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Posted September 28, 2026
Last modified October 22, 2026

Algebra and Number Theory Seminar Questions or comments?

Yifeng Huang, Emory University
Rogers--Ramanujan identities from singular curves

The first Rogers—Ramanujan identity $$\sum_{n\ge 0} \frac{q^{n^2}}{(1-q)(1-q^2)\cdots (1-q^n)}=\prod_{i\ge 1, i\equiv 1,4\pmod 5} (1-q^i)^{-1}$$ is an ``infinite sum=infinite product'' identity. Combinatorially, it means that partitions of $n$ with gaps between adjacent parts at least two are as many as partitions of $n$ whose parts are congruent to 1 or 4 modulo 5. Much less known is that the identity also counts zero-dimensional sheaves on the cuspidal curve $X^2=Y^3$, obtained in an earlier work with Jiang. In recent joint works with Jiang and Oblomkov and with Lau and Ono, we show that this phenomenon extends to any coprime $a,b$, resulting in infinitely many new Rogers—Ramanujan identities. It uses a wide range of ingredients, from Quot scheme of points, quiver representations, and poset flag varieties used in the geometric computation, to cylindric partitions, symmetric functions, and compositional rational shuffle theorem used in the proof of the new identities

Posted August 22, 2026

Algebra and Number Theory Seminar Questions or comments?

Isabella Negrini, University of Toronto
TBA

Event contact: Gene Kopp

Posted September 20, 2026

Algebra and Number Theory Seminar Questions or comments?

Ngoc Trinh Le, Tulane University
TBA

Event contact: Gene Kopp

Posted September 20, 2026
Last modified October 20, 2026

Algebra and Number Theory Seminar Questions or comments?

Murtadha Aljanabi, LSU
TBA