Portrait
Education
2015 - 2020
Steklov Mathematical Institute of Russian Academy of Sciences
PhD in mathematics
Department of Geometry and Topology
Scientific advisor: Prof. Alexander A. Gaifullin
Thesis topic: Explicit combinatorial computation of the first Pontryagin class and applications (defended February 25th, 2021)
2016 - 2020
Skolkovo Institute of Science and Technology PhD in mathematics Center for Advanced Studies Scientific advisor: Prof. Alexander A. Gaifullin
2010 - 2015
Lomonosov Moscow State University
Specialist degree in mathematics (Master equivalent)
Diploma cum laude, GPA: 4.8/5
Department of Mechanics and Mathematics
Major in Higher Geometry and Topology
Scientific advisor: Prof. Alexander Gaifullin
Diploma topic: Computation of the Pontryagin classes of some triangulated 8-dimensional manifolds
Employment
2026 - present
Department of Computer & Mathematical Sciences, University of Toronto, Scarborough Sessional instructor
January - April 2026
Mercor Subject Domain Expert Participated in the reinforcement-learning-from-human-feedback (RLHF) process for a leading AI company.
2025 - 2026
Department of Mathematical & Computational Sciences, University of Toronto, Mississauga Sessional instructor
2020 - present
Russian School of Mathematics Competition mathematics teacher and curriculum designer RSM is an award-winning, afterschool US math program for K-12 students.
2022 - 2025
Department of Mathematics, University of Toronto Postdoctoral research scholar
2021 - 2022
Steklov Mathematical Institute of RAS Postdoctoral student
2020 - 2021
Huawei Big Data algorithm engineer Algorithm design and algorithm research for big graphs on projects that went into production.
2017 - 2018
Steklov Mathematical Institute of RAS Research fellow Position sponsored by Russian Science Foundation grant
2016 - 2018
Moscow State University Gymnasium High school teacher Teaching algebra, geometry, competition mathematics and undergraduate level courses for classes specialized in mathematics and engineering.
Teaching
University teaching experience
Summer 2026
University of Toronto, Scarborough
Linear Algebra I (MATA22) instructor
Sole instructor and designer of a large (~180-student) first linear-algebra course — lectures, six tutorial sections, and assessments. The conceptual, proof-oriented lectures are built as an inquiry-based concept network; tutorials centre on collaborative group work, with reflection-based assessment, a Piazza discussion community, and Padlet and anonymous feedback channels.
Fall 2025 - 2026
University of Toronto, Mississauga
Introduction to Proofs (MAT102) instructor
Two sections of an active-learning, partially-flipped introductory proof course built on pre-class readings and in-class activities; through the term I placed growing emphasis on explicit learning skills and meta-cognitive strategies to help students read and write formal mathematics.
Winter 2024 - 2025
University of Toronto
Concepts in Abstract Mathematics (MAT246) instructor
My first fully uncoordinated course, redesigned from scratch around peer-to-peer learning (a graded Piazza community), explicit learning objectives, and assessment optionality — a “soft start” for students moving into upper-year proof-based mathematics.
Fall 2024 - 2025
University of Toronto
Linear Algebra (MAT188) instructor (Faculty of Applied Science and Engineering)
Active-learning course with a standards-based grading component; I designed concept maps linking the material to individual learning standards and ran several feedback channels (weekly reflections, anonymous forms, dedicated in-class time), adapting the course in response to student input.
Winter 2023 - 2024
University of Toronto
Linear Algebra II (MAT224) instructor
Coordinated course taught with components of active learning inside the lecture-and-office-hours format: lectures structured to draw out as many student questions as possible, and office hours run to encourage peer-to-peer discussion.
Winter 2022 - 2023
University of Toronto
Linear Algebra II (MAT224) instructor
The first of my two iterations of this course; my teaching of MAT224 was distinguished by the F.V. Atkinson Teaching Award.
Course key notions: fields, complex numbers, vector spaces over a field, linear transformations, matrix of a linear transformation, kernel, range, dimension theorem, isomorphisms, change of basis, eigenvalues, eigenvectors, diagonalizability, real and complex inner products, spectral theorem, adjoint/self-adjoint/normal linear operators, triangular form, nilpotent mappings, Jordan canonical form.
2018 - 2019
Higher School of Economics
Differential topology instructor/assistant
The main aim of the course was to prove the h-cobordism theorem and to approach Chern-Weyl theory. Through the semester the main topics were: homology and cohomology (simplicial and de Rham), Poincar’{e} duality, basics of Morse theory, cohomology of grassmanians, transversality theorem, h-cobordism theorem, smooth structures on spheres (supplementary). (Course held in Russian and English.)
2018 - 2019
Independent University of Moscow
Topology (undergraduate course) teaching assistant
Additional teaching experience and training
June 2023
MAA
Team-Based Inquiry Learning workshop participation
May 2023
University of Toronto Teaching & Learning Symposium participation
2020 - present
Russian School of Mathematics
Competition mathematics teacher
- Teaching competition mathematics to K-12 US high school students preparing them for the AMC 8/10/12, AIME and USA(J)MO competitions.
