Taha Hedayat

Current Life

• Pronouns: he/him/his
• School: University of Calgary
• Degree: Bachelor of Science - Honours
• Graduating Year: 2026
• Major: Mathematics
• Minor: Music
• Employment: Tutoring
• Going to the University of Waterloo in the upcoming fall for my master's in math.

• Research Experience,
• Mentorship Program,
• Talks Given,
• Community and volunteering,
• Teaching Assistant Experience,
• Tutoring Experience,
• Publications,
• Unpublished work and Resources,
• Research Awards Received,
• Awards Received.

Research Experience

• The Spine: A Supersingular Highway
• January 2026 - April 2026
• Superisors:
• Dr. Sarah Arpin
• Dr. Renate Scheidler
• Undergraduate Thesis
• We consider the structure of the spine of the supersingular $\ell$-isogeny graph for one of the cases which we (in 2024) were not able to fully describe, $\ell = 2$ and $p = 71, 119\pmod{120}$. We find the distance, eccentricity, and diameter functions, of the components of the spine without the non-trivial edge not defined over $\F_p$. Using these functions, we find the mean diameter of the spine and show how this value distinguishes the different structures of the spine. Thus allowing us to use explicit computations to provide heuristics on the behavior of the spine's structure as $p$ varies.
• The connection between Graph Theory and Markov Chains
• May 2025 - August 2025
• Supervisor: Dr. Deniz Sezer
• Funded by the Undergraduate Student Research Award
• The goal of this research project was to explore the connections between graph theory and the graphical representation of a Markov chain. The project concluded with us examining a particular Markov chain that sampled st-paths within a planar graph. This MC had a mixing time dependent on the diameter of the graphical representation of the MC, which in turn depended on the planar representation of the sampling graph. Sage code was written to generate the graphical representation given a planar graph with a specific embedding. Future work will use algorithms and Sage code already written to gather data on which embeddings of a planar graph result in the most optimized mixing time.


• The Intelligent Tutoring System
• July 2024 - April 2025
• Supervisors
• Dr. Thomas Bitoun
• Dr. Anna Funk
• Funded by the Taylor Institute for Teaching and Learning
• This research project focused on developing and testing prompts for an LLM to see if and how an LLM can best help students learn within a proof-based course. We focused particularly on the introductory abstract algebra course at the University of Calgary, MATH 315. We spend the summer studying which parts of the student learning process LLM was good at, and which ones the LLM was lacking. At the same time, we developed a prompt that addressed the issues we faced and made the LLM communicate with students in the methods advised by teaching agencies. In the next rendition of the course, we ran a study to see how the prompted LLM (dubbed the Intelligent Tutoring System) actually helped the students in their approach to understanding abstract algebra.


• The Spine of a Supersingular Ell-Isogeny Graph 2024
• May 2024 - August 2024
• Superisors:
• Dr. Sarah Arpin
• Dr. Renate Scheidler
• Funded by the Undergraduate Student Research Award
• This research project was a continuation of our research in 2023. From the great amount of data collected last year, we wanted to spend time analyzing what they represented. However, what became clear was that we did not have a theoretical idea of how the graph should be. Hence, we spent time to make the structure of the spine of the supersingular $\ell$-isogeny graph as explicit as possible. Dr. Arpin and her co-authors had made precise statements about the structure of the spine in their 2021 paper Adventures in Supersingularland. However, we made more precise statements about the precise structure of the spine through parameters of $p$ and $\ell$. This project resulted in our paper getting accepted at LuCaNT. The pre-print for which is available here.


• The Spine of a Supersingular Ell-Isogeny Graph 2023
• May 2024 - August 2024
• Superisors:
• Dr. Sarah Arpin
• Dr. Renate Scheidler
• Funded by the Undergraduate Student Research Award
• This project was aimed at us trying to understand the graph theoretic structures behind the, assumed to be random, supersingular $\ell$-sogeny graph. The majority of the time of the project was spent on me catching up on the material, but once I had enough background, we spent time writing Sage code which generates the isogney graph over the finite field or finite field squared, and the spine. This code also grabbed a metric load of data about the spine, the full isogeny graph, and how the two interacted with each other. The project ended with us making plans to analyze the gathered data the following summer.

Mentorship Program

• Sage Enhancement Protocal
• Mentor: Vincent Macri
• Date: 11/09/2025 - Present
• In this project, we are focusing on implementing improved public key exchange protocols into Sage, including post-quantum protocols such as SIDH.


• Algebraic Graph Theory and Conductance of a Graph
• Mentor: Kristap Balodis
• Date: 01/05/2025 - 30/08/2025
• During this project, I was introduced to the world of Algebraic Graph Theory. The project ended up with me focusing on proving a formula for the conductance of a path graph and a cycle graph. This project resulted in a presentation within the group of mentors and mentees and a math jam within SUMC

Talks Given

• Celebrating Undergraduate Research 2025
• Title: Optimization of Sampling Simple 𝒔𝒕-Paths on Planar Graphs According to their Length
• Date: 23/09/2025
• Location: Unvisersity of Calgary


• Isogeny Graphs in Cryptography
• Title: The Spine of the Supersingular $\ell$-Isogeny Graph
• Date: 07/08/2025
• Location: Banff International Research Station for Mathematical Innovation and Discovery


• LMFDB, Computation, and Number Theory 2025
• Title: The Spine of a Supersingular Ell-Isogeny Graph
• Date: 08/07/2025
• Location: Institute for Computational and Experimental Research in Mathematics, Brown University


