Stably exotic surfaces and Khovanov homology

(Virtual)

We will embark on a case study of two exotically knotted surfaces in the 4-ball (with boundary in the 3-sphere) that arise from the "atomic approach" to Wall-type stabilization problems. I will sketch the arguments that show these two surfaces are topologically isotopic yet are not smoothly isotopic and, moreover, remain smoothly distinct after "internally" stabilizing via connected sum with T2. The key obstruction comes from the universal version of Khovanov homology and builds on prior joint work with Sundberg. Time permitting, I will discuss a speculative approach for using the spectral sequence from Khovanov homology to monopole Floer homology to study the branched double covers of these surfaces, which are exotic 4-manifolds that are candidates to remain exotic after connected sum with S2xS2.