9 problems

Let $N\to S^1$ be a fibration with a family $D$ of twisted Dirac operators on the fibers, and let $\delta_t$ be the associated self-adjoint adiabatic family of operators for $t>0$.…

Let a Riemannian metric on a contact manifold be blown up along the direction orthogonal to the contact distribution. Although the curvatures become unbounded, the metric converges…

Adiabatic-limit conjecture. Over an open subset away from the bubbling loci, the limiting connection on $X \times B$ should solve the family Hermite–Einstein equation.

Let $\boldsymbol{\eta}$ be a profile, let $C\in\mathcal{F}$ be a polynomial in fields and their derivatives, and let $\Psi,\Psi'\in\mathcal{D}_2$. A renormalization scheme for time…

Let $(M,g)$ be a Riemannian manifold endowed with a Riemannian foliation, and let conclusion (2) refer to the preceding assertion that, under the stated adiabatic collapse hypothes…

Adiabatic limit conjecture. If there is a positive section $h$ of ${\cal H}_{\chi}$ which avoids excess $-2$ classes, then for sufficiently large $R$ there is a closed positive $3$…

Let ${\cal M}$ be the moduli space of flat connections identified with the Lie group appearing in the adiabatic Yang–Mills ansatz, and let $\phi$ be a curve in ${\cal M}$ satisfyin…

Let $\Sigma$ be the underlying compact Riemann surface, let $\nu_{k,0}(s)$ be the relevant open subset of the vortex moduli space, and let … be the diffeomorphic correspondence. Le…

Let $H$ be the coupled Hamiltonian, let $P^{d}(H)$ be the projection onto the subspace generated by the discrete eigenfunctions of $H$, and let ${\varrho}_{\alpha}(t)$ denote the t…