• Alberta Math Diologue 2025
• Talk 1:
  • Title: The Math Behind a Post-Quantum Cryptographic System: Supersingular Ell-Isogeny Graphs
  • Date: 01/05/2025
  • Location: University of Calgary
• Talk 2:
  • Title: Can AI teach proof? Student experiences with a custom chatbot in an introductory Algebra course
  • Date: 01/05/2025
  • Location: University of Calgary


• Canadian Undergraduate Mathematics Conference 2025
• Talk 1:
  • Title: Post-Quantum Cryptography: The Spine of the Supersingular Ell-Isogeny Graph
  • Date: 24/06/2025
  • Location: University of Waterloo
• Talk 2:
  • Title: Can AI Teach Proof? Student experiences with a custom chatbot in an introductory Algebra course
  • Date: 25/06/2025
  • Location: University of Waterloo


• SUM-C Summer Seminars
• 2025:
• What is SQIsign?
• Markov Chains! What is it? And why should you care?
• 2024:
• Using Sieves Instead of CRT
• x^2+1 = 0 Does Not Imply x = i
• 2023:
• Supersingular ell-isogeny graphs
• Kissing Fractions and their ~Intimate~ Connections
• 2022:
• Pop It Cryptographic System
• N-Dimensional Polytopes
• 2021:
• A Function for Phi


• SUM-C Math Jams
• Algebraic Graph Theory: Conductance
• 18/03/2025
• What is a Number?
• 09/09/2025
• Euclidean Geometry: The Heptadecagon
• 27/03/2024
• An Intuitive Introduction to Graph Theory
• 06/03/2023


• The Calgary Peripatetic Seminar
• Title: The Intersection between Number Theory, Abstract Algebra, and Cryptography
• Date: 04/10/204
• Location: University of Calgary

Community and Volunteering

• Abstract Algebra Practice Problem Sessions
• Date: October 2025 - Present
• Description: Working with projective abstract algebra students so that they may get a sense for working with abstract objects and solving problems using abstract methods.


• U of C Open House
• Date: 25/10/2025
• Description: Volunteered as a representative of the Mathematics and Statistics Department to help students make a decision in regards to doing a math-related degree.


• You at Ucalgary Science Panelist
• Date: 12/04/2025
• Description: I was a panelist on the You at Ucalgary event, which invited the incoming first years to hear and learn about university life and how to succeed during your time at U of C.


• Organizer of the Alberta Math Dialogue 2025 Undergraduate Sessions
• Date: 01/05/2025 - 02/05/2025
• I was the main coordinator and organizer of the Undergraduate Sessions of the Alberta Math Duologue. This was a group effort of all the directors of the Society of Undergraduate Mathematics - Calgary. We had students from all over join us and present on their very cool mathematical research!
• Undergraduate Research Mentor
• Date: May 2025 - August 2025
• Description: I volunteered as a mentor to two undergraduate student researchers during this time to pass on some of the knowledge that I have gained throughout my three terms of undergraduate research. I had two amazing mentees!


• Society of Undergraduate Mathematics - Calgary (SUM-C)
• Vice President of Events
• Date: 01/05/2025 - Present
• President
• Date: 01/05/2024 - 30/04/2025
• Achievements include: Restructuring the constitution of the club, coordinating the club's first networking night event, which also ended up being our most successful event in years, and coordinating the most successful review sessions in years.
• Vice President of Academics
• Date: 17/10/2022 - 30/04/2024
• Achievements Include: Making the designs for membership cards, expanding our club's exam bank for the first time in many years, and starting the math competition series for SUMC.
• Representative
• Date:08/08/2022 - 16/10/2022

Teaching Assistant Experience

• Fall 2025: MATH 311.
• I was one of four Teaching Assistants assigned to this course.
• I was tasked with leading the tutorial lectures during the semester and running the exams as they come up.
• Under the direction of Dr. Thi Dinh.


• Fall 2023: MATH 275.
• I was one of sixteen Teaching Assistants assigned to this course.
• I was tasked with aiding students in their work during the active learning sessions scheduled for the course.
• Under the direction of Dr. Jerrod Smith and Dr. Ryan Hamilton.

Tutoring

• Fall 2025:
• MATH 211 (Linear Methods 1)
• MATH 267 (Calculus 2)


• Summer/Spring 2025:
• MATH 249 (Calculus 1)
• MATH 211 (Linear Methods 1)


• Winter 2025:
• MATH 411 (Linear Methods 3)
• MATH 319 (Transformational Geometry)


• Fall 2024:
• MATH 249 (Calculus 1)
• MATH 265 (Calculus 1)
• MATH 267 (Calculus 2)
• math 20-1 (Pre-Calculus 2)
• math 30-1 (Pre-Calculus 3)
• math 31 (High School Calculus)


• Summer/Spring 2024:
• math 30-1 (Pre-Calculus 3)
• math 31 (High School Calculus)

Publications

• Hedayat, Arpin, Scheidler, The Spine of a Supersingular $\ell$-Isogeny Graph. ArXiv pre-print version: here

Unpublished work and Resourses

• Final notes on sampleing st-paths from a planar graph.
• Final notes on the cheeger constant of a path graph.
• My notes of Supersingular Ell Isogeny Graphs.

Reserach Awards Received

• Summer 2025: Undergraduate Student Research Award (USRA) provided by the Natural Sciences and Engineering Research Council of Canada (NSERC).
• Summer 2024: Undergraduate Student Research Award (USRA) provided by the Natural Sciences and Engineering Research Council of Canada (NSERC).
• Summer 2023: Undergraduate Student Research Award (USRA) provided by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Awards Received

• 2025: Bhagwan Dass Aggarwala Memorial Award in Mathematics and Statistics
• 2025: University of Calgary Science Dean's List
• 2024: University of Calgary Science Dean's List