Vanny is a research fellow at IIT Kharagpur and is working on rational equivariant stable homotopy theory under the guidance of Prof. Samik Basu at ISI Kolkata. Apart from this, he is also a member of the Mathematical Association of Cambodia (MAC), where he has taught and helped many Cambodian students to pursue their higher studies abroad in various areas of both pure and applied mathematics.
Reach me @ vanny.doem@kgpian.iitkgp.ac.in / vanny.doem@gmail.com
RESEARCH
Research interest includes algebraic topology, homotopy theory and higher algebra.
Algebraic models for rational equivariant cohomology theories: A survey article. In preparation
Rational equivariant stable homotopy groups for torus actions. In preparation
Rational stable homotopy type of equivariant projective spaces and Grassmannians (with S. Basu & C. Nahak). Preprint arXiv, 2026
Coloring discrete pseudomanifolds (with B. Basak & C. Nahak). Electron. J. Graph Theory Appl. (EJGTA), V.14, No.1, 2026
ACTIVITY
ORGANIZING PROGRAMS
Representation theory of finite groups. MAC's AiM School, Cambodia, Nov. 14 - 15, 2026
Homological algebra. MAC's AiM School, Cambodia, Oct. 11 - 12, 2025
Linear algebra, real analysis and topology. MAC's BiM School, Cambodia, Nov. 09 - 10, 2024
ISI topology seminars. Organized by our topology groups, semester-wise, 2023 - present
GIVING TALKS
The ring structure of RO(G)-graded stable homotopy groups of spheres for finite Abelian groups G. Young Topologists Meeting (YTM), Uni. of Copenhagen, Denmark, June 28 - July 03, 2026
Rational stable homotopy type of complex projective spaces. RUPP, Cambodia, Jan. 31, 2026
Kan extensions. MAC, Cambodia, March 31, 2024
Spectral sequences and Serre classes. MAC, Cambodia, March 31, 2023
Sphere coloring conjecture. MAC, Cambodia, Nov. 28, 2022
Coloring discrete pseudomanifolds. Geo. & Top. sectional workshop of the International Conference of Mathematicians (ICM), Uni. of Copenhagen, Denmark, July 06 - 14, 2022
From old to new computation and intuition of classification problems in topology. RUPP, Cambodia, Aug. 18, 2021
ATTENDING SCHOOLS / CONFERENCES
From Hochschild homology to topological Hochschild homology. ICTS, India, May 25 - June 05, 2026
Recent advances in stable homotopical computations. IIT Roorkee, India, Dec. 26 - 31, 2025
Bengal topology circle meeting. IISER Kolkata, India, Jan. 12, 2024
Holomorphic and topological methods in symplectic geometry. ISI Kolkata, India, June 03 - 08, 2024
Operads in topology. IIT Bombay, India, Nov. 29 - Dec. 04, 2024
Bengal topology circle meeting. CREST, India, Jan. 20, 2023
Dualities in topology and algebra. ICTS, Bangalore, India, May 15 - 26, 2023
Hochschild homology. IISER Kolkata, India, Dec. 04 - 16, 2023
Global homotopy theory. ATM School, IIT Bombay, India, Feb. 10 - 14, 2020
Scientific computational and environmental science. CMU-IWR, Chiang Mai Uni., Thailand, March 08 - 16, 2018
TEACHING
ITC - Institute of Technology of Cambodia
Duration: Feb-July 2021
Teaching: Calculus I & II, Linear Algebra, ODE
Duration: Jan-May 2021
Teaching: Differential Geometry
MAC - Mathematical Association of Cambodia
Teaching courses 2020 - present:
Infinity category theory (upcoming course in 2027)
Adams spectral sequence (Aug. - Dec. 2026) - Serre spectral sequence (Jan. - June 2026) - Basic homotopy theory (June - Dec. 2025) - Representation theory (Jan. - May 2025) - Linear algebra (Jan. - May 2024) - Category theory (Jan. - May 2024) - Homological algebra (June - Oct. 2024) - Abstract algebra (June - Nov. 2024) - General topology (Jan. - May 2023) - Ring, module, and field theory (May - July 2023) - Algebraic topology (Aug. - Dec. 2023) - Differential geometry (Jan. - April 2022) - Differential topology (May - Aug. 2022) - Graph theory (Sep. - Dec. 2022) - Calculus (Jan. - April 2021) - General topology (Jan. - April 2021) - Real analysis (June - Nov. 2021) - Abstract algebra (June - Nov. 2021) - Calculus I-II (Jan. - May 2020) - Real analysis (June - Nov. 2020)
Writing
Articles in Khmer: Abstract Mathematics - The Poincaré Conjecture and Grigori Perelman
