Several polytopes arise from finite graphs. For edge and symmetric edge polytopes, in particular, exhaustive computation of the Ehrhart polynomials n…

The first author studied spacelike constant mean curvature one (CMC-1) surfaces in de Sitter 3-space when the surfaces have no singularities except w…

We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We estimate the Bowen parameters (zeros of the p…

Applying logarithmic transformations along 2-tori, we construct a generalized complex structure J_n with n type changing luci for every $n\geq 0$ on …

Let $b$ be a pseudo-Anosov braid whose permutation has a fixed point and let $M_b$ be the mapping torus by the pseudo-Anosov homeomorphism defined on…

Generalizing Howie and Greene's characterization of alternating knots, we give a topological characterization of almost alternating knots.

Let $\delta_{g,n}$ be the minimal dilatation of pseudo-Anosovs defined on an orientable surface of genus $g$ with $n$ punctures. Tsai proved that for…

We investigate the dynamics of semigroups generated by polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is b…

In the previous paper, the authors constructed a complete holomorphic immersion of the unit disk D into C^2 whose image is bounded. In this paper, we…

Let $G$ be a finite simple graph on $[n]$ and $I(G) \subset S$ the edge ideal of $G$, where $S = K[x_{1}, \ldots, x_{n}]$ is the polynomial ring over…

We answer Question 6.12 in the paper "Monoids in the mapping class group" written by Etnyre and Van Horn-Morris.

We investigate the dynamics of polynomial semigroups (semigroups generated by a family of polynomial maps on the Riemann sphere) and the random dynam…

We introduce several new families of relations in the mapping class groups of planar surfaces, each equating two products of right-handed Dehn twists…

It is well-known that there is a faithful representation of braid groups on automorphism groups of free groups, and it is also well-known that free g…

Let K be a nontrivial knot in the 3-sphere with the exterior E(K). A slope element u in the knot group G(K) is a nontrivial element represented by a …

This paper deals with both complex dynamical systems and conformal iterated function systems. We study finitely generated expanding semigroups of rat…

The notion of causality is used in many situations dealing with uncertainty. We consider the problem whether causality can be identified given data s…

The branched virtual fibering theorem by Sakuma states that every closed orientable $3$-manifold with a Heegaard surface of genus $g$ has a branched …

We study Question 7.9 in the paper "Monoids in the mapping class group" by Etnyre and Van Horn-Morris; whether a symmetric mapping class admitting a …

We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the comple…

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