Organisers:
Dzmitry Badziahin (University of Sydney),
Shreyasi Datta (Indian Statistical Institute, Bangalore)
Alexander Fish (University of Sydney),
Mumtaz Hussain (La Trobe University)

Program Description:

This workshop will explore the advanced-level interconnected research problems in Ergodic Theory and Analytical Number Theory, focusing on Diophantine Approximation and Geometric Measure Theory. This activity will provide opportunities to discuss␣cutting-edge and mainstream research problems connecting both of these topics with the experts of the field. The focus will be on exploring various methods and techniques that could make progress in some of the␣long-standing open problems such as the Littlewood Conjecture (1930), Furstenberg x2, x3 conjecture (1967), Duffin-Schaeffer Conjecture on manifolds, Generalised Baker-Schmidt Problem (1970) to name a few.

Program Structure:

Talk title:
Technau: Fine-scale statistics of monomials modulo one
Badziahin: Well approximable points on manifolds
Srivastava: Counting Rational Points Near Space Curves
Fish: Quantitative Directional Expansivity and Monochromatic Geometric Patterns
Shulga: Minkowski’s conjecture on Critical Lattices
Li: Some problems related to times 2 and times 3
Gorodnik: Fully inhomogeneous version of the de-Mathan-Teulie problem
Schleischitz: Disproof of the uniform Littlewood conjecture
de Saxce: Distribution of rational points in flag varieties
Hauke-Treuer: Multiplicative Diophantine approximation: Littlewood, Cassels and friends
Datta: Counting rational point near manifolds
Aggarwal: Fine-scale statistics for Q^n
Marshall: Quantum ergodicity for sequences of locally symmetric spaces

Participant List:
Rajula Srivastava (University of Wisconsin Madison)
Mumtaz Hussain (La Trobe University)
Gaurav Aggarwal (Institute of Mathematics, University of Zurich, Switzerland)
Dzmitry Badziahin (School of Maths and Stats, the University of Sydney)
Caroline Wormell (School of Mathematics and Statistics, The University of Sydney)
Michael Björklund (Chalmers University, Gothenburg)
Shreyasi Datta (Indian Statistical Institute)
Johannes Schleischitz (METU NCC)
Bing Li (South China University of Technology)
Polina Vytnova (University of Surrey)
Alexander Fish (University of Sydney)
Manuel Hauke (TU Graz)
Nicolas DE SAXCE (CNRS – Université Sorbonne Paris Nord)
Alexander Gorodnik (University of Zurich)
Nikita Shulga (The University of Sydney)
Simon Marshall (School of Mathematics and Statistics, University of Melbourne)
Bryce Kerr (UNSW)
Benjamin Ward (University of york)
Niclas Alexander Ruediger Technau (UW Madison)
Hiroki Takahashi (Keio University)

Registration:

• Registration is now closed
• Arrival date: 21 June 2026
• Departure date: 3 July 2026

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 23 June 2026
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.