Mathematical Research
Random Topology
Randomized topological objects such as simplicial, cubical, and cell complexes have been actively studied in recent years. This research streamline corresponds to higher dimensional generalizations of random graph theory and, in addition, is strongly related with applications in materials science and information and communication systems. We are studying random topology by combining commutative algebra, probability and measure theories.
literatureY. Hiraoka and K. Tsunoda. Limit theorems for random cubical homology. arXiv:1612.08485.
T. K. Duy, Y. Hiraoka, and T. Shirai. Limit theorems for persistence diagrams. arXiv:1612.08371.
Y. Hiraoka and T. Shirai. Tutte polynomials and random-cluster models in Bernoulli cell complexes. RIMS Kokyuroku Bessatsu B59 (2016), 289-304.
Y. Hiraoka and T. Shirai. Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process. Random Struct. Alg.. doi:10.1002/rsa.20718 (2017).