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  1. Topology of configuration spaces on graphs

  2. Topology and number theory

  3. Topological surgery through singularity in mean curvature flow

  4. Topological aspects in the theory of aperiodic solids and tiling spaces

  5. Theory and applications of partial differential equations

  6. The significance of dimensions in mathematics

  7. The Shape of Data

  8. The process of mathematical modelling for complex and stochastic biological systems

  9. The phase retrieval problem

  10. The Mathematics of the Bose Gas and its Condensation

  11. The Lagrange and Markov Spectra of Pythagorean triples

  12. The classification of fusion categories and operator algebras

  13. Symplectic topology and mirror symmetry of partial flag manifolds

  14. Symplectic Geometry, Mirror symmetry and Holomorphic Curves

  15. Symmetry Breaking in Quasi-1D Coulomb Systems

  16. Sums of squares in quadratic number rings

  17. Subword complexity, expansion of real numbers and irrationality exponents

  18. Subgroups of Mapping Class Groups

  19. Study stochastic biochemical systems via their underlying network structures

  20. Structures of Formal Proofs

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