If you are by any chances affiliated to a Canadian university you get free access to DMTI POI data that includes public schools and universities.
All of this is located in the Scholar GeoPortal repository at http://geo2.scholarsportal.info/
The data is loaded from an RPC endpoint. Here's an example for the page you linked.
curl 'https://www.sapsailing.com/gwt/service/dispatch/leaderboard/HWCS_2020_Round_1___RS_X_Men' \
-H 'Content-Type: text/x-gwt-rpc; charset=utf-8' \
-H 'X-GWT-Permutation: ED484971D331FCA3E1C2F5147D82354E' \
Thanks for submitting your questions. I forwarded your questions to our helpdesk and received the following responses. I hope you find them helpful.
What is the best way to determine the concrete subset percentage [of
TIV students] used for a given measure? Is it a "cohort" column, like
Number of students in the family income cohort?
For some metrics ...
Although I am unaware of any existing list, it certainly is possible to create one using the IPEDS Use The Data tool (https://nces.ed.gov/ipeds/use-the-data) which allows for the downloading of the IPEDS Completions survey data, which includes all awards conferred (by CIP and by level) for all 7000+ IPEDS-participating institutions.
I found a portal that lists PhD topics, coincidentally called "find a phd"
returns these 3 PhD programs (2019-03-12):
University of East Anglia, School of Environmental Sciences
University of Bath, Centre for Accountable, Responsible and Transparent AI
Northumbria University, Faculty of Business ...