$CONJ conjecture

Latest papers

1. The existence of small defining polynomials for number fields math.NT · 14 Oct · 1 hit

   …integral polynomial of degree $n$ whose coefficients are all $O_n(\sqrt D)$ in size, thus resolving a 1998 conjecture of Ruppert. Our proof compares ideal lattices with their trace duals, via which we handle all…

2. Complex generalized spin-c Killing spinors in low dimensions math.DG · 14 Oct · 1 hit

   …characteristic vector field of the associated trans-Sasakian structure is complete. These results settle a conjecture by Gro{\ss}e and Nakad (Results in Mathematics, 2015) stating that on two- and three-dimensional…

3. Minimal Resolutions of $k$-divisible and $(k-1)$-dominant Ideals math.AC · 14 Oct · 1 hit

   …$d$-dominant ideals when $d=k-1$ via a Lyubeznik resolution. This framework allows us to prove a conjecture made by Alesandroni. Using these invariants, we also provide a characterization of monomial ideals…

4. Proof of the Penrose Conjecture for Maximally Parameterized Initial Data Sets math.DG · 14 Oct · 3 hits

   …argument that allows singular boundaries. More generally, in the spirit of [8, 9], we note that the Penrose conjecture follows whenever a certain system of PDEs (3.18) involving $k$ can be solved, in which case our…

5. On Meeks' conjecture on disjoint minimal graphs math.DG · 14 Oct · 3 hits

   …solution pairs $(u,D)$ to the minimal surface equation in $\mathbb{R}^n$, with $u=0$ on $\partial D.$ A conjecture of W. Meeks states that at most two such pairs can exist in $\mathbb{R}^n.$ We confirm the…

6. Allen--Cahn and mean curvature flows from Clifford hypersurfaces to equators math.DG · 14 Oct · 1 hit

   In this short note, using OpenAI's resolution of the Solomon--Yau conjecture, we extend our joint work with Pedro Gaspar to all dimensions $n\geq2$. We construct eternal…

7. Tracking a Small Set of Experts in Online Convex Optimization cs.LG · 14 Oct · 1 hit

   …and polynomial-time regret achievable for this problem. Specifically, under the hypergraphic planted-clique conjecture, we show that for every polynomial-time algorithm there exist instances for which it incurs at…

8. Two Perfect One-Factorizations of $K_{92}$ math.CO · 14 Oct · 1 hit

   …1-factorization for every $t \ge 2$, but apart from some infinite families and a list of sporadic orders the conjecture is open, and $92$ was one of the nine orders up to $100$ for which no perfect 1-factorization was…