Welcome to my homepage!

     My Ph.D. degree conferral receipt date was May 3, 2019. My research thesis adviser was Karen E. Smith (Karen E. Smith). I do research in asymptotic-, combinatorial-,  and homological commutative algebra as they interface with algebraic geometry.  I served as an NSF-funded graduate student research assistant, namely  under Karen's grant DMS-1501625 "Frobenius in Geometry and Combinatorics". 
     Right now, I am an NSF Postdoctoral Researcher + Van Vleck Visiting Professor based at the University of Wisconsin - Madison. My NSF sponsoring scientist based in Madison is Daniel Erman.  
        Some Notes Related to these outcomes: 
        1. The official citation of record on nsf.gov is Linked Here (DMS-1902748).
        2. I am so "(Navier-)stoked" for this next postdoctoral phase of my career as a mathematician :) !
        3. I am in process of brainstorming/logging ideas for postdoctoral math projects (collaborative and otherwise) to pursue and turn around as publications in the 2019-2023 academic year window. If you'd care to inquire or pitch stuff, feel free to reach out -- I'll aim to respond carefully in kind! 
    Link to Most Current Author Profile on AMS MathSciNet (Author ID =  MR 1031098): Linked Here 
    My ORCID is  0000-0002-8517-8603  

Publications / Accepted Submissions
(in Reverse Chronological Order of Receipt of Acceptance to Journal)
  1. H. Banos, N. Bushek, R. Davidson, E. Gross, P.E. Harris, R. Krone, C. Long, A. Stewart, R.M. Walker. "Phylogenetic Trees: a package for Macaulay2." Accepted to Journal of Software for Algebra and Geometry. (arXiv/1611.05805)
  2. R.M. Walker. "Uniform Symbolic Topologies in Non-Regular Rings." This is my Ph.D. Dissertation, to be linked on Karen E. Smith's webpage (her Ph.D. Students section).  Linked Google Drive Upload
  3. I. Swanson and R.M. Walker. "Tensor-Multinomial Sums of Ideals: Primary Decompositions and Persistence of Associated Primes." Accepted to Proceedings of the AMS as of 03/21/2019, with all relevant ZIP files sent along to the AMS folks 04/04/2919 so all set there. (arXiv/1806.03545; the Proc. AMS Online Published Version ; my JMM 2019 Slides expositing this joint work :) !
  4. R.M. Walker. "Uniform Symbolic Topologies in Normal Toric Rings."  Journal of Algebra 511 (2018), pp. 292-298.  Link to Science Direct (https://doi.org/10.1016/j.jalgebra.2018.05.038). (arXiv/1706.06576The results advertised in this paper were the original motivation for my thesis back in Fall 2014!  After a sinuous journey, I did pin down my thesis problem -- eventually!
  5. H. Banos, N. Bushek, R. Davidson, E. Gross, P.E. Harris, R. Krone, C. Long, A. Stewart, R.M. Walker. "Dimensions of Group-based Phylogenetic Mixtures." Accepted to appear in The Bulletin of Mathematical Biology (Special Issue: Algebraic Methods in Phylogenetics). (arXiv/1711.08686Springer Link (Bull Math Biol (2018). https://doi.org/10.1007/s11538-018-0489-0 )Link to Full-Text View-Only PDF of the Published Version This work is based on participation in the 2016 AMS MRC workshop in Algebraic Statistics. I was part of the Phylogenetic Algebraic Geometry group led by Elizabeth Gross and Colby Long, who were each advised/mentored by Seth Sullivant, formerly a student of Bernd Sturmfels.  
  6. T. Hammonds, J. Johnson, A. Patini, and R.M. Walker. "Counting Roots of Polynomials over Z/ p^2 Z." Houston Journal of Mathematics (2018), Vol. 44, no. 4, pp. 1111-1119. (This paper is based on research conducted in the 2017 Mathematical Sciences Research Institute Undergraduate Program, or MSRI-UP for short!) (arXiv/1708.04713) (Video Link)  Note that this work has been extended to full generality in a joint paper (arXiv: 1711.01355) by Qi Cheng, Shuhong Gao, J. Maurice Rojas, and Daqing Wan. A more recent Summer 2018 entry in this vein by Rojas and REU collaborators is the following preprint (arXiv: 1808.10531)!
  7. R.M. Walker. "Uniform Harbourne-Huneke Bounds via Flat Extensions." Journal of Algebra 516 (2018), pp. 125-148. Link to Science Direct (https://www.sciencedirect.com/science/article/pii/S0021869318305106) (arXiv/1608.02320For context, while published last chronologically this work is a successor to item (7), and precedes/motivates items (1) and (5) as far as my thesis work.  
  8. R.M. Walker. "Uniform Symbolic Topologies via Multinomial Expansions."  Proc. Amer. Math. Soc. 146 (2018), pp. 3735-3746. (arXiv/1703.04530AMS Proceedings Link)
  9. E. Canton, D. Hernandez, K. Schwede, E. Witt, A. De Stefani, J. Jeffries, Z. Kadyrsizova, R.M. Walker, G. Whelan. "On the behavior of singularities at the F-pure threshold." Illinois Journal of Mathematics. Volume 60, No. 3-4, Fall/Winter 2016, pp. 669-685. I am a co-author of the appendix to this paper based on participation in the 2015 AMS MRC workshop in Commutative Algebra. I was part of the Positive Characteristic group led by Karl Schwede. (arXiv/1508.05427)
  10. R.M. Walker. "Rational Singularities and Uniform Symbolic Topologies." Illinois Journal of Mathematics. Volume 60, No. 2, Summer 2016, pp. 541-550. (arXiv/1510.0299310/1/15 talk notes1/8/16 JMM Talk 
  11. D.J. Bruce, M. Logue, and R. Walker. "Monomial Valuations, Cusp Singularities, and Continued Fractions." J. Comm. Algebra (2015) Volume 7, Number 4 (2015), 495-522. (arXiv/1311.6493, MAA MathFest Beamer Talk)
  12. A. Schultz and R. Walker. "A generalization of the Gaussian formula and a q-analog of Fleck's congruence." J. Number Theory 133 (2013), no. 11, 3717-3738. (arXiv/1202.0199

