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## Niranjan Balachandran

 Description: Title: A function field analogue of a theorem of Sarkozy, due to B Green. Speaker: Niranjan Balachandran Date-Time: Wednesday, February 28 2018, 2 PM to 3.30 PM Venue: Ramanujan Hall Abstract: In the late 70s Sarkozy proved the following theorem: Given a polynomial f(T) over the integers with f(0)=0, there exists a constant c_f such that for any set $A\subset [n]$ of size at least $n/(log n)^{c_f}$ there exist distinct $a,b\in A$ such that $a-b=f(x)$ for some $x$. In 2016, Ben Green proved a function field analog of the same result but with a much better bound for $|A|$: Given a polynomial $F\in\bF_q[T]$ of degree $k$ with $F(0)=0$, there exists $0 q^{(1-c)n}$ there exist $\alpha(T)\neq\beta(T)$ in $A$ such that $\alpha(T)-\beta(T)=F(\gamma(T))$ for some $\gamma(T)\in\bF_q[T]$. We will see a proof of this result. Location: Ramanujan Hall, Department of Mathematics Date: Wednesday, February 28, 2018 Time: 2:00pm-3:30pm IST Duration: 1 hour 30 minutes Access: Public