Blog

My blog features surveys and informal posts offering background information and insights into my recent publications. I assume the reader has at least an undergraduate-level understanding of mathematics. In addition, I may also take the opportunity to explore a range of other interesting topics and discuss various subjects as they arise.

  1. The real Trojan horse
    Christopher Nolan's The Odyssey does not misread Homer; it switches epics

  2. All-directions projections of self-affine sets
    Exceptional directions in the Marstrand-Mattila projection theorem for self-affine sets

  3. How wild can projections of Assouad-type dimensions be?
    The Marstrand-Mattila projection theorem for Assouad-type dimensions

  4. Level sets of prevalent Hölder and Weierstrass functions
    Exploring level set dimensions of Hölder and Weierstrass functions

  5. Dissonance of self-conformal measures on the real line
    Motivation via Furstenberg conjectures and Marstrand's theorems

  6. Thermodynamic formalism of countably generated self-affine sets
    Equilibrium states and Hausdorff dimension of self-affine sets

  7. Finer geometry of planar self-affine sets
    Marstrand's slicing theorem, Ahlfors regularity, and projections

  8. Super-exponential condensation without exact overlaps
    Exponential separation and dimension drop conjecture

  9. Self-conformal sets with positive Hausdorff measure
    Weak separation condition and Ahlfors regularity

  10. Subadditive ergodic theory and applications
    Introduction to subadditive ergodic theory and its applications

  11. Rigidity of quasisymmetric maps on self-affine carpets
    Quasi-Lipschitz maps and conformal Assouad dimension

  12. Scenery flow, conical densities, and rectifiability
    Tangent distributions and geometric measure theory