# REU Site: Algebra, Combinatorics, and Statistics

The Department of Mathematics at Texas State University will host an 8 week summer REU in the summers of 2022, 2023 and 2024, involving nine students per year working in teams of three under the supervision of a faculty mentor. The program will provide lodging, meals, transportation, as well as a stipend for all students. The chosen participants will come from a selective pool of applicants, and the program will directly involve them in research projects guided by faculty mentors. Beyond successful research outcomes the objectives of the program are to introduce students to aspects of mathematical research and the broader mathematical community. At the same time the students will develop mentoring relationships with faculty as they consider pursuing graduate degrees and a career in mathematics. Students will be part of an active community at Texas State; in addition to the REU there are a number of summer programs and world-renowned mathematicians who visit campus, and participants will be involved in various activities that bring students and faculty together. A diverse body of participants is strongly desired and priority will be given to applicants from groups that are underrepresented in the mathematical community. This includes minority students, women, as well as those students coming from institutions with limited resources to support independent research projects for their undergraduates.

The research projects include a diverse collection of topics based on the research interests of the faculty mentors. Specific projects include commutative algebra arising from graphs and matroids, algebraic and combinatorial aspects of higher dimensional tilings, combinatorial problems arising from group theory, arithmetical properties of group invariants, linear and permutational representations of groups, statistical analysis on biological data, and survival analysis. Participants will spend some of the time learning the necessary background while pursuing original research. Students will be asked to present their findings in oral presentations, and will be guided in summarizing their work in a mathematical research paper. In the course of the program students will be trained in various skills including literature review, using software such as GAP, Macaulay2, and R to make and check examples, oral presentation skills, as well as written mathematical communication using Latex. Communication with the participants will continue after the program ends, and for instance students will be encouraged to present their work at local, regional, and national conferences in the subsequent academic year.

**This program is supported by NSF and Texas State University.**

**(Due to NSF rules, only US citizens and permanent residents are eligible for funding assistance.)**

**Future publications from the 2021 program:**

- Michael Gintz*, Matthew Kortje*, Megan Laurence*, Zili Wang*, and Yong Yang, “Finite permutation groups with few orbits under the action on the power set, II”, submitted.
- Michael Gintz*, Thomas Keller, Matthew Kortje*, Zili Wang*, Yong Yang, “The number of set orbits of permutation groups and the group order”,
*Bulletin of the Australian Mathematical Society*, accepted. - Michael Gintz*, Matthew Kortje*, Megan Laurence*, Yang Liu, Zili Wang*, and Yong Yang, “On the characterization of some non-abelian simple groups with few codegrees”, submitted.
- Michael Gintz*, Matthew Kortje*, Megan Laurence*, Yang Liu, Zili Wang*, and Yong Yang, “Square-free character degrees of projective representations”, in preparation.
- Awildo Gutierrez*, Yuqiao Huang*, Duncan Peckham*, and Yong Yang, “On the even abelian composition factors of finite linear groups”, submitted.
- Awildo Gutierrez*, Yuqiao Huang*, Nguyen Ngoc Hung, Duncan Peckham*, and Yong Yang, “On the fixed field in a cyclotomic field of the Frobenius automorphism”, submitted.
- Ziyu Huang*, Thomas Keller, Shane Kissinger*, Wen Plotnick*, Maya Roma*, “On the prime graphs of pseudo-solvable groups", in preparation.
- Ziyu Huang*, Thomas Keller, Shane Kissinger*, Wen Plotnick*, Maya Roma*, “Further results on minimal prime graphs of finite solvable groups", in preparation.
- RJ Barnes*, Anton Dochtermann, Cece Henderson*, Fran Herr*, Suho Oh, Ethan Partida*, “Simon’s conjecture for 1-decomposable complexes", in preparation.
- Shuying Sun, Ashley Pritchard*, Emma McFall*, and Raymond Jiang*, “Methylation patterns of tumor suppressor genes and oncogenes in breast cancer", in preparation.

