Mathematical and computational modeling have become an indispensible component of research across the sciences. Nevertheless, there are still many examples of research across the sciences where decision making processes are strongly influenced by empirical approaches rather than theory. One of the primary challenges in developing rigorous models of complex processes is capturing the nonlinear interactions of processes across multiple scales in space and time. At the same time, because such models may contain many parameters and can describe wide ranges of behaviors, new methods for parameter estimation and inference are needed as well. In this talk, I will give several examples of new multiscale models and novel applications of parameter inference methodologies in applications ranging from tumor biology to engineering. I will discuss some open problems where there are significant opportunities for future research.
Algebraic topology was invented by Poincare in 1895 to study the behavior of algebraic functions. In his seminal ICM address 5 years later, Hilbert posed a fundamental challenge to the field: find a topological obstruction to reducing the solution of the general degree 7 polynomial to an expression in functions of two or fewer variables. In this talk, I'll review some of the beautiful history of algebraic topology and algebraic functions, discuss Hilbert's problem(s), and outline ongoing work in applying the topology of braids and algebraic functions to this problem. This is joint work with Benson Farb.
Probability theorey is now being inspired and transformed by challenges of big data. This decade is marked by a fascinating convergence of mathematics, statistics, computer science and electrical engineering. I will describe some data-driven advances in high-dimensional probability and high-dimensional inference.
The last seminar of fall quarter will have Neil Donaldson bracing us for the common final exams, and then we'll discuss what worked and didn't work in our teaching this quarter.
When different issues come up in teaching, there are many different people who can potentially help... we'll play a game related to deciding whom to ask for assistance in different circumstances (as well as when something can probably be handled on your own).
How should you read your TA evaluations? How do I read them? I'd like to talk about this and I'd also like to review the first half of the seminar, talking about questions like "What was the main point of the Week ? meeting?".
In this workshop we will discuss techniques to facilitate group work, and make discussion sessions more active. We will also introduce tasks aimed at actively involve students in various phases of the learning process (e.g., introduce/explore/review a topic, learn the steps to solve a particular problem or the lay out of a proof).
