Stephen Melczer

Office - MC 6028

smelczer (at) uwaterloo.ca

1-519-888-4567 x41282

I’m an associate professor in the Department of Combinatorics and Optimization at the University of Waterloo (with a cross-appointment in the School of Computer Science), interested in leveraging computational algebraic geometry, analysis, and topology to create effective tools for combinatorics, computer science, and mathematics.

An overview of some of my research interests can be found in the first chapter of An Invitation to Enumeration. More details can be found on my research page.

Previously I was a CRM-ISM postdoctoral fellow at UQAM (2019 – 2020) and a postdoc at the University of Pennsylvania (2017 – 2019). I received doctorates from the École normale supérieure de Lyon and the University of Waterloo in 2017.

I’ve written a set of lecture notes and two textbooks,

An Invitation to Enumeration (online lecture notes). An elementary introduction to enumerative combinatorics for math undergrads working up to the basics of analytic combinatorics.
An Invitation to Analytic Combinatorics: From One to Several Variables (Springer). A gentle introduction to analytic combinatorics and analytic combinatorics in several variables (ACSV), focused on explicit computational methods.
Analytic Combinatorics in Several Variables, 2nd Edition (Cambridge, with R. Pemantle and M. C. Wilson). The most complete and expansive treatment of ACSV, making use of topological methods to present a comprehensive framework for studying multivariate generating functions.

These references give a pathway from first year university mathematics to the frontiers of research in analytic combinatorics.

You should also try our sage_acsv package that will rigorously do (much of it) for you – feedback always welcome!

News / Events

Joined CanaDAM Executive Committee, May 2025

Next event in Kelowna, BC (2027)

FPSAC 2025 (Plenary Speaker), July 2025

At Hokkaido University, Japan

AofA 2025 (Organizing Committee Co-Chair), May 2025

At the Fields Institute, Toronto

Joined AofA Steering Committee, June 2024

Next events in Toronto (2025) and Munich (2026)

Jeremy Chizewer wins 2024 Governor General Gold Medal

Congratulations Jeremy!

Analytic Combinatorics in Several Variables, 2nd Edition Now Available

An Invitation to Analytic Combinatorics hits 13k chapter downloads

Map to Office

My office is MC 6028 (click for a larger version).

Coauthors

Yuliy Baryshnikov, Alin Bostan, Mireille Bousquet-Mélou, Sophie Burrill, Jeremy Chizewer, Julien Courtiel, Ruiwen Dong, Éric Fusy, Torin Greenwood, Benjamin Hackl, Kevin Hyun, Veronika Irvine, Manuel Kauers, Jessica Khera, Alexander Kroitor, Kisun Lee, Andreas Lenz, Erik Lundberg, Andrew Luo, Marc Mezzarobba, Marcus Michelen, Marni Mishna, Somabha Mukherjee, J. Ian Munro, Greta Panova, Robin Pemantle, Ava Pun, Kilian Raschel, Cyrus Rashtchian, Frank Ruskey, Tiadora Ruza, Bruno Salvy, Éric Schost, Jesse Selover, Paul H. Siegel, Josip Smolčić, Catherine St-Pierre, Armin Straub, Mark Wilson, Elaine Wong