**The International Center for Mathematical Sciences – Sofia (ICMS-Sofia)**

**presents**

## ICMS Seminar

10.09.2024, 14:00 Sofia time,

ICMS-Sofia, Room 403

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**Generalized integral points and strong approximation**

**Generalized integral points and strong approximation**

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Boaz Moerman

Utrecht University

Utrecht University

**Abstract:**

The Chinese remainder theorem states that given coprime integers p_1, …, p_n and integers a_1, …, a_n, we can always find an integer m such that m ~ a_i mod p_i for all i. Similarly given distinct numbers x_1,…, x_n and y_1, …, y_n we can find a polynomial f such that f(x_i)=y_i. These statements are two instances of strong approximation for the affine line (over the integers Z and the polynomials k[x] over a field k). In this talk we will consider when an analogue of this holds for special subsets of Z and k[x], such as squarefree integers or polynomials without simple roots, and different varieties. We give a precise description for which subsets this holds on a toric variety.