7 problems

Let $(M,\omega)$ be a symplectic manifold and let $L$ be an exact Lagrangian. For any Hamiltonianly isotopic exact Lagrangian $L_1$ such that $\gamma(L,L_1)$ is sufficiently small,…

Let $r$-graphs be finite uniform hypergraphs, let $\lambda(m,r)$ denote the maximum Lagrangian of an $r$-graph with $m$ edges, and let $\binom{x}{r}$ be the generalized binomial co…

Frankl–Füredi conjecture. If $G$ is an $r$-graph with $m$ edges, then

Let $G$ be a $t$-intersecting $r$-graph, meaning that any two edges of $G$ have intersection of size at least $t$. For integers $t\geq 1$, $i\geq 0$, and $r\geq t+i$, let…

Let $r\geq 4$ and let $H_{2r}^{M_2^r}$ be the extension of the $r$-uniform matching $M_2^r$ consisting of two pairwise disjoint edges. Let $G$ be an $r$-graph on $[n]$, and let…

Pikhurko–Zhao conjecture. The Lagrangian of $G$ satisfies

Let $t$, $m$, and $r\ge 3$ be positive integers satisfying … Let $G$ be an $r$-graph with $m$ edges that contains a clique of order $t-1$. Peng–Zhao's Motzkin–Straus-type conjectur…