In this talk, we will first discuss the motivations for motivic classes coming from point counting over finite fields. Then we will give the definitions of the motivic classes of varieties, in particular we explain that an extra relation is needed in finite characteristic. We will introduce symmetric powers and motivic zeta functions that are universal versions of local zeta functions.
The most skilled mathematicians in the world must also be effective communicators. In the first three years of my Ph.D., I gave seven math talks, all with undergraduate math students in mind. In this talk, I will discuss the benefits of giving undergrad-friendly talks, both for your progress as a Ph.D. student and for preparing to apply to academic jobs. I will offer some advice on topic selection, and then I will share some key principles to keep in mind when making undergraduate-friendly talks, using my own past talks as examples.
Abstract: Modern probability theory is founded upon measure theory. We will show how to take advantage of this framework to rigorously model stochastic processes such as coin flipping and random walks. For such models, what questions can we answer, and what applications are there? Aside from one recent research application, this will primarily be an expository talk, not a research talk. Similar content can be found in the book Probability with Martingales by David Williams.