I’m happy to say that many of my research projects and activities over the years have involved students, both undergraduates from here at W&L and also highschool students from around the world (by way of the Pioneer Academics). If you’re interested in doing the same, this page will give you an idea of the kind of work we do. Not every project leads to publication, but it’s always nice when that does happen.
 Muhammad Adam Dombrowski (from Pennsbury High School) and I spent quite some time working on an extension of the Chapman/Cheng area problem (see below). This led to a 31page article that we recently submitted to the Journal of Integer Sequences. (pdf).
 Neil Sriram (from Scarsdale High School) and I spent some time working on cyclicharmonic curves, and we came up with a nice problem that will appear soon in Math Horizons. (pdf)
 John Chapman and Yvonne Cheng (both W&L students) worked with me on a nice problem on the area between cosines, and we submitted it to Mathematics Magazine in early 2023. It’s now problem #2191 in the March 2024 issue (pdf).
 My student Yike Li (Beijing City International School) came up with a delightful formula in 2022 that connected cosines, Fibonaccis, and binomial coefficients, and that led to a joint article now in print (October 2023) at the Journal of Integer Sequences volume 26, article 23.8.7. (pdf).
 My student Yunqi Liu (now at Carnegie Mellon University) and I worked on a nice problem about a variation of Zeckendorf’s Theorem; it’s now problem #1276 in the College Math Journal, May 2024. (pdf).
 In 2022, Michael Tulskikh (Columbia U.) and I finished up a nice article on convolutions of linear recurrence sequences. It’s now in print at the Journal of Integer Sequences volume 25, article 22.3.3. (pdf).
 In that same volume of the Journal of Integer Sequences is this article on tiling graph compositions by my former student Liam Buttitta, from work we did together over the summer of 2021.
 Highschool student Yichen Wang (now at UCLA) and I just finished an article on convolutions of Fibonaccitype and Lucastype sequences, now in print in Mathematics Magazine (April 2024 pages 98109). (pdf).
 Cheney and I also wrote a nice article on kbonacci and kLucas numbers. It’s now published as article #A56 in the journal INTEGERS (2021, volume 21). (pdf).
 Highschool student Yu Xiao (now at Oxford) and I wrote up a nice paper on Fibonacci and Lucas identities via rainbow tilings. It’s now in print in the Fibonacci Quarterly (May 2022, volume 60, number 2, pages 126135). (pdf).
 A few summers ago (2020) I worked with W&L students Kathleen McNeil and Jackson Gazin on matrices and continued fractions. Along the way, we produced this problem (#2120) on the normalizer of a subgroup, which was published in the April, 2021 issue of Mathematics Magazine.
 Highschool student Myanna Nash and I produced a nice problem about gentle diagonals in Pascal’s Triangle. It was published in the March, 2022 issue of Crux Mathematicorum as problem #4721 (English version, French version).
 In the spring of 2020, my work with highschool student Oluwatobi Alabi (now at Grinnell) led to a nice article on faultfree tilings (pdf). This article is now in print at the Journal of Integer Sequences, volume 24 (it’s the second article from the top of that link).
 Oluwatobi and I also worked on another nice problem on tiling squares with long rectangles, which has now appeared in print as problem #1216 in the College Math Journal (January 2022).
 In 2019, I worked with highschool student Ziqian Alexa Jin (now at U. Chicago) on a nice article on Tetranacci numbers and hexagonal tilings. It’s finally (!!) appeared in print in the Fibonacci Quarterly (May 2022, volume 60, number 2, pages 99103). (pdf).
 Also from 2019, highschool student ZhenShu Luan (now at Cornell) and I worked on continued fractions, which led to this problem (#1186) in the College Math Journal (November 2020, solution published November 2021).
 Another student from 2019, Michael Tulskikh (now at Columbia), worked with me on a really fun article on tiling 2 x n boards with dominos and Lshaped trominos. This article is now in print in the Journal of Integer Sequences (2021, volume 24, issue 4) (pdf).
 For the summer of 2018, I worked with W&L students Saimon Islam (we also worked together in 2016) and Eric Zhang (likewise, in 2017) on a nice article about polynomial roots with common tails (here it is, revised in 2019 and published in 2020 in the MAA Monthly vol. 127, number 4). We also had this problem (on the Galois group of a degreesix polynomial) appear in print in Mathematics Magazine (December 2018).
 Over the years, I’ve helped many students add or edit entries in the Online Encyclopedia of Integer Sequences. Unless stated otherwise, these are all international highschool students who worked with me through Pioneer Academics.
 W&L students Saimon Islam, Aaron Schmitt, and Yue Pan: A272069.
 Shaoxiong Yuan (Chongqing): A049669 and others.
 Eldin Sijaric (Wales): A326369 and others.
 Michael Tulskikh (New Mexico): A052980 and others.
 Shuer Jiang (Maryland): A003269.
 Shahreer Al Hossain (New York): A000129.
 Ruijia Liu (Nanjing): A001644.
 ZhenShu Luan (Vancouver, BC): A048879.
