Tootfinder

Top- and bottom-heavy vertical velocity structures: physical modes of layered atmospheric models
Fiaz Ahmed, J. David Neelin
https://arxiv.org/abs/2509.15166 https://

Top- and bottom-heavy vertical velocity structures: physical modes of layered atmospheric models
Tropical East and West Pacific Oceans display differences in their vertical velocity (or omega) profiles. The East Pacific is characterized by bottom-heavy profiles, while the West Pacific is characterized by top-heavy profiles. Although inter-basin differences in the horizontal SST gradient are known to be important, physical reasons for why these omega structure variants exist are not fully understood. This question is addressed using a steady, linear model on an $f$-plane with $n$ atmospheri…

Does the Grothendieck ring of varieties contain nilpotent elements?
Anna Bot, Alessio Cangini, Immanuel van Santen
https://arxiv.org/abs/2509.10464 https://

Does the Grothendieck ring of varieties contain nilpotent elements?
We show that a ring closely related to the Grothendieck ring of varieties has nilpotent elements, provided that the characteristic of the ground field is equal to $11$ or at least $17$.

Macroscopic coherence and vorticity in room-temperature polariton condensate confined in a self-assembled perovskite microcavity
Martin Montagnac, Yesenia A. Garc\'ia Jomaso, Emiliano Robledo Ibarra, Rodrigo S\'anchez-Mart\'inez, Moroni Santiago Garc\'ia, C\'esar L. Ord\'o\~nez-Romero, Hugo A. Lara-Garc\'ia, Arturo Camacho-Guardian, Giuseppe Pirruccio

Macroscopic coherence and vorticity in room-temperature polariton condensate confined in a self-assembled perovskite microcavity
Exciton-polariton Bose-Einstein condensation at room temperature offers a promising pathway toward quantum photonic technologies that can operate under ambient conditions. A key challenge in this field is to engineer a controlled platform where strong confinement, nonlinear interactions, and structural disorder coexist, unlocking access to rich collective behavior and unconventional condensate dynamics. We demonstrate polariton condensation in CsPbBr$_3$ microplatelets that self-assemble into w…

OK, this is more what I was expecting from my Sweet Peas; I think there's a couple of different varieties in this really high grade LIdl pack of sweet peas. Next year I should get some from better #gardening supplier.

Partially open Pink rose and rosebuds. Mary and Joseph Retreat Center, Rancho Palos Verdes, California, USA. August, 2025. #ranchopalosverdes #garden #rosegarden

White Echinacea Flowers in the Prairie Garden in Front of the Vet Research Tower of which the facade is visible
#ithaca #cornell #photography

Improved Bounds on Ultra-Log Concavity of the Grothendieck Class of $\overline{\mathcal{M}_{0,n}}$
Eduardo Nascimento
https://arxiv.org/abs/2509.11805 https://

Improved Bounds on Ultra-Log Concavity of the Grothendieck Class of $\overline{\mathcal{M}_{0,n}}$
The class of the fine moduli space of stable $n$-pointed curves of genus zero, $\overline{\mathcal{M}_{0,n}}$, in the Grothendieck ring of varieties encodes its Poincaré polynomial. Aluffi-Chen-Marcolli conjecture that the Grothendieck class of $\overline{\mathcal{M}_{0,n}}$ is real-rooted (and hence ultra-log-concave), and they proved an asymptotic ultra-log-concavity result for these polynomials. We build upon their work, by providing effectively computable bounds for the error term in their…

Weird Greco II 🇬🇷
怪异希腊 II 🇬🇷
📷 Nikon FE
🎞️FOMAPAN Action 400
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

Abelian motives and Shimura varieties in nonzero characteristic
James S. Milne
https://arxiv.org/abs/2508.09972 https://arxiv.org/pdf/2508.09972

Abelian motives and Shimura varieties in nonzero characteristic
Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences.

Homogeneous locally nilpotent derivations on trinomial varieties
Kirill Rassolov
https://arxiv.org/abs/2509.08491 https://arxiv.org/pdf/2509.08491

Homogeneous locally nilpotent derivations on trinomial varieties
We consider the finest grading of the algebra of regular functions of a trinomial variety. An explicit description of locally nilpotent derivations that are homogeneous with respect to this grading is obtained.