MathOverflow

In our preprint On solving linear equations over {0, 1, −1}
We are trying to solve the NP-hard problem of monotone 1-in-3 SATvia solving system of the form $x_i + x_j + x_k=1$ over $\{0,1,-1\}$
The algorithm is efficient on planted instances, but on craftedinstances like 3SAT with $n$ variables to 1-in-3 the reduction givesmatrix with $52 n$ columns and the algorithm takes prohibitively long....

Let $G=\mathrm{GL}_n$ (say over $F=\mathbb{Q}_p$) and consider the stack $\mathrm{Bun}_G$ of rank $n$ vector bundles on the Fargues-Fontaine curve. Let $\mu$ be a dominant character of $G^\vee$ and $V=V(\mu)$ the corresponding highest weight representation...

Let (Q_n) be the (n)-dimensional hypercube, and let (f(n)) denote the maximum number of edges in a (C_4)-free subgraph of (Q_n).
Using Minamo Minamoto's recent (Q_7/Q_8) constructions (arXiv:2603.29127) as the immediate baseline, I found explicit (C_4)-free edge-list certificates for (Q_9) through (Q_{15})....

I had to step away from research for about three years due to health reasons, and I am now trying to get back up to speed in arithmetic geometry. Before my break, I was working in areas related to Shimura varieties, Galois representations, and p-adic...