**Title:** Arithmetic Combinatorics in Function Fields

**Speaker:** Le Thai Hoang

**Speaker Info:** UCLA

**Brief Description:**

**Special Note**:

**Abstract:**

Analogies between the integers and the ring F_q[t] have been long known. However, from an arithmetic combinatorics perspective, these analogies have been little and only recently explored. As it turns out, in many cases existing methods can be transfered directly to F_q[t], while at times extra difficulties will arise. In this talk, I will discuss about analogs of some well-known results in this setting, including:-Green-Tao theorem for F_q[t]: The irreducible polynomials in F_q[t] contain affine spaces of arbitrarily high dimension.

-Sarkozy's theorem for F_q[t]: In any subset of positive density in F_q[t], we can find polynomials f, g such that f-g = h^2 for some nonzero polynomial h in F_q[t].

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