The IBS Discrete Mathematics Group welcomes Dr. Semin Yoo (유세민), a new research fellow at the IBS Discrete Mathematics Group, from April 1, 2024. She received her Ph.D. from the University of Rochester under the supervision of Prof. Jonathan Pakianathan. She is interested in combinatorics, discrete geometry, and number theory in finite fields.

## Semin Yoo (유세민), TBA

## Semin Yoo (유세민) gave a talk on an analogue of q-binomial coefficients at the Discrete Math Seminar

On July 20, 2021, Semin Yoo (유세민) from the University of Rochester gave a talk on an analogue of q-binomial coefficients, counting subspaces having the Euclidean quadratic form, and its applications at the Discrete Math Seminar. She will move to KIAS next month as a postdoc. The title of her talk was “Combinatorics of Euclidean spaces over finite fields“.

## Semin Yoo (유세민), Combinatorics of Euclidean spaces over finite fields

$q$-analogues of quantities in mathematics involve perturbations of classical quantities using the parameter $q$, and revert to the original quantities when $q$ goes $1$. An important example is the $q$-analogues of binomial coefficients, denoted by $\binom{n}{k}_{q}$, which give the number of $k$-dimensional subspaces in $\mathbb{F}_{q}^{n}$. When $q$ goes to $1$, this reverts to the binomial coefficients which measure the number of $k$-sets in $\left [ n \right ]$.

In this talk, we add one more structure in $\mathbb{F}_{q}^{n}$, which is the Euclidean quadratic form: $\text{dot}_{n}:=x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}$. It turns out that the number of quadratic subspaces of Euclidean type in $(\mathbb{F}_{q}^{n},\text{dot}_{n})$ can be described as the form of the analogue of binomial coefficients. The main goal of this talk is to define the *dot-analogues* of the binomial coefficients and to study related combinatorics. No prior knowledge about the theory of quadratic form is required.