VIETNAM POLYMATH REU

2023-2024

Organizers

University of Virginia,

USA

Geometric Group Theory, Logic,

Geometric topology, Dynamical Systems

VNU University of Science,

Hanoi

Discrete Geometry, Additive Combinatorics, Geometric Measure Theory

Western University,

USA

Computational/Algebraic Number Theory, Non-commutative Algebras, and Nonlinear Dynamics

University of Science and Technology of China,

China

Extremal and Probabilistic Combinatorics,

Ramsey Theory, and Additive Combinatorics

## List of students, groups and minicourses 2023-2024

Tentative Plan and Applications

Tentative plan:

Accept applications: 5 August to 27 August 2023

Interview: 28-31 August 2023

Mini-courses: 1-30 September 2023

Research phase: October 2023-October 2024

REU workshop at VIASM: July 1-5 2024

Note that the whole program will take place online via Zoom, other than the in-person workshop.

To apply: Please fill out this form by August 27, 2023.

For any questions, please don't hesitate to contact one of the following organizers:

Thomas Koberda: thomas.koberda@gmail.com

Anh Tu Nguyen: natu@hcmiu.edu.vn

Tho Tung Nguyen: nguyenthotung@gmail.com

Thang Pham: phamanhthang.vnu@gmail.com

Tuan Tran: manhtuankhtn@gmail.com

## List of projects for 2023-2024

Topic 1: Random walks on Cayley graphs and unimodular random graphs.

Topic 2: The Tiling Conjecture.

Topic 3: Prime orthogeodesics in the truncated thrice-punctured sphere.

Topic 4: LOT groups and the Whitehead Conjecture.

Topic 5: Incidence Geometry.

Topic 6: On the structure and realizability of some reconfiguration graphs.

Topic 7: Period collapse phenomena in characteristic quasi-polynomials.

Topic 9: The finite field sum-product problem and related questions (for a group of 8 students).

Topic 10: Polynomial methods and applications.

Topic 11: Three-term arithmetic progressions.

Topic 12: The Cauchy-Davenport bound.

Topic 13: Shannon entropy and application to sum-product problem.

Topic 14: Hausdorff dimensions of fractal sets, fractal projections, and intersections problems.

## Mentors

University of Virginia,

USA

Operator Algebras, Ergodic Theory, Measured Group Theory, Sofic Groups

Korea Institute for Advanced Study,

Korea

Geometric Group Theory,

Low-dimensional Topology

University of Virginia,

USA

Geometric Group Theory, Logic,

Geometric topology, Dynamical Systems

VNU University of Science,

Hanoi

Discrete Geometry, Additive Combinatorics, Geometric Measure Theory

National University of Singapore

Singapore

Low-dimensional Topology, Geometric Structures, Representation Varieties, Dynamics of Group Actions

Leibniz Universitat Hannover,

Germany

Algebra, Combinatorics, Reflection Groups, Hyperplane Arrangements

## Acknowledgements

We gratefully acknowledge the support of a "Faculty Global Research with Undergraduates" grant from the University of Virginia Center for Global Inquiry and Innovation, which makes the in-person workshop possible.