**Elon Lindenstrauss, Hebrew University of Jerusalem, Israel**

**Title : Joining of higher rank homogenous actions,**

**Victoria Sadovskaya, Pennsylvania State University, USA**

**Tushar Das, University of Wisconsin-La Crosse, USA**

We establish a new connection between metric Diophantine approximation

and the parametric geometry of numbers by proving a variational

principle facilitating the dimension computation of a number of sets

of interest in the theory of numbers. I will present certain

applications of our theorems that include computing the Hausdorff and

packing dimensions of the set of points witnessing a conjecture of

Starkov (2000), and of the set of points witnessing a conjecture of

Schmidt (1983). This is ongoing joint work with Lior Fishman

(NorthTexas), David Simmons (York) and Mariusz Urbanski (North Texas).

**Michael Lin, Ben Gourion University, Israel**

**Olena Karpel, Institute for Low Temperature Physics, Ukraine / Institute of Mathematics, Poland**

**Daniel Mansfield, UNSW, Australia**

Title: The Hausdorff dimension of a G-measure

Abstract: The Hausdorff dimension for a measure is a standard notion of dimension for probability measures. This talk shows that there is a simple connection between the Hausdorff dimension of a measure and its G-measure representation. Both concepts will be introduced, and the theory will be applied to the problem of finding the Hausdorff dimension for a variety of ergodic measures.

**Joe Rosenblatt, Indiana University-Purdue University Indianapolis, USA**

**Anton Solomko, University of Bristol, UK**

Title : On rank and isomorphism of von Neumann special flows

A von Neumann flow is a special flow over an irrational rotation of the circle and under a piecewise smooth roof function with a non-zero sum of jumps. Such flows appear naturally as special representations of Hamiltonian flows on the torus with critical points. We consider the class of von Neumann flows with one discontinuity. I will show that any such flow has infinite rank and that the absolute value of the jump of the roof function is a measure theoretic invariant. The main ingredient in the proofs is a Ranter type property of parabolic divergence of orbits of two nearby points in the flow direction.

Joint work with Adam Kanigowski.

**Mrinal Roychowdhury,University of Texas Rio Grande Valley, USA**

**Title: An overview of optimal quantization**

Abstract: The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixed distributions are an exciting new area for optimal quantization. Recently, in the paper “An overview of the quantization for mixed distributions”, available in arXiv, I have determined the optimal sets of $n$-means, the $n$th quantization error, and the quantization dimensions of different mixed distributions. Besides, I have discussed whether the quantization coefficients for the mixed distributions exist. The results in this paper will give a motivation and insight into more general problems in quantization of mixed distributions.

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**Sebastian Donoso, University of O’higgins, Chile. **

**Francesco Cellarosi, Queen’s University, Canada**

Title: The dynamical construction of an automorphic function

Abstract:I will present the construction of an automorphic function on the Jacobi group G (the Lie group consisting of the semidirect product of SL(2,R) and the Heisenberg group). This function generalizes Jacobi theta function. The function is invariant under the action of a lattice in G and thus well defined in the quotient, but a priori only as a square-integrable function.

We are able to show that the function is actually defined pointwise along the whole orbit of almost every point, under the geodesic flow. The construction uses dynamical ideals of renormalization, ergodicity of the geodesic flow, equidistribution of horocycle lifts, and a partition of unity suitably “adapted” to the flow. Joint work with Jens Marklof.