Advising students is one of the most important and fun parts of my job! I am interested in making academia more welcoming, more open, more transparent, more accessible, and less intimidating.

### Postdoctoral advisees

- Alex Elchesen, Postdoctoral Fellow in Topology, co-advised with Amit Patel. 2022-present.

### Graduate student advisees

- Sucharita Mallick, Mathematics PhD student, 1st year.
- Michael Moy,
Mathematics PhD student, 4th year.

Masters in Spring 2021.

[Master's Thesis, Master's Slides] - Lander Ver Hoef (co-advised by Emily King), Mathematics PhD student, 4th year.
- Daniel Vargas-Rosario,
Mathematics PhD student, 5th year.

Masters in 2020 under the direction of Jeanne Duflot. - Mark Heim (co-advised by Chris Peterson),
PhD student and Computer Science Masters student.

Masters in Spring 2020.

[Master's Thesis, Master's Slides] - Péguy Kem-Meka (main supervisor is Ismail Akhalwaya), Data Science PhD student at Quantum Leap Africa, 1st year.

### Graduate student alumni

- Brittany Story,
Mathematics PhD in Spring 2022 and Masters in Spring 2019.

Currently a Postdoctoral Researcher in the Department of Mathematics at the University of Tennessee, Knoxville, and jointly at the Aberdeen Proving Ground.

[PhD Thesis, PhD Slides, Master's Thesis, Master's Slides] - Lara Kassab,
Mathematics PhD in Fall 2021 and Masters in Spring 2019.

Outstanding Graduate Teaching Award in 2020.

Currently a Postdoctoral Researcher in the Department of Mathematics at the University of California, Los Angeles.

Formerly a Postdoctoral Researcher in the data science and analytics group at Pacific Northwest National Laboratories.

[PhD Thesis, PhD Slides, Master's Thesis, Thesis on arXiv, Master's Slides] - Johnathan Bush,
Mathematics PhD in Spring 2021 and Masters in Fall 2018.

Currently a Postdoctoral Researcher position in the Department of Mathematics at the University of Florida.

[PhD Thesis, PhD Slides, Master's Thesis, Master's Slides] - Joshua Mirth,
Mathematics PhD in Spring 2020 and Masters in Fall 2017.

Outstanding Graduate Teaching Award in 2019.

Currently a Faculty Member in Mathematics at St John's College.

Formerly a Senior Data Science Analyst in the department of Physiology and Biomedical Engineering at the Mayo Clinic.

Formerly a Postdoctoral Research Fellow in the Department of Mathematics at Michigan State University.

[PhD Thesis, PhD Slides, Master's Thesis, Master's Slides]

### External evaluator for graduate students

- External committee member, Patrick Gillespie, University of Tennessee, PhD preliminary exam, 2023
- External examiner, Bright Effah, Nipissing University (Canada), Masters, 2023
- External examiner, Junjie Wee, Nanyang Technological University (Singapore), PhD, 2023
- External opponent, Alvin Jin, KTH Royal Institute of Technology (Sweden), PhD, 2022
- External committee member, Rolando Kindelan, Universidad de Chile, PhD preliminary exam, 2021
- External committee member, Parker Gara, CU Boulder, Masters, 2021
- External committee member, Denis Khryashchev, CUNY, PhD preliminary exam, 2021
- External examiner, Francisco Belchí Guillamón, Universidad de Málaga (Spain), PhD, 2015

### Undergraduate student advisees

- Tia Karkos, Mobile sensor networks and time-varying homeomorphisms, 2022-present.
- Nicholas McBride, Geometric complexes and their shadows, 2022-present.
- Leah Gibson and Jack Pfaffinger. Research paper
*Lions and contamination, triangular grids, and Cheeger constants*, 2020-2021.

[Conference Version Link, arXiv:2012.06702] - Ty Jensen, Sophia Ressler, Taylor Rogers, Caroline Wendt, Laplacian eigenmaps, 2020.
- Natalie Burke, Bachelor's thesis
*An exploration in Perron's theorem*, 2019-2020.

[Bachelor's thesis, Thesis website] - Lu Xian from Macalester College; main advisor is Professor Lori Ziegelmeier. Research paper
*Capturing dynamics of time-varying data via topology*, 2018-2021.

[Publisher Link, arXiv:2010.05780] - Sophia Coldren. Bachelor's thesis
*On Vietoris-Rips complexes: The persistent homology of cyclic graphs*and research paper*The persistent homology of cyclic graphs*, 2018-2019.

[Publisher Link, arXiv:1812.03374, Bachelor's thesis] - Sean Willmot. Research paper
*The persistent homology of cyclic graphs*, 2017-2019.

[Publisher Link, arXiv:1812.03374] - Adam Jaffe (Stanford University) and Bonginkosi Sibanda (Brown University), via the Summer@ICERM 2017 program. Research paper
*Vietoris-Rips complexes of regular polygons*, 2017-2020.

[arXiv:1807.10971, Slides, Webpage, Photo] - Samadwara Reddy via the Duke PRUV Fellowship. Bachelor's thesis
*The Vietoris-Rips complexes of finite subsets of an ellipse of small eccentricity*and research paper*On Vietoris-Rips complexes of ellipses*, 2015-2017.

