The PIMS Virtual Experimental Mathematics Lab (VXML), brings together faculty & postdocs with graduate and undergraduate students from across the PIMS network to work on challenging and exciting research mathematics questions.

To learn more, see the about section and if you are a faculty member, postdoc, graduate or undergraduate student at a PIMS member university and you want to get involved, please get in touch!

The PIMS Virtual Experimental Math Lab (VXML) program brings together world-leading faculty members, postdocs, graduate students and undergraduate students to work on exciting research problems in mathematics. Project teams from throughout the PIMS network work together to tackle challenging research problems through experimental, computational and visual mathematics, showcasing mathematics as a creative discipline.

Research problems are proposed by a faculty member or postdoc at a PIMS member (or affilate member) university, and a project team consisting of the mentor, a graduate student and 2-4 undergraduate students are formed to work on the problem (we encourage teams that integrate members from multiple PIMS sites). Teams commit 6-8 hours per week to work on the project and to meet to discuss their discoveries. Students will use a mixture of computational tools such as CoCalc (Sage Math Cloud), to work and collaborate.

At the end of the year there is an open-house event where discoveries can be showcased and any results presented. The laboratory is virtual so participants can join from anywhere in the PIMS network of universities and the projects focus on experimentation and discovery.

The PIMS VXML builds on the success of the Washington eXperimental Mathematical Laboratory (WXML) and similar initiatives at other universities. In addition, the PIMS VXML leverages the distributed structure of PIMS to bring together more dispersed and diverse teams to contribute and work on the projects.

The VXML strongly believes in Federico Ardila-Mantilla’s axioms :

**Axiom 1**: Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.**Axiom 2**: Everyone can have joyful, meaningful, and empowering mathematical experiences.**Axiom 3**: Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.**Axiom 4**: Every student deserves to be treated with dignity and respect.

New projects will appear here as they are accepted into the VXML program. To get an idea of existing successful projects see the Past Projects section. If you are interested in submitting a project, please see the Get Involved section.

In this project, students will strengthen their knowledge of graph theory and delve into geometric techniques for graph representation. Beginning with a review of relevant literature on the notion of boxicity, participants will apply different methodologies to establish bounds for boxicity across various graph classes. In addition, students will be tasked with developing heuristics and algorithms to ascertain the boxicity of select graphs from the studied graph classes. This pivotal step often yields critical insights and intuitions regarding the behavior of the respective graph classes.

Here are some completed projects from previous iterations of the VXML program.

Project Leader Venkata Raghu Tej Pantangi, University of Lethbridge Mahsa N Shirazi, University of Manitoba Graduate Mentor Junaid Hasan, University of Washington Undergraduate Team Members Jaskaran Singh, University of Manitoba Anu Singh, University of Saskatchewan Problem Statement The Smith Normal Forms (SNF) of an incidence matrix is a powerful invariant that may help distinguish the underlying incidence structure.

Topological Data Analysis (TDA) applies classical methods of algebraic topology to investigate and make inferences about the topology of (possibly large/complex) data sets. In this project, students will learn the fundamentals of topological data analysis and apply them to areas of current interest at the interface of geometry, topology and physics.

If you’d like to get involved with the VXML, please find the relevant section below and get in touch. We anticipate supporting 4-5 projects each year with each project consisting of a faculty member or postdoc, a graduate mentor and 2-4 undergraduates.

PIMS VXML is all about getting undergraduate students involved in research mathematics. Motivated students will work with leading researchers on exciting projects and perform cutting edge mathematical research.

PIMS VXML is open to undergraduate students at any of the PIMS Member or Affiliate Member Universities. You must be prepared to commit around 6-8 hours per week working on the project and meeting with the other members of your project team. When applying you’ll be asked to tell us about your mathematical interests and pick from a list of potential projects.

Upon completion, undergraduate team members will receive a certificate from PIMS attesting to their participation in undergraduate research in the mathematical sciences via the VXML.

Student applications are now open and will close on **November 5th**. Full
project descriptions will be available on this site shortly.

Graduate students mentors work closely with their faculty lead and the undergraduate students, providing an anchor for the project. You must be a graduate student at a PIMS member (or affiliate member) university and you must be in at least your second year. You should expect to commit 6-8 hours per week to the project, including team meetings.

Graduate student mentors will receive a modest ($500 CAD) stipend, for their participation.

Project submissions are now open soon and will close on **November 5th**. Full
project descriptions will be available on this site shortly.

Any faculty member or postdoctoral researcher at a PIMS Member or Affiliate Member University can propose projects for the VXML program. From prior experience, successful projects usually have some computational element that students get into while learning the relevant background, and have achievable intermediate goals.

The projects will be advertised to students on this website and should include details on the areas of mathematical interest and any prerequisites they have. We also ask that each project sponsor nominate a graduate student to help bridge the gap between research and undergraduate.

If you have an idea for a project please complete the project proposal form to get the process started. Please don’t hesitate to contact us if you have questions about proposing a project.

Project submissions are now. Selected project applications will be notified by email and project details will be added to this website shortly.

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