- Designing high school competition classes curricula.
- Preparing and conducting AMC 8/10/12 preparation webinars for groups of 300-500 students.
- Preparing and conducting an AIME preparation workshop.
2020 - 2022
Private teaching of graduate mathematics for post-quantum cryptography
Complete higher algebra and basic algebraic geometry course design and teaching for a cryptography specialist.
2019
Skolkovo Institute of Science and Technology
Pedagogy of Higher Education course passed
A higher education pedagogy course passed in the framework of PhD studies focused on learning to align learning outcomes with with learning activities and assessment strategies. Emphasis was also put on highlighting potential effects of language and culture barriers and on ways to address them. While practical in assignments (the final assignment was to develop or upgrade a course curriculum), the course also introduced reading and interpreting education research literature.
2017
Skolkovo Gymnasium
Elementary school teacher
Teaching primary school advanced mathematics course. The main aim of the course was to make pupils think “out of the box”, understand the concept of strict reasoning and develop a basic mathematical intuition. The course was designed by the author.
2016 - 2018
Moscow State University Gymnasium
Teacher of mathematics in high school
The school class was specialized in mathematics, the aim was to give a firm basis of undergraduate mathematics in high school. The courses taught were algebra, geometry, pre-calculus, special mathematics (a course created from scratch presenting basics of different areas of pure mathematics), calculus and popular mathematics.
2013 - 2014
High school # 1543 (Moscow, Russia)
Teaching assistant in a course in olympiad mathematics
Research
Publications and preprints
2026
I. Frolov, D. Gorodkov, D. Korshunov, A. Nabutovsky. Geodesic nets on the Euclidean plane and closed geodesic nets on Euclidean surfaces, preprint arXiv: 2606.14080.
2025
A. Chervov et al. CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs, preprint arXiv: 2502.18663, to appear in Advances in Theoretical and Mathematical Physics.
2024
D. Gorodkov. On Mikhail Gromov’s talk “Life through the keyhole of Mathematics”, Fields Notes, 2024, 21(5): 20-22. Online version.
2024
R. Fesler, D. Gorodkov, M. Karev. Hurwitz numbers for reflection groups
2019
A. Gaifullin, D. Gorodkov. An explicit local combinatorial formula for the first Pontryagin class, Russian Mathematical Surveys, 2019, 74 (6): 450. DOI.
2019
D. Gorodkov. A 15-vertex triangulation of the quaternionic projective plane, Discrete & Computational Geometry, Springer, (2019) 62: 348. DOI, arXiv
2016
D. Gorodkov. A minimal triangulation of the quaternionic projective plane, Russian Mathematical Surveys} (2016), 71 (6):1140. DOI
To appear
2026
D. Gorodkov. Geodesic nets on the plane with few boundary points, to appear.
2026
D. Gorodkov. Vertex-minimal equilibrium triangulations of projective planes, to appear.
2026
R. Fesler, D. Gorodkov. Hurwitz numbers for reflection groups
Grants
2026
LEAF Grant — Graph-Based Concept Mapping for Introductory Proofs, Learning and Education Advancement Fund, University of Toronto Mississauga (approved)
2016 - 2018
Participant of the RSF grant 14-50-00005 Modern mathematics and applications
2017 - 2018
Co-executor of Presidential grant for young Doctors of Sciences MD-2907.2017.1 Characteristic classes of surface bundles and cohomology of the mapping class group and its subgroups
2014 - 2015
Co-executor of Presidential grant (under the direction of Prof. Alexander Gaifullin) for young Doctors of Sciences MD-2969.2014.1 Geometry of flexible polyhedra
Awards
2023
F.V. Atkinson Teaching Award for Postdoctoral Fellows, University of Toronto
2016
Winner of Contest Young Russian Mathematics
2015
Absolute winner of August Möbius Contest for young mathematicians works among undergraduate students
2014 - 2015
Special stipend provided to best students of Lomonosov MSU
Chosen conferences and talks
Mathematics education talks
Aug 5–8, 2026
MAA MathFest 2026, Boston, MA; Contributed Paper Session on Inquiry, Conjecture and Discovery: A High-Impact Approach to Mathematical Learning and Problem Solving; talk Making Inquiry the Curriculum, Not the Exception: A Graph-Based IBL Architecture
Abstract
Consider organizing a mathematics curriculum as a directed graph: each node introduces a single idea, and each directed edge is a question students would naturally ask next. After establishing that
, for instance, a natural edge asks: is addition always commutative, or did we just get lucky? Students navigate by following and contributing such questions rather than a fixed sequence. This structure extends concept maps so that inquiry is the curriculum’s flexible skeleton, not an enrichment layer. The design follows Tao’s three stages of mathematical maturation: informal intuition first, formalism only when students’ own questions demand it, and eventually fluency between the two. We present the graph architecture, a concrete implementation progressing from informal counting to formal logic and set theory, and a framework for course, assessment, and feedback design using the proposed curriculum structure.