 Ziqian Jin (Beijing): A000078.
 Advika Srivastava (Noida, India): A000078 and A001591.
 Rana Ürek (Istanbul): A030186.
 Miles Wu (Shanghai): A316726.
 Yu Xiao (Shenzhen): A004146 and others.
 Kengbo Lu (Guangzhou): A015518 and A015521.
 Areebah Mahdia (Bangladesh): A179070 and others.
 Qianyu Guo (Shanghai): A335559.
 Oluwatobi Alabi (Nigeria): A335560 and others.
 Yiming Tan (Singapore): A102307.
 Alexander Mark (Florida): A006130 and A075118.
 Kevin Zhanming Zhang (Hong Kong): A236428 and A175395.
 Myanna Nash (Chicago, IL): A005251.
 Tianshu Ouyang (Beijing): A334047.
 Xilin Wang (Beijing): A119749.
 Sujay Champati (Santa Clara, CA): A337492.
 Yichen Wang (Shanghai): A000073.
 Chinmay Dandekar (Cupertino, CA): A005203 and A063896.
 Seung Ju Lee (Saipan): A337521 and A135829.
 Elena Yutong Li (Beijing): A337024.
 Tracy Z. Wu (Hangzhou): A056854.
 Yiwen Zhang (Nanjing): A345448.
 Drisana Bhatia (Sacramento, CA): A345953.
 Zi Ye (Hangzhou): A000931.
 Shraya Pal (San José, CA): A003499.
 Ziyao Geng (Auckland, NZ): A346054.
 Liam Buttitta (Chapel Hill, NC): A346273 and A344638.
 Reeva Bohra (Jaipur, India): A022124 and others.
 Hexuan Wang (Mercersburg, PA): A344684 and others.
 Noah Carey (Ashland, KY): A208638 and A347584.
 Tongjia Rao (San Diego, CA): A048654 and A221174.
 Osondu Ugochukwu (Suleja, Nigeria): A347636.
 Yichen Wang (Wuxi, China): A005314 and A347493.
 W&L students Sam Neale and Kyle Wood: A022120.
 W&L student Gavron Campbell: A006190 and A206608.
 W&L student Steve Warren: A022121.
 W&L student Kathleen Wilson: A022125.
 W&L student Christina Savory: A022114.
 W&L student Tyler Zidlicky: A022139.
 W&L student Erin Addison: A184959.
 W&L student Michael Nyc: A022098.
 W&L students Austin Sharrett and Aoife Chow: A022126.
 W&L student Kyle Wood: A022132.
 W&L student Russ Zimmerman: A022389.
 W&L student Griffin Donaldson: A022095.
 W&L student Henry Sauer: A022113.
 W&L student Sam Neale: A022096.
 W&L student Mary Beth Pittman: A022099.
 Aamen Muharram (Egypt): A022102 and others.
 Tianle Yao (Beijing, China): A350834.
 Veda Garigipati (San José, CA): A100683 and A354080.
 Zijie He (Bloomfield Hills, MI): A136429, A355327, and others.
 Wajdi Maaloul (Tunisia): A022138 and others.
 Max Winnick (Florida): A070313 and A355659.
 Ding Hao (Huizhou, China): A052941, A356463, and others.
 Hanzhang Fang (Wuhan, China): A356563 and A077996.
 Aarnav Gogri (Mumbai, India): A356622 and A356623.
 Ivan Kuznetsov (Pacific Palisades, CA): A068102.
 Andrew Chang (Cupertino, CA): A219968.
 Yike Li (Beijing): A000032 and A000045.
 Zeno Song (Washington, DC): A354541.
 Sadek Mohammed (Giza, Egypt): A356692.
 Shravan Haribalaraman (Bangalore, India): A220123.
 Hangyu Liang (Claremont, CA): A356807.
 Aaron Zhou (Dallas, TX): A077998.
 Jiaqi Wang (Shenzhen, China): A111572 and A362388.
 Max Liu (Shanghai, China): A061646 and A079472.
 Yunxin Renee Li (Kingston, PA): A363958.
 Arjun Datta (Singapore): A001835.
 Muhammad Adam Dombrowski (Philadelphia, PA): A364145.
 Yushu Fan (Beijing): A052540 and A052971.
 Mina Basilious (Asyut, Egypt): A006356 and A214997.
 Snezhana Tuneska (Skopje, North Macedonia): A163102 and A365511.
 Ziyi Xie (Hangzhou, China): A135318.
 Bora Bursalı (Istanbul): A100477, A122552, and others.
 Bowen Shi (Beijing): A099156.
 Yiwei Wang (La Canada, CA): A365352.
 Yiming Wu (Shanghai, China): A190996.
 Hasita Kanamarlapudi (San Diego, CA): A192879.
 Yomna Bakr (Gamasa, Egypt): A307395, A110527, and others.
 Ruotong Li (Singapore): A001631 and A129847
 Xiaoyuan Wang (Nanjing, China): A373445.
 Guanji Chen (Shanghai, China): A048573 and A294627.
