Thursday September 06, 2018 4:00 PM  5:00 PM Math Tower P131
 Mark Pollicott, University of Warwick
Dimensions of Cantor sets and Diophantine approximationThere are two recent cases where a specific knowledge of the dimension of certain Cantor set in the unit interval has had applications to problems in the Diophantine approximation. The first is on estimates by Matheus and Moriera on the size of the difference between the Lagrange and Markoff spectra, and the second is on the work of BourgainKontorovich and Huang on the Zaremba conjecture. We will talk about these problems and, in particular, about the progress that has been made in estimating the dimension of such dynamically defined Cantor sets.

Thursday September 13, 2018 4:00 PM  5:00 PM Math Tower P131

No Colloquium

Thursday September 20, 2018 4:00 PM  5:00 PM Math Tower P131
 Pace Nielsen, Brigham Young University
Why Euclidean domains are both easier and harder than you thinkWe give a gentle introduction to the proof that there is a Euclidean domain with no multiplicative norm.

Thursday September 27, 2018 4:00 PM  5:00 PM Math Tower P131
 Boris Bukh, Carnegie Mellon
Bipartite Turan problem
What is the largest graph not containing a copy of a fixed graph H? This question of Turan from 1941 remains open. The most challenging case is when H is bipartite. This case leads to interesting graph embedding problems on one hand, and mysterious algebrogeometric constructions on the other. In the talk, I will discuss the key problems and recent progress in the area.

Friday September 28, 2018 4:00 PM  5:00 PM SCGP 102
 Federico Rodriguez Hertz, Penn State University
On the geometry of invariant measuresIn this talk I will try to explain that, in dynamical systems with some hyperbolicity, some invariant measures present a very nice geometric structure. I also will explain how this geometric structures can be used to recover certain rigidity of the system in study. The goal is to show this approach through examples, so I plan to spend some time describing these examples, their relevant measures and geometry.

Thursday October 04, 2018 4:00 PM  5:00 PM Math Tower P131
 Kevin Ford, Univ. of Illinois at UrbanaChampaign
Probabilistic aspects of number theoryWe describe how probabilistic tools and reasoning are used to study problems about gaps
between prime numbers in various sequences, for example the sequence of all primes, and the sequence of prime values of a polynomial. This is joint work with Ben Green, Sergei Konyagin, James Maynard, Carl Pomerance and Terence Tao.

Thursday October 11, 2018 4:00 PM  5:00 PM Math Tower P131
 Lenny Ng, Duke
TBATBA

Thursday October 18, 2018 4:00 PM  5:00 PM Math Tower P131
 Ailana Fraser, UBC
TBATBA

Thursday October 25, 2018 4:00 PM  5:00 PM SCGP 102
 Nigel Hitchin, University of Oxford
TBAThis is a joint lecture with the SCGP Workshop Geometrical Aspects of Supersymmetry.

Thursday November 29, 2018 4:00 PM  5:00 PM Math Tower P131
 Bhargav Bhatt, University of Michigan
TBATBA

