Midwest Dynamics Meeting at Ohio State: Oct 30th-Nov 1st 2015

The 2015 Midwest Dynamics Meetings will take place October 30th-November 1st at the Ohio State University.  The  list of speakers is:
Keith Burns (Northwestern)
Jon Chaika (Utah)
Jana Rodriguez Hertz (IMERL, Uruguay)
Yakov Pesin (Penn State)
Charles Pugh (UC Berkeley)
Don Saari (UC Irvine)
Anush Tserunyan (UIUC)
Zhiren Wang (Penn State)
Jeff Xia (Northwestern)
Jim Yorke (Maryland)
The plenary talk for the conference will be given by Yakov Pesin.
The saturday p.m. session and the conference dinner are dedicated to Carl Simon (Michigan) in honor of his 70th birthday.
There will also be a poster session, for which we invite the contribution of all interested participants.
The conference is supported by the NSF, and the Ohio State University MRI. There are funds available for participant support, which will be allocated in keeping with NSF guideline – students, recent PhDs, underrepresented groups, and people with no other federal support get priority. Registration, and information on lodging, etc, will be made available on the conference website u.osu.edu/mwds2015.
For more information, please contact the local organizer, Dan Thompson, at thompson@math.osu.edu.

Seminar 4.9.15

Title: A discrete to continuous framework for projection theorems

Speaker: Daniel Glasscock

Abstract: Projection theorems for planar sets take the following form: the image of a “large” set A2 under “most” orthogonal projections πθ (to the line through the origin corresponding to θS1) is “large”; the set of those directions for which this does not hold is “small.” The first such projection theorem was given by J. M. Marstrand in 1954: assuming the Hausdorff dimension of A is less than 1, the Hausdorff dimension of πθA is equal to that of A for Lebesgue-almost every θS1.

Recent progress has been made on some fundamental problems in geometric measure theory by discretizing and using tools from additive combinatorics.  In 2003, for example, J. Bourgain building on work of N. Katz and T. Tao, used this approach to prove that a Borel subring of  cannot have Hausdorff dimension strictly between 0 and 1 (a result shown independently by G. A. Edgar and C. Miller), answering a question of P. Erd\H{o}s and B. Volkmann. The goal of my talk is to explain a discrete approach to continuous projection theorems.  I will show, for example, how Marstrand’s original theorem and a recent result of Bourgain and D. Oberlin can be obtained combinatorially through their discrete analogues. This discrete to continuous framework connects finitary combinatorial techniques to continuous ones and hints at further parallels between the two regimes.

Seminar 3.31.15 Sharp

Title: Noncommutative geometry and measures on dynamical systems

Speaker: Richard Sharp (University of Warwick)

Abstract: Noncommutative geometry aims to describe a wide range of mathematical objects in terms of C^*-algebras, in particular through the notion of a spectral triple. We will discuss how to recover important classes of invariant measures for certain dynamical systems on Cantor sets.