##### Department of Mathematics,

University of California San Diego

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### Department Colloquium

## Wendy Cheng

## Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials

##### Abstract:

Let $f_1,\ldots, f_r \in k[x_1,\ldots, x_n]$ be homogeneous polynomial of degree $d$. Ananyan and

Hochster (2016) proved that there exists a bound $N = N(r, d)$ where if collective strength

of $f_1, \ldots, f_r \geq N$, then $f_1, \ldots, f_r$ are regular sequence. In this paper, we study the explicit

bound $N(r, d)$ when $r = 3$ and $d = 2, 3$ and show that $N(3, 2) = 2$ and $N(3; 3) > 2$.

Lei Ni

### April 20, 2023

### 4:00 PM

APM 6402

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