Doron Leonardo Grossman-Naples

My research generally concerns algebraic topology and homotopy theory. I am particularly interested in higher algebra, spectral algebraic geometry, and their connections to topology. One of modern homotopy theory's most fascinating insights is that topology (the study of spaces) and algebra (the study of categories and their internal logics) can both be seen as special cases of the theory of ∞-categories; this is famously expressed via Grothendieck's homotopy hypothesis, which states that spaces are the same as ∞-groupoids. In my research, I aim to explore this connection further, examining the still-developing landscape of "Brave New Algebra" and its applications to topology and mathematical physics.