Karthik Ganapathy

I am a postdoc in the Department of Mathematics at the University of California, San Diego.

My research interests lie in algebra. I was Andrew Snowden's PhD student at the University of Michigan, earned my undergraduate degree from the Chennai Mathematical Institute, and grew up in Kochi, Kerala.

Some activities I am or was part of:

Algebra Seminar at San Diego (2024-present);
the Leiden Declaration on Artificial Intelligence and Mathematics (2025-present).
Special Session on Tensor Categories at the 2026 Joint Mathematics Meetings; and
the Michigan Stability Seminar 2023-24.

Research

GL-algebras in positive characteristic III: The divided power algebra. (Email to request preliminary draft.)
arXiv:2506.15134. Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic. Submitted version.
arXiv:2502.16675. Noncommutative invariants of finite and classical groups. To appear in Algebra Number Theory (Final version).
arXiv:2408.04630. Non-noetherian GL-algebras in characteristic two. Submitted version.
arXiv:2407.16071. Resolutions of symmetric monomial ideals via stratifications of derived categories. Submitted version.
arXiv:2407.13604. GL-algebras in positive characteristic II: The polynomial ring. Proc. Lond. Math. Soc. (3) 131 (2025), no. 6, Paper No. e70112, 39pp
arXiv:2203.03693. GL-algebras in positive characteristic I: The exterior algebra. Selecta Math. (N.S.) 30 (2024), no. 4, Paper No. 63, 33 pp.
arXiv:2007.03038. Stillman's question for twisted commutative algebras. J. Commut. Algebra, 14 (2022), no. 3, 315-318.

My thesis submitted to the University of Michigan is available here.

Recently, I have been thinking, at varying levels of depth, about Weyl's polarization theorem in positive characteristic, Sam--Snowden's noetherianity problem for twisted commutative algebras, ranks and stabilizers of tensors in infinite-dimensions, and the strong Lannes--Schwartz artinian conjecture.

Teaching

At San Diego:

Winter 2027: Math 187A Introduction to Cryptography, Section A and B
Fall 2026: Math 105 Basic Number Theory; Math 187A Introduction to Cryptography
Winter 2026: Math 109 Mathematical Reasoning, Section C; Math 187A Introduction to Cryptography
Fall 2025: Math 105 Basic Number Theory; Math 187A Introduction to Cryptography
Winter 2025: Math 109 Mathematical Reasoning, Sections A and B
Fall 2024: Math 18 Linear Algebra, Sections B and C

At Michigan:

Winter 2024: Math 216 Differential Equations, Lab Instructor for Sections 011-014
Fall 2022: Math 115 Calculus 1, Section 025
Fall 2021: Math 105 Precalculus, Section 024
Winter 2020: Math 115 Calculus 1, Section 003
Fall 2019: Math 115 Calculus 1, Section 001
Winter 2019: Supervisory position in MathLab
Fall 2018: Math 105 Precalculus, Section 004

Mentoring and Supervision

Directed research at San Diego:

Sanay Sehgal (Columbia) on Non-noetherian GL-algebras in positive characteristic (Summer 2026)
Henry Gustafson (Caltech) on Measures on Fraïssé classes (Spring 2026)

Through the Laboratory of Geometry at Michigan:

Atharva Kulkarni, Arnav Shah, Tony Zhang on Statistics of the character table of symmetric groups with Prof. Sarah Peluse (Winter 2024)
Jenna Elwing, Theresa Liu, Xiaotong Xu on Citation Networks with Samuel Hansen (Fall 2022)

Through the Directed Reading Program at Michigan:

Tony Zhang on Representation theory of symmetric groups (Summer 2024)
Ramon Diego-Guerra on Representation theory of finite groups (Fall 2023)
Jonah Weinbaum on Fundamental groups and covering spaces (Summer 2020)

Talks

Recordings of some talks: Noncommutative invariants of finite groups (SLMath, Dec 2025); Syzygies of symmetric monomial ideals (UNL URiCA conference, May 2025); Commutative algebra with strict polynomial functors (virtual Tensor categories seminar, Apr 2025); Non-noetherian GL-algebras in characteristic two (UGA Algebra seminar, Sep 2024);

May 2026: Algebra Seminar at University of California, Los Angeles.
Sep 2025: Algebra Seminar at Universität Bern.
May 2025: URiCA 2025 at University of Nebraska–Lincoln.
Apr 2025: Tensor Categories Seminar virtual.
Apr 2025: Geometry Seminar at Texas A&M University.
Mar 2025: Algebra Seminar at University of California, San Diego.
Oct 2024: Postdoc Seminar at University of California, San Diego.
Sep 2024: Combinatorics Seminar at University of Michigan, Ann Arbor.
Sep 2024: Commutative Algebra Seminar at University of Michigan, Ann Arbor.
Sep 2024: Algebra Seminar at University of Georgia.
May 2024: Special Session on Homological methods in Commutative Algebra & Algebraic Geometry at AMS Spring Western Sectional Meeting.
Jan 2024: Special Session on Group Actions in Commutative Algebra at Joint Mathematics Meeting.
Jan 2024: Special Session on Commutative Algebra and Algebraic Geometry (associated with Invited Address by Daniel Erman) at JMM.
Nov 2023: Algebraic Geometry/Commutative Algebra Seminar at University of Notre Dame.
Nov 2023: Algebra Days at Arizona State University.
Oct 2023: Algebra Seminar at University of Oregon.
Oct 2023: Representation Theory and Tensor Categories Seminar at University of California, Berkeley.
Oct 2023: Algebraic Geometry Seminar at University of California, San Diego.
Oct 2023: Commutative Algebra Seminar at University of Michigan, Ann Arbor.
Sep 2023: Algebra Seminar at University of Georgia. (Link to recording.)
Jul 2023: Stability in Topology, Arithmetic, and Representation Theory at Purdue University.
Sep 2022: Algebra and Representation Theory seminar at University of Oklahoma.
Aug 2022: MAGGC 2022 at University of Illinois Chicago.
Jun 2022: WARTHOG 2022 Infinite-dimensional methods in commutative algebra at University of Oregon.
May 2022: GradMoCCa at University of Minnesota.
Apr 2021: Special Session on Commutative Algebra at AMS Spring Central Sectional Meeting.

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Research

Teaching

Mentoring and Supervision

Talks

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