Tootfinder

Weighted surfaces with maximal Picard number
Louis Esser, Jennifer Li
https://arxiv.org/abs/2506.14037 https://arxiv.org/pdf/2506.140…

Weighted surfaces with maximal Picard number
An algorithm due to Shioda computes the Picard number for certain surfaces which are defined by a single equation with exactly four monomials, called Delsarte surfaces. We consider this method for surfaces in weighted projective $3$-space with quotient singularities. We give a criterion for such a weighted Delsarte surface $X$ to have maximal Picard number. This condition is surprisingly related to the automorphism group of $X$. For every positive integer $s$, we find a weighted Delsarte surfac…

On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms
Zelong Chen, Sheng Meng, Guolei Zhong
https://arxiv.org/abs/2506.14274

On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms
We prove that a smooth rationally connected projective threefold of Picard number two is toric if and only if it admits an int-amplified endomorphism. As a corollary, we show that a totally invariant smooth curve of a non-isomorphic surjective endomorphism of $\mathbb{P}^3$ must be a line when it is blowup-equivariant.

250th anniversary of the military.
Massive military display planned in the capital.
Apropos of nothing, who saw season 3 of #StarTrek #Picard?

Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module
Vsevolod Chestnov, Wojciech Flieger, Pierpaolo Mastrolia, Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama, William J. Torres Bobadilla
https://arxiv.org/abs/2506.10456

Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module
We present a novel algorithm for constructing differential operators with respect to external variables that annihilate Feynman-like integrals and give rise to the associated $\mathcal{D}$-modules, based on Griffiths-Dwork reduction. By leveraging the Macaulay matrix method, we derive corresponding relations among partial differential operators, including systems of Pfaffian equations and Picard-Fuchs operators. Our computational approach is applicable to twisted period integrals in projective …

Parallel computations for Metropolis Markov chains with Picard maps
Sebastiano Grazzi, Giacomo Zanella
https://arxiv.org/abs/2506.09762 https://

Parallel computations for Metropolis Markov chains with Picard maps
We develop parallel algorithms for simulating zeroth-order (aka gradient-free) Metropolis Markov chains based on the Picard map. For Random Walk Metropolis Markov chains targeting log-concave distributions $π$ on $\mathbb{R}^d$, our algorithm generates samples close to $π$ in $\mathcal{O}(\sqrt{d})$ parallel iterations with $\mathcal{O}(\sqrt{d})$ processors, therefore speeding up the convergence of the corresponding sequential implementation by a factor $\sqrt{d}$. Furthermore, a modificatio…

Classifying weak Fano toric varieties of Picard rank $3$
Zhengning Hu, Rohan Joshi
https://arxiv.org/abs/2506.00715 https://arxiv.org…

Classifying weak Fano toric varieties of Picard rank $3$
We provide a systematic method to classify all smooth weak Fano toric varieties of Picard rank $3$ in any dimension using Macaulay2, and describe the classification explicitly in dimensions $3$ and $4$. There are $28$ and $114$ isomorphism classes of rank $3$ weak Fano toric threefolds and fourfolds, respectively.

Is Crane--Yetter fully extended?
Luuk Stehouwer
https://arxiv.org/abs/2506.04864 https://arxiv.org/pdf/2506.04864

Is Crane--Yetter fully extended?
We revisit the question of whether the Crane-Yetter topological quantum field theory (TQFT) associated to a modular tensor category admits a fully extended refinement. More specifically, we use tools from stable homotopy theory to classify extensions of invertible four-dimensional TQFTs to theories valued in symmetric monoidal 4-categories whose Picard spectrum has nontrivial homotopy only in degrees 0 and 4. We show that such extensions are classified by two pieces of data: an equivalence clas…

#Jeopardy editions as #StarTrek series:
1964–1975: TOS
1978–1979: TAS
1984–2021: TNG §
2021–present: DS9 §
Rock 'n' Roll: Lower Decks
Celebrity: Picard
Jep: Prodigy
Sports: Voyager
Pop Culture: Discovery
Happy with all but t…

This https://arxiv.org/abs/2403.04088 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The classification of endotrivial complexes
Let $G$ be a finite group and $k$ a field of prime characteristic $p$. We give a complete classification of endotrivial complexes, i.e. determine the Picard group $\mathcal{E}_k(G)$ of the tensor-triangulated category $K^b({}_{kG}\mathbf{triv})$, the bounded homotopy category of $p$-permutation modules, which Balmer and Gallauer recently considered. For $p$-groups, we identify $\mathcal{E}_k(-)$ with the rational $p$-biset functor $CF_b(-)$ of Borel-Smith functions and recover a short exact seq…

GIT-BO: High-Dimensional Bayesian Optimization with Tabular Foundation Models
Rosen Ting-Ying Yu, Cyril Picard, Faez Ahmed
https://arxiv.org/abs/2505.20685

GIT-BO: High-Dimensional Bayesian Optimization with Tabular Foundation Models
Bayesian optimization (BO) effectively optimizes expensive black-box functions but faces significant challenges in high-dimensional spaces (dimensions exceeding 100) due to the curse of dimensionality. Existing high-dimensional BO methods typically leverage low-dimensional embeddings or structural assumptions to mitigate this challenge, yet these approaches frequently incur considerable computational overhead and rigidity due to iterative surrogate retraining and fixed assumptions. To address t…

This https://arxiv.org/abs/2205.10143 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the classification of non-big Ulrich vector bundles on fourfolds
We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$-folds for $n \le 4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$-folds, $n \ge 2$.

The numerical Amitsur group
Alexander Duncan, Shreya Sharma
https://arxiv.org/abs/2505.23957 https://arxiv.org/pdf/2505.23957

The numerical Amitsur group
The Amitsur subgroup of a variety with a group action measures the failure of the action to lift to the total spaces of its line bundles. We introduce the "numerical Amitsur group," which is an approximation of the ordinary Amitsur subgroup that can be computed using only the Euler-Poincaré characteristic on the Picard group. As an application, we find a uniform upper bound on the exponent of the Amitsur subgroup that depends only on the dimension and arithmetic genus of the variety and is ind…