Erik Holmes
Email: eholmes "at" math.toronto.edu
Office: (Mostly zoom rooms ATM)
A bit about me (mathematically)
I am currently on the job market for positions beginning in Fall 2026.
I am a postdoctoral fellow at the University of Toronto working with Ila Varma. Previously I was a postdoc at the University of Calgary working with Khoa Nguyen and a member of the number theory group.
I received my PhD in 2021 from the University of Hawaii at Manoa under the supervision of Rob Harron.
My research focuses on the geometry and distribution of lattices attached to number fields—both integral and log-unit lattices. I study how their shapes evolve across natural families, connecting algebraic structures with geometric patterns. This perspective informs questions in arithmetic statistics (such as Malle-type phenomena) and has potential applications to the design and analysis of lattice-based cryptography.
Some recent works
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with
Sergio Ricardo Zapata Ceballos,
Sara Chari,
Fatemeh Jalalvand,
Rahinatou Yuh Njah Nchiwo,
Kelly O'Connor,
Fabian Ramirez,
and
Sameera Vemulapalli.
(Accepted to Journal of Number Theory, 2026)
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with Rob Harron and Sameera Vemulapalli.
(Accepted to Mathematische Zeitschrift, 2026)
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with Félix Baril Boudreau and Khoa Nguyen.
(accepted to Math. Annalen, 2025)
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(accepted to Journal de Théorie des Nombres de Bordeaux, 2025)
Organization
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At the University of Calgary, Seda Albayrak and I co-founded a weekly writing café for graduate students and postdocs in mathematics.
The café fostered community, accountability, and a supportive environment for writing tasks—from theses to research papers.
Note: Since our move to new institutions, the event has been successfully continued by graduate students.
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Together with Kübra Benli and Brandon Gill, I co-organized the 14th iteration of Alberta Number Theory Days at BIRS (Banff, March 31–April 2, 2023).
University of Toronto
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Fall 2025: Math 135 (Calculus I)
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Spring 2025: Math 136 (Calculus II)
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Winter 2023: Math 136 (Calculus II): I was on parental leave after the first month of the term.
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Fall 2023: Math 135 (Calculus I)
University of Calgary
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Spring 2023: Math 211 (Linear methods I)
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Fall 2022: Math 275 (Calculus for Engineers and Scientists)
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Fall 2021: Math 265 (University Calculus I)
(see teaching page for more information about past courses/departmental syllabi)
A bit about me (non-mathematical)
Outside of math I enjoy coffee, cooking (and eating!), dogs, time with friends and family, stories, traveling, and plenty of outdoor activities.
Before rediscovering a childhood passion for mathematics during my undergraduate years, I worked in construction, on farms, and in logging/forest management, and became certified as a wildland firefighter. During graduate school I also worked in video production—primarily editing, color, and post-production—helping tell stories through film.
These days, most of my focus is on mathematics (with some rabbit holes in AI/ML), but I remain fond of crafting. In my free time I experiment with photography, woodworking, leatherwork, and pottery. You can see some of my crafting attempts here.
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