4 problems

Topological critical-exponent conjecture. The exponent $\alpha_{H_1}$ is a genuinely new exponent characterizing the topological content of alpha-complex persistent homology at cri…

Limit theorem for negative critical $(k+1)$-face processes. The same limit theorem as the one established for the positive critical $k$-face process and the restricted negative cri…

Let $\mathcal{M}$ be an $m$-dimensional manifold, let $\hat\beta_i(n,r)=\beta_i(n,r)-\beta_i(\mathcal{M})$ denote the noisy $i$-th Betti number, and define … The radii $\rho_i$ and…

Let the random complex $\Delta$ have $n$ edges, and let $\Delta^i$ denote the set of all complexes derived from $\Delta$ by removing exactly $i$ edges. When two edges are removed f…