https://osu.zoom.us/j/94184103646?pwd=TkRPVFQrYkNuQzRFTk9LSmtSYVR6dz09

*passcode is*: 772704

https://osu.zoom.us/j/94184103646?pwd=TkRPVFQrYkNuQzRFTk9LSmtSYVR6dz09

*passcode is*: 772704

MIDWEST DYNAMICS MEETING 2015: SCHEDULE AVAILABLE AT go.osu.edu/mwdsschedule.

The 2015 Midwest Dynamics Meetings will take place October 30th-November 1st at the Ohio State University. The list of speakers is:

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.

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 A⊆ℝ2 under “most” orthogonal projections πθ (to the line through the origin corresponding to θ∈S1) 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 θ∈S1.

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 ℝ 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.

Speaker: Sergey Bezuglyi (University of Iowa & Institute for Low Temperature Physics, Ukraine)

Title: Homeomorphic measures on Cantor sets and dimension groups

Abstract: Two measures, m and m’ on a topological space X are called homeomorphic if there is a homeomorphism f of X such that m(f(A)) = m'(A) for any Borel set A. The question when two Borel probability non-atomic measures are homeomorphic has a long history beginning with the work of Oxtoby and Ulam: they found a criterion when a probability Borel measure on the n-dimensional cube [0, 1]^n is homeomorphic to the Lebesgue measure. The situation is more interesting for measures on a Cantor set. There is no complete characterization of homeomorphic measures. But, for the class of the so called good measures (introduced by E. Akin), the answer is simple: two good measures are homeomorphic if and only if the sets of their values on clopen sets are the same.

In my talk I will focus on the study of probability measures invariant with respect to a minimal (or aperiodic) homeomorphism. These measures are in one-to-one correspondence with traces on the corresponding dimension group. The technique of dimension groups allows us to apply new methods for studying good traces. A good trace is characterized by its kernel having dense image in the annihilating set of affine functions on the trace space. A number of examples with seemingly paradoxical properties is considered.

The talk will be based on joint papers with D. Handelman and with O. Karpel.

The Midwest Dynamical Systems meeting 2015 will take place at OSU from 30th October to 1st November 2015.

The MWDS meeting has been held annually for over 40 years, and rotates around various universities in the Midwest and beyond. This will be the first time that MWDS has come to Ohio State. An archive of past MWDS conferences can be found at http://www.math.northwestern.edu/mwds/.

Details will be announced soon!

Speaker: Ilya Vinogradov (Bristol, UK)

Title: Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1

Abstract: Let G=SL(2,\R)\ltimes R^2 and Gamma=SL(2,Z)\ltimes Z^2. Building on recent work of Strombergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Gamma\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of sqrt n mod 1.

Title: Convergence of ergodic averages and structure in subsequences

Speaker: Andy Parrish, Saint Louis University

Our Spring/Summer seminar schedule looked like this:

Feb 13: Donald Robertson (OSU)

Feb 27: Andy Parrish (Saint Louis University)

Mar 6: Marc Carnovale (OSU)

Mar 13: **Colloquium talk**: Todd Fisher (Brigham Young)

Mar 20 Dima Burago (Penn State)

April 3: **Colloquium talk**: Alex Eskin (University of Chicago)

April 17: Daniel Glasscock (OSU)

May 14: Sebastian Van Strien (Imperial, UK)

May 29: Younghwan Son (Weizmann Institute)

June 25: Terry Adams (US DoD)

Titles and abstracts will be posted here another day!

All of a sudden we have a rather healthy seminar schedule for February and March. Here’s a preview of the schedule.

Feb 13: Donald Robertson (OSU)

Feb 20:

Feb 27: Andy Parrish (Saint Louis University)

Mar 6: Marc Carnovale (OSU)

Mar 13: **Colloquium talk**: Todd Fisher (Brigham Young)

Mar 20 Dima Burago (Penn State)

Mar 27 Daniel Glasscock (OSU)

Titles and abstracts will be posted here another day!

This is the new website for ergodic theory at Ohio State. It is under construction.

Our final two seminars for the Fall 2013 semester are:

14th November: Joe Rosenblatt (UIUC)

21st November: Ronnie Pavlov (Denver)

Feb 28 2013 – 3:00pm – 4:00 pm

MW154

Manfred Denker (The Pennsylvania State University)

Let T be a measure preserving transformation on a probability space. I will present three theorems on the almost sure and weak convergence of sums of the form

∑0≤ik<n,k=1,…,dh(Ti1,…,h(Tid).

The difficulty here arises from the fact that the summands are not well defined as random variables on the probability space. Therefore I will explain how to describe reasonable subspaces of L2 where these variables can be defined a.s.

As a result I will state new ergodic theorems and new central limit theorems obtained from a suitable martingale approximation in the sense of Gordin’s 1968 paper.

Sep 26 2013 – 3:00pm – 4:00 pm

MW154

Daniel J Thompson (The Ohio State University)

For a broad class of symbolic dynamical systems without the Markov property, including the coding spaces of many piecewise continuous interval maps, we show how to approximate an arbitrary ergodic measure with a measure of almost the same entropy supported on a sofic subshift. This is interpreted as a symbolic analogue of a `hyperbolic horseshoe’ theorem. In addition to the intrinsic interest of this result as a structure theorem, it can be a useful tool in large deviations theory and multifractal analysis. I will discuss two ways to establish this result, both based on surgery on a single generic orbit. One proof is based on Ornstein’s d bar metric, and the other is based on the theory of Kolmogorov complexity. Both techniques can be explained in a simple and intuitive way.

Oct 10 2013 – 3:00pm – 4:00 pm

MW154

Tamara Kucherenko (CUNY)

We introduce the notion of localized topological pressure for continuous maps on compact metric spaces and establish a local version of the variational principle for several classes of dynamical systems and potentials. We also construct examples showing that the assumptions in the localized variational principle are fairly sharp. Next, we study localized equilibrium states and show that even in the case of subshifts of finite type and Holder continuous potentials, there are several new phenomena that do not occur in the theory of classical equilibrium states. In particular, ergodic localized equilibrium states for Holder continuous potentials are in general not unique. (joint work with C.Wolf)

This is a new website for the ergodic theory group at the Ohio State University. It is under construction.