Preprints on arXiv

In (Various Stages of) Preparation

  1. R.M. Walker. "On A.S.P. Ideals." I've been traveling during Winter 2019 giving seminar talks on this work-in-progress. I have given some preliminary report talk(s) at the UM-Ann Arbor Combinatorics Seminar, the AMS Sectional meeting in Boston, the UIUC Algebra-Geometry-Combinatorics Seminar, and the 2018 Temple University Grad Student Conference in Algebra, Geometry, and Topology.  
  2. R.M. Walker. "Polynomial Algebraic Matroids." 
  3. R.M. Walker. "On the diagonal F-regularity of locally acyclic cluster algebras." 
  4. R.M. Walker. "TBD."

Undergrad-Graduate General Audience Talks (2018)

Occasionally, I may offer to pair formal Research Seminar visits at other U.S. math departments  with giving these General Audience Talks with an aim of doing "recruitment ambassadorship" for the UM-Ann Arbor math graduate program. If you'd be interested in having me speak with undergrads Q&A style ahead of the 2021-22 grad school application cycle, and can work with me to defray travel/housing costs, feel free to reach out! 

  1. R.M. Walker. M.A.D. Tapas. Notes from a talk on 04/25 in UIUC Math 496 course (Honors Seminar: Introduction to Mathematical Research), taught by Professor Bruce Reznick. Rough Spiel: We record a "fast exponentiation" fact from p-adic analysis and extend it using undergrad-level algebra. We indicate how this fact can interact and blend with modular arithmetic divisibility tests. Click Here
  2. R.M. Walker. Beamer Talk on 04/25 for UIUC MATRIX undergraduate math club, combining slides from my two talks in the UM-Ann Arbor undergraduate math club in 2017. Click Here 

Contact Information: 

E-mail address:   robmarsw@umich.edu or rwalker23@wisc.edu

Office: 407 Van Vleck Hall 

Mailing address:

215 Van Vleck Hall

Department of Mathematics

480 Lincoln Drive

Madison, WI 53706

An instance of "Geometric Modeling" using Algebraic Geometry: 
A "Yin-Yang" symbol with cubic rotisserie skewer, using WolframAlpha. 

The above photo appears under "Rising Stars," on the Mathematically Gifted and Black website. MG&B 2018 Rising Stars Link

2015 MathFest, with my adviser