June 18, 2026
Tri-Campus Math Education Meeting, University of Toronto; talk Creating the Conditions for Peer Learning in a Proof-Based Course
Abstract
In large courses at U of T, students often have no relationship with the people sitting next to them. In a proof-based course, this is a particular problem: peer learning requires hearing how someone else reasons, and without social bonds or a structured occasion for it, it simply doesn’t happen. This talk describes a tutorial format designed to create that occasion. Students work in groups on parallel but distinct problem variants, then voluntarily present to a section that has worked on structurally similar problems, making every presentation genuinely informative to the room. Presenting a partial or unresolved solution is explicitly worth full credit. I will describe the design subtleties, the features making the structure work in my opinion and some preliminary student feedback of the approach.
International conferences and talks
08/2019
Topology, Geometry, and Dynamics: Rokhlin –- 100, Euler Mathematical Institute, Saint Petersburg, Russia; talk Triangulations of the quaternionic projective plane and Pontryagin classes
10/2017
Geometric and topological combinatorics: Modern techniques and methods, Berkeley, CA, United States; participation in workshop
03/2017
British-Russian Seminar on Toric Topology and Homotopy Theory, Steklov Mathematical Institute of RAS, Moscow, Russia; talk Combinatorial formulas for Miller-Morita-Mumford classes
09/2016
International workshop “Probability, analysis and geometry”, Moscow State University, Russia; talk Minimal triangulations of the quaternionic projective plane
09/2016
Geometry days in Novosibirsk — 2016, Novosibirsk, Russia; talk Three minimal triangulations of the quaternionic projective plane
08/2016
XIX Geometrical Seminar, Zlatibor, Serbia; talk A 15-vertex triangulation of the quaternionic projective plane
06/2016
International Summer School & Workshop “The 6th Summer School on Geometry and Mathematical Physics”, Krasnovidovo, Russia; talk Minimal triangulations of projective planes (Proceedings and abstracts published)
Participation in the 2nd to 5th Summer Schools on Geometry and Mathematical Physics in 2012 - 2015 respectively
Latest seminar talks
03/2023
Geometric Structures Laboratory Seminar, University of Toronto, Canada; talk Combinatorial computation of characteristic classes
02/2020
Geometric Group Theory Seminar, Ohio State University, OH, USA; talk Combinatorial formulas for the first rational Pontryagin class and applications
10/2019
Geometry, topology and mathematical physics seminar, Moscow State University, Moscow, Russia; talk Redistribution of curvature under bistellar flips and a combinatorial formula for the first Pontryagin class
10/2018
Stanford Topology Seminar, Stanford, CA, USA; talk Combinatorial characteristic classes and the minimal triangulation of the quaternionic projective plane
03/2018
Chebyshev Laboratory Seminar, St Petersburg, Russia; talk Combinatorial Miller-Morita-Mumford classes
11/2017
Higher School of Economics, Moscow, Russia; talk Combinatorial Miller-Morita-Mumford classes
Popular mathematical talks
10/2018
Student Math Circle, University of Northern Colorado, USA; talk Music and mathematics on the harmonic series and tuning pianos
11/2017
Krasnoyarsk book fair, Krasnoyarsk, Russia; talk How are rabbits related to geometry? on the counter-intuitivity of infinity, the Dirichlet principle and Banach-Tarsky paradox; joint project with Skolkovo Institute of Science and Technology
07/2017
Summer linguistics school, Voronovo, Russia; Mathematics and music, joint with Nikolai Andreev
07/2016
Summer school “Contemporary mathematics”, Dubna, Russia; talk Music and mathematics, joint with Nikolai Andreev
Other mathematical activities
Participant in the 14-week workshop AI-assisted mathematical discovery run by Nebius Academy (2026).
Scientific editor of the “Weird Maths” popular mathematical book translation to Russian.
Organization of conferences and summer schools
September 5-6, 2018
International conference “Topology and physics” dedicated to the 80th birthday of S.P. Novikov.
May 24-30, 2018
International conference “Algebraic Topology, Combinatorics and Mathematical Physics” on occasion of V.M. Buchstaber’s 75th birthday.
2017 - 2021
Summer schools “Contemporary mathematics” (Dubna, Russia).
Community activity
2023
U of T Department of Mathematics EDI committee member
2023 --
CAT member at the CUPE3902
2023 --
MGSA postdoc representative
Other skills
Programming
- Programming languages: Python, Sage, GAP, C++
- Typesetting and web languages: LaTeX, HTML, CSS, JavaScript
Languages
- English (proficient)
- French (native speaker)
- Russian (native speaker)
In my free time…
- Culture: reading (both fiction and non-fiction), art (modern and classical), music (mainly classical or modern classical), violin, piano, educational YouTube content
- Sports: skiing, bouldering, calisthenics, alpine hiking
- Sciences: neuropsychology, cryptography, biology
- Games: chess, PC games (RPG, strategies, sandbox or various indie titles)
- Just learning bits of what I find interesting