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amp;gt;amp;gt; Yes. So, thanks for the invitation. Yes, so Iamp;#39;ll be talking about cutoff for product replacement on finite groups. The content of this talk is based on joint work with Youamp;#39;ve all pairs and Real Kitschy Tanaka. All right, so let me start by explaining what the product replacement work is. So, let G be a finite group, and weamp;#39;re going to consider n-tuples of group elements, weamp;#39;ll call that a configuration. For purposes of this example, letamp;#39;s suppose that our group is Z mod 11 and n is six. So, here I have six elements of Z mod 11. So, the product of replacement step is the following; we randomly pick two of the elements out of these six, call them a and b, and we simply modify the a to become a plus b or a minus b. So, this is for an additive group Z mod 11, in general, if itamp;#39;s non-abelian, it would be a times b or a times b inverse. Okay, so letamp;#39;s just do a quick example. So, letamp;#39;s say my a is the one and my
