4 problems

Let $(Y,\tau,\mathbf{p})$ be a multi-based real three-manifold, let $\widetilde{\operatorname{HMR}}_*(Y,\tau,\mathbf{p})$ denote framed real monopole Floer homology, and let…

Let $\mathbb{F}=\mathbb{R}$, and let $n$ nonidentical equi-isoclinic subspaces of dimension $r$ lie in a space of dimension $d$. The real Gerzon bound is…

Even-lacuna conjecture. The deformations of $f$ have no even local lacunas unless $f$ has an extremum at the origin. If $f$ has a minimum at the origin, then all critical values of…

Let $X$ be a space with a $\mathbb{Z}/2$-action. A T-dual pair consists of a pair $(E,h)$, where $\mathbb{Z}/2$ acts equivariantly on the circle bundle $pi:E\to X$ and…