All lectures to be held in Frances Searle Building Room 1-441. Click here for a campus map.
Please be aware that because of construction on campus some paths to the Frances Searle Building may be closed. Please give yourself an extra time to find the building on Monday morning.
Registration and coffee starts at 8.30am on Monday, July 24, in Frances Searle Building Room 1-441.
| Monday, July 24 | Tuesday, July 25 | Wednesday, July 26 | Thursday, July 27 | Friday, July 28 | |
| 9.00am - 10.30am | Weinkove | Peterson | Peterson | Binder | Weinkove |
| 11.00am - 12.00pm | Problem Session Weinkove | Problem Session Binder | Problem Session Binder | Problem Session Peterson | Problem Session Weinkove |
| 2.00pm - 3.30pm | Binder | Binder | Free afternoon | Weinkove | Peterson |
| 4.00pm - 5.00pm | Special Lecture DeMarco | Problem Session Peterson | Free afternoon | Problem Session Weinkove | Problem Session Peterson |
Monday July 24, 5.15pm there will be Pizza in the Mathematics Department Common Room, 2nd floor Lunt Hall
Ilia Binder (Toronto). Title: Cantor sets and dimension
Abstract: In the mini-course, we will introduce the various ways to define the dimension of fractal sets. After discussing the strengths and weaknesses of each of these definitions, we will examine a number of methods for computing these dimensions and apply them to Cantor-like sets. In particular, we will investigate the dimensional properties of dynamically defined and random Cantor sets. We will also talk about the connections with the Potential Theory. No background in Potential Theory or Dimension Theory is assumed; I will introduce all the relevant definitions, notations, and theorems.
Aaron Peterson (Northwestern). Title: Differentiating the non-differentiable
Abstract: Students of analysis are sometimes frustrated that routine computations involving functions are limited by the regularity of the functions involved. For example, not all functions on the real line are continuous, and fewer are differentiable. It even seems that the very notion of function is too restrictive: the so-called 'Dirac Delta Function' δ0 from physics, defined by δ0(x)=0 for all x≠0 and ∫R δ0(x) dx = 1, is designed to model impulses and is extraordinarily useful in (for example) the study of differential equations. However, no function possesses the defining properties of δ0! This mini-course will explore a generalized notion of function that removes these sticky problems, allowing us to treat δ0 as a generalized function and to differentiate non-differentiable functions as many times as we'd like.
Ben Weinkove (Northwestern). Title: Laplace's equation and conformal maps
Abstract: Conformal maps are functions, defined on domains in the complex plane, which preserve angles. They have the property of transforming harmonic maps (solutions of Laplace's equation) to harmonic maps and so can be used to solve Laplace's equation on domains in the complex plane. The same techniques can be applied to solve problems in fluid dynamics. In this mini-course we will discuss these ideas and more, with an emphasis on problem solving and explicit examples. I will assume some familiarity with complex numbers and partial derivatives, but no other background is necessary.
Special Lecture: Laura DeMarco (Northwestern). Title: The Mandelbrot set: What we know today
Abstract: The Mandelbrot set is one of the most famous objects in modern mathematics. We see images of it everywhere, but despite its popularity and decades of research, we still don't fully understand it. I will survey results about the Mandelbrot set, from its discovery to today.