 Canran Wang (Beijing, China): A006497 and A189735.
 Elkhan Aday (Almaty, Kazakhstan): A001630.
 Adam Dahshan (6th of October, Egypt): A099923.
 Haoran Xu (Shanghai, China): A374391.
 Winnie Zhu (Wuxi, China): A374729.
 Shaolan Han (Beijing, China): A374512.
 Arnim Kuchhal (Pittsburgh, PA): A077997, A276225, and others.
 Yuan Shen (Changshu, China): A001638 and A195971.
 Mulong Xu (Nanjing, China): A018902.
 Ahmed ElKhatib (6th of October, Egypt): A000124.
 Jiayi Liu (Nanjing, China): A003266.
 Emma Li (Princeton, NJ): A214899 and A013655.
 Ruishan Wu (Beijing, China): A001519.
 In 2017, I worked with W&L students Prakriti Panthi (rising sophomore), Anukriti Shrestha (rising junior), and Eric Zhang (rising sophomore) on a number of different topics. We had this problem about decimal roots appear in print in Mathematics Magazine (December 2017) and this article about Ramanujan cubics also appear in Mathematics Magazine (December 2019, volume 92, number 5), and this article about finite subgroups of the modular group was published by the Rocky Mountain Journal of Mathematics (2019, volume 49, number 4). Thanks to this collaboration, Prakriti, Anukriti, and Eric now have an Erdös number of 4.
 Oh, and the December 2019 cover of Mathematics Magazine was inspired by our article on Ramanujan cubics (which we did in 2017)! (Artwork by David Riemann).
 Oh, and Anukriti was featured in this article on the W&L home page!
 In 2016, I worked with W&L students Saimon Islam (rising sophomore), Aaron Schmitt (rising junior), and Yue Pan (rising sophomore) on a nice little problem concerning the sum of two squares. We collaborated with another professor/undergraduate team from Wake Forest and ended up with this 21page article which has now been published in Involve (2019, volume 12, issue 4, page 585605). Thanks to this paper, Saimon, Aaron, and Pan now have an Erdös number of 4.
 Back in 2015, exchange student Gabriella Iwasaki, rising W&L senior Luke Quigley, and I worked on a lovely project involving graphs associated with rings modulo 16. This picture here shows one of the problems we worked on, demonstrating that the digraph associated with multiplication by 6 modulo 16 will be of genus 2.
 In the summer of 2013, I worked with W&L student Wenda Tu (rising senior) on a nifty problem involving digraphs. This work continued with Wenda’s honor thesis in the academic year 201314, and that led to a joint paper which appeared in print in the undergraduate math journal Involve (2018, volume 2, pages 181194) . I also worked with Ginger (Qiuchi) Sun that same summer on her interesting ideas involving the Goldbach Conjecture with polynomials.
 Back in 2012, W&L students Ginny Huang (rising sophomore) and Cathy Wang (rising junior) worked with me on a very nice problem involving Fibonacci numbers.
 Kuan Si and I did a yearlong independent study course on Fibonacci identities, during the academic year 201112.
 Elizabeth Twentyman wrote her honors thesis “Finding Factors of Factor Rings” with me over 200506; she graduated with honors in 2006.
 I worked with Elizabeth Townsend on her honors thesis on the inverse Galois problem; Liz graduated with honors in 2003.
 My first research student was Adam Henry; back in the summer of 1999, we did a nice project on Gaussian integers.
Where are they now? My research and honors students have done lots of different things after graduating W&L! But for those who went on a bit further in academia, here’s what they did.


 Jiahao Zhang (W&L ’20) is a math PhD student at the University of Washington.
 Anukriti Shrestha (W&L ’19) went to UVa for a PhD program in engineering.
 Yue Pan (W&L ’19) went to Univ. of Iowa for a PhD in statistics.
 Gabriela Iwasaki (transfer student 201415) returned to Brazil and changed her major to mathematics!
 Wenda Tu (W&L ’14) attended graduate school in statistics at the University of Iowa.
 I think that Qiuchi Sun (W&L ’13) went to grad school in economics.
 Kuan Si (W&L ’12) went to graduate school in math at Georgia Tech.
 Elizabeth Twentyman (W&L ’06) went on to math graduate school at the University of Michgan.
 Elizabeth Townsend (W&L ’03) went on to graduate school in math at the University of Chicago; after a postdoc at Michigan and some time at Williams, she is now a math professor at Haverford.
 Adam Henry (W&L ’00) got his PhD in Transportation Technology and Policy at UC Davis, and went on to posts at Harvard, Boston University, and the University of West Virginia. Adam is now a Professor of Environmental Politics and a Distinguished Scholar at the University of Arizona.

Plenty of other W&L students have also gone on to graduate school and to careers as math professors. For example, Jonathan Graber (’08) is a math professor at Baylor University, and both Matt Morena (’05) and Neville Fogarty (’10) teach at Christopher Newport University. Recent graduate Hung Viet Chu (’20) is a graduate student at UIUC and has already published more than 20 articles, including some based on my old papers!