An infinite-rank summand of knots with trivial Alexander polynomial

The subgroup $\mathcal{T}$ of the smooth knot concordance group generated by topologically slice knots portrays the significant difference between the topological and smooth categories in 4--dimension. Last decade, some structural problems (such as splitting and divisibility) of $\mathcal{T}$ have been answered due to the development of homological invariants of knots. In this talk I will review some recent results related to this topic and show that there exists an infinite rank summand in the subgroup of $\mathcal{T}$ generated by knots with trivial Alexander polynomial. To this end we use the invariant Upsilon recently introduced by Ozsv\'{a}th, Stipsicz and Szab\'{o} using knot Floer homology. This is joint work with Min Hoon Kim.