Sumun Iyer

I am an NSF postdoctoral associate at Carnegie Mellon University, mentored by Clinton Conley. Previously, I received my PhD in math in 2024 at Cornell University, under the supervision of Slawomir Solecki. 

My research is in topology, dynamics, and descriptive set theory. Specific interests include actions of homeomorphism groups, amenability-type properties, Ramsey theory, mapping class groups, connections with large scale geometry. 

Papers and preprints:

• [joint with T. Ghaswala, R. Lyman, and N. Vlamis] Mapping class groups have a unique Polish group structure, preprint [arxiv]

• Universal minimal flows of homeomorphism groups of continua, preprint [arxiv]

• Direct limits of large orbits and the Knaster continuum homeomorphism group, preprint [pdf]

• [joint with F. Shinko] Asymptotic dimension and hyperfiniteness of generic Cantor actions, accepted in Groups Geom. Dyn., [arxiv][journal (online first)]

• The homeomorphism group of the universal Knaster continuum. Israel J. Math. (2026) [arxiv][journal]

• [joint with P. Baird-Smith, D. Davis, and E. Fromm] Tiling billiards on triangle tilings, and interval exchange transformations. J. Lond. Math. Soc. (2024) [arxiv][journal]

• [joint with C. Defant] Domination and upper domination of direct-product graphs. Discrete Math. (2018) [arxiv][journal]

Research notes:

• A Ramsey-type phenomenon in two and three dimensional simplices, 2023, [arxiv]

Courses taught:

at CMU:

• Math 122- Integration and Approximation (Fall 2025, Fall 2026)

• Math 329- Set Theory (Spring 2026)

at Cornell:

• Calculus II (instructor, Spring 2021)

at Cayuga correctional facility through Cornell's Prison Education Program:

• Math 112- Thinking Mathematically (Fall 2022) 

Courses taught (as recitation TA):

at Cornell:

• Math 1106- Modeling with Calculus for the Life Sciences (Spring 2024)

• Math 3040- Prove it! (Fall 2023)

• Calculus I (Fall 2020)