**Publications from the 2020 program:**

- C. Florez*, J. Higgins*, K. Huang*, T. M. Keller, D. Shen*, Y. Yang, The Prime Graphs of Some Classes of Finite Groups,
*Journal of Pure and Applied Algebra*, 226 (2022), 106990, 19 pp. - C. Florez*, J. Higgins*, K. Huang*, T. M. Keller, D. Shen*, Minimal Prime Graphs of Solvable Groups.
- C. Florez*, J. Higgins*, K. Huang*, T. M. Keller, D. Shen*, The Adjacency Spectra of Some Families of Minimally Connected Prime Graphs.
- M. Coleman*, A. Dochtermann, N. Geist*, S. Oh, Completing and extending shellings of vertex decomposable complexes,
*Seminaire Lotharingien de Combinatoire*, 85B (2021), Art. 88, 12 pp. - L. Anesti*, M. Harding*, M. Pridemore*, E. Shao*, Q. Zhao, Generalized log-rank test for left-truncated and interval-censored data, in preparation.

* undergraduate

**Publications from the 2019 program:**

- A. Betz*, M. Chao-Haft*, T. Gong*, T. M. Keller, A. Ter-Saakov*, and Y. Yang, Finite permutation groups with few orbits under the action on the power set,
*Rocky Mountain Journal of Mathematics*, accepted. - A. Betz*, M. Chao-Haft*, T. Gong*, A. Ter-Saakov*, and Y. Yang, On the odd order composition factors of finite linear groups,
*Journal of Group Theory*, 23 (2020), 1057-1068. - P. Cranford*, A. Dochtermann, E. Haithcock*, J. Marsh*, S. Oh, and A. Truman*, Biconed graphs, edge-rooted forests, and h-vectors of matroid complexes,
*Electronic**Journal of Combnatorics*, accepted. - S. Sun, A. Zane*, C. Fulton*, and J. Philipoom*, Statistical and Bioinformatic Analysis of Hemimethylation Patterns in Non-small Cell Lung Cancer,
*BMC Cancer*, (2021) 21:268.

* undergraduate

## Research Posters 2021

## Research Posters 2020

### On the prime graphs of several classes of groups is the winner of the Joint Mathematics Meeting's 2021 Outstanding Poster Award.

## Research Posters 2019

### Bi-coned graphs and Stanley's H-vector conjecture is the winner of Joint Mathematics Meeting's 2020 Outstanding Poster Award.

### Bounding the products of the Abelian Composition Factors is the winner of the Joint Mathematics Meeting's 2021 Honorable Mention Poster Award.

## Mentors

Yong Yang is currently an associate professor at the mathematics department of Texas State University. He received his PhD in 2009 from University of Florida under Alexandre Turull.He has published more than 70 high quality research papers, and his research interests are in finite groups and group representations, combinatorics, and number theory.

Thomas Keller is a Professor of Mathematics at Texas State University and has research interests in finite group theory. He has published more than 30 peer-reviewed research articles in prominent math journals. He is interested in the orbit structure of finite linear group actions and in conjugacy classes of finite groups. He has also done research with undergraduate and graduate students.

Anton Dochtermann received his PhD from the University of Washington where his advisors were Eric Babson and Isabella Novik. After postdoctoral positions at TU Berlin, Stanford, and U Miami, he joined the faculty at Texas State in 2016. His research interests are in topological and geometric combinatorics, and combinatorial commutative algebra. Recent projects include the commutative algebra of chip-firing, generalizations of parking functions for matroids, notions of higher-dimensional chordality, and topological methods in graph theory.

Suho Oh is currently an Associate Professor at the mathematics department of Texas State University. He received his PhD from Massachusetts Institute of Technology under Alexander Postnikov and did postdoctoral studies in University of Michigan under Sergey Fomin. His research interests are in algebraic combinatorics. He mainly deals with problems regarding matroids and polytopes, with applications to geometry and representation theory.

Shuying Sun received her PhD in statistics from the University of Toronto in Canada. Dr. Sun has interests in statistical genetics and bioinformatics and has published more than 20 peer-reviewed research articles in high-impact journals. Dr. Sun's research focuses on addressing challenging genetic and epigenetic questions using statistical and computational methods. She has been developing statistical methodologies and software packages for genomic problems using Bayesian methods, hidden Markov models, Markov Chain Monte Carlo algorithms, and linear models.

Qiang Zhao received his PhD in statistics from the University of Missouri-Columbia in 2004. He joined the faculty at Texas State in 2006 after working at the University of Texas–Pan American for two years as an assistant professor. His research interest is in survival analysis. Recent projects involve estimation of survival function and treatment comparisons for censored failure time data; estimation of mean functions and treatment comparisons for recurrent event data.