- 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, Journal of Commutative Algebra, 11, (2019), no. 3, 363-388. https://arxiv.org/abs/1604.04176
- Johann Gaebler, Alexander Kastner, Cesar E. Silva, Xiaoyu Xu, Zirui Zhou, Partially Bounded Transformations have trivial centralizers. Proc. Amer. Math. Soc. 146 (2018), no. 12, 5113–5127. 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
- S. Loepp and A. Michaelsen*, Uncountable n-Dimensional Excellent Regular Local Rings with Countable Spectra, Transactions of the American Mathematical Society, 373, (2020), 479-490. https://arxiv.org/abs/1811.07675
- Isaac Loh and Cesar E. Silva, Strict doubly ergodic infinite transformations, Dynamical Systems, 32 (2017), no. 4, 519–543.
- Isaac Loh, Cesar Silva, Ben Athiwaratkun, Infinite symmetric ergodic index and related examples in infinite measure, Studia Math. 243 (2018), no. 1, 101–115. 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
- Nat Sothanaphan, Double Bubbles on the Line with Log-convex Density f with (log f)’ Bounded, Missouri J. Math. 30 (2018), 166-175; arxiv.org/abs/1807.02661
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 er? 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
- J. Hallett*, L. Manuelli*, C.E. Silva, On Li-Yorke Measurable Sensitivity, Proceedings Amer. Math. Soc., 143 (2015), no. 6, 2411-2426.
- 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.
- 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, Colloq. Math. 140 (2015), no. 2,149–170. .
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 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.