[Publisher Link, arXiv:1704.04956, Oberwolfach Preprint, Bachelor's thesis, Slides] - Colin Roberts. Bachelor's thesis
*Sweeping costs of simply-connected domains*and research paper*Sweeping costs of planar domains*, 2016-2017.

[Publisher Link, arXiv:1612.03540, Bachelor's thesis] - Brooks Adams. Research paper
*Sweeping costs of planar domains*, 2016-2017.

[Publisher Link, arXiv:1612.03540] - John Obuch. Undergraduate research paper Crystallization processes in 1-D, 2016, co-advisied with Patrick Shipman.
- Honors option for 4 students (Natalie Burke, Math 301, Fall 2019, Isabella Zapata, Math 366, Spring 2019; Leah Gibson, Math 301, Fall 2018; Andrea Vigil, Math 301, Fall 2015).

I used to be a coach of the CSU Putnam team, 2015-2020.

### Where can I find resources if I am interested in applied topology?

- You may be interested in the Applied Algebraic Topology Research Network (AATRN). Become a member to receive email invites to the online research seminars. Recorded talks are available at the YouTube Channel.
- Other online research seminars on applied topology include GEOTOP-A: Applications of Geometry and Topology and the Asia Pacific Seminar on Applied Topology and Geometry (APATG).
- An important source of applied topology news is appliedtopology.org. Mailing lists with announcements in applied topology include WinCompTop and ALGTOP-L. You may also be interested in joining the Slack channel "Geometry & Topology in ML".
- See this partial list of applied topology software options.
- See this partial list of applied topology book options.

### Unsolicited advice

### All students

**Attending talks:**Whenever you attend a talk, and*especially*if you are a student, prepare at least one question that you could possibly ask (this is possible even if you understood only the first sentence of the talk). If nobody else asks a question at the end of the talk, then you are required to ask your question! The speaker and the seminar organizer will both greatly appreciate it. Half of the questions I try to ask are misinterpreted to be more interesting than I intended them to be. If there's not time to ask your question after the talk, you now have a question prepared if the speaker sits next to you at lunch. Asking a question is a great way to meet people!**Letters:**Here are instructions if I am writing a letter of recommendation for you.**Grading:**Here are my tips for serving as a grader for one of my classes.**LaTeX:**Here is a LaTeX template for beginning LaTeX users. For more advanced LaTeX users, here are some LaTeX guidelines that I generally follow.**Overleaf:**Here are my tips for using git with Overleaf. Please email Henry if you'd like a link that will allow you to clone and play with this practice repository.*UPDATE: It turns out that using git with Overleaf for free is only possible if you were grandfathered in as an Overleaf v1 user.***High school math:**Here is a list of mathematics opportunities for advanced high school (or middle school) students, primarily in Colorado.

### Graduate students

**Conferences:**It's important for students to keep their eyes open for conferences they want to attend, for example by subscribing to the WinCompTop and ALGTOP-L mailing linsts. A good place to look for conferences is at the math institutes, such as the following, where you are often able to apply for travel funding: ICERM, MSRI, IMA, IPAM, Mathematical Problems in Industry (MPI) Workshop. For folks two years prior through 5 years after receiving their PhD, I highly recommend the MRC program, which is a great way to meet new folks in your research area, start a new research area, obtain funding for follow-up collaboration travel, and to travel to the Joint Meetings the following year.**arXiv:**Here are my tips for posting a paper to arXiv.**MSC codes:**Here are my tips for choosing MSC codes for a paper with me!**CSU thesis formatting:**The webpage on formatting your CSU thesis contains a link to a semi-official LaTeX thesis template, which several of my students have used.**Sharing your thesis with your committee:**One optional trick is that when you share your thesis with your committee, don't send them a PDF. Instead, email them a link to your thesis posted on your webpage. This allows you to make tiny changes and your committee "automatically" has the most up-to-date version (depending on how long they procrastinate their reading). Even if you don't make any changes then you're no worse off!**Applying for academic jobs after your PhD:**Here are some sample materials for applying to academic jobs after your PhD.

### Everybody!

**Giving talks:**Here are my tips for giving a math talk.**Moderating talks:**Here are my ``minutes remaining" signs, for use at conferences like the Joint Mathematical Meetings where you may be moderating many talks back-to-back, with limited time in-between talks. It is important to preserve the time between talks, and thus the need for these signs! Print them dual sided; that way you can tell speakers that when you hold up the sign, they will know how many minutes they have left, and also the audience will know how many minutes they have left! Hopefully that will keep the speakers honest :). I show each speaker the 5 min sign, and then show them the 2, 1, or 0 min sign only as needed (for example, depending on how close they seem to be to finishing). Give each speaker their full allotted time, even if their talk starts a few minutes late.**Women in math:**See Lara Kassab's collection of resources for women in math and related disciplines.**Applied topology software:**See this partial list of applied topology software options.**Online instruction:**See my current thoughts and plans for online instruction. In particular, I explain how to make screen-capture videos of class content, along with an inset talking head.**How to develop an online research seminar:**I wrote an article*How do I ... develop an online research seminar?*for the September 2020 issue of the Notices of the American Mathematical Society. See this list of online math seminars that I currently know about.