On a Conjecture of Cai–Zhang–Shen for Figurate Primes by Junli Zhang, Pengcheng Niu

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Monotonicity conjecture for multi-party entanglement. Part I by Abhijit Gadde, Shraiyance Jain, Vineeth Krishna, Harshal Kulkarni, Trakshu Sharma

“…Abstract In this paper, we conjecture a monotonicity property that we call monotonicity under coarse-graining for a class of multi-partite entanglement measures. …”
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AN INCIDENCE CONJECTURE OF BOURGAIN OVER FIELDS OF POSITIVE CHARACTERISTIC by JORDAN S. ELLENBERG, MÁRTON HABLICSEK

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Around a conjecture of Erdos in graph Ramsey theory by Leila Maherani, Gholamreza Omidi

“…Recently this conjecture was proved by Sudakov. In this short note, we give an extention of this result. …”
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Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture by Achar, Pramod N., Rider, Laura

“…We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. …”
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The Saxl conjecture for fourth powers via the semigroup property by Luo, Sammy Y., Sellke, Mark A.

“…The tensor square conjecture states that for n ≥ 10, there is an irreducible representation V of the symmetric group Sn such that V⊗V contains every irreducible representation of S[subscript n]. …”
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The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions by Zanello, Fabrizio, Stanley, Richard P

“…A beautiful recent conjecture of Armstrong predicts the average size of a partition that is simultaneously an s-core and a t-core, where s and t are coprime. …”
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Holomorphic anomaly equations and the Igusa cusp form conjecture by Oberdieck, Georg, Pixton, Aaron

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Matching Triangles and Basing Hardness on an Extremely Popular Conjecture by Abboud, Amir, Williams, Virginia Vassilevska, Yu, Huacheng

“…The vast majority of these lower bounds are based on one of three famous hypotheses: the 3-SUM conjecture, the all pairs shortest paths (APSP) conjecture, and the Strong Exponential Time Hypothesis. …”
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On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives by Liu, Yifeng, Tian, Yichao, Xiao, Liang, Zhang, Wei, Zhu, Xinwen

“…Abstract In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to Rankin–Selberg products of conjugate self-dual automorphic representations, within the framework of the Gan–Gross–Prasad conjecture. …”
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Hitchin fibrations, abelian surfaces, and the P=W conjecture by de Cataldo, Mark, Maulik, Davesh, Shen, Junliang

“…Furthermore, we show that all tautological generators lie in the correct pieces of the perverse filtration as predicted by the P=W conjecture. In combination with recent work of Mellit, this reduces the full conjecture to the multiplicativity of the perverse filtration.…”
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On the P = W conjecture for $$SL_n$$ S L n by de Cataldo, Mark A., Maulik, Davesh, Shen, Junliang

“…We prove that the $$P=W$$ P = W conjecture for $$\mathrm {SL}_p$$ SL p is equivalent to the $$P=W$$ P = W conjecture for $$\mathrm {GL}_p$$ GL p . …”
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A conjecture for the eigenvalues of pseudo-Anosov mappings of surfaces by Aravinth, Krishnan Ravi

“…In Geometric Topology, there is a conjectured relation between the supremum of the set containing virtual homological spectral radius of finite type covers of a surface and the hyperbolic volume of the mapping torus with respect to a pseduo-Anosov mapping class. …”
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On the skein theory of surfaces and the Bonahon-Wong asymptotic conjecture by Yu, Xiaoming

“…One of the most important developments in low-dimensional topology is the Bonahon-Wong-Yang intertwiners [BWY21][BWY22], which are used to study the representa- tion theory of skein algebra and to explore a version of the volume conjecture. In this paper, we first discuss some topological properties of the four-punctured sphere such as its mapping class groups, triangulations and shear parameters; and then we investigate the Bonahon-Wong- Yang intertwiners of four-punctured sphere and try to make relevant calculations of certain pseudo-Anosov maps.…”
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Model theory of special subvarieties and Schanuel-type conjectures by Zilber, B

Odd order cases of the logarithmically averaged Chowla conjecture by Tao, T, Teräväinen, J

“…A famous conjecture of Chowla states that the Liouville function $\lambda (n)$ has negligible correlations with its shifts. …”

The Andre-Oort conjecture for the moduli space of Abelian Surfaces by Pila, J, Tsimerman, J

“…We provide an unconditional proof of the Andr\'e-Oort conjecture for the coarse moduli space $\mathcal{A}_{2,1}$ of principally polarized Abelian surfaces, following the strategy outlined by Pila-Zannier.…”

The de Sitter swampland conjecture and supersymmetric AdS vacua by Conlon, J

“…It has recently been conjectured that string theory does not admit de Sitter critical points. …”

O-minimality and the Andre-Oort conjecture for C-n by Pila, J

“…We give an unconditional proof of the Andŕe-Oort conjecture for arbitrary products of modular curves. …”

The André-Oort conjecture for the moduli space of abelian surfaces by Pila, J, Tsimerman, J

“…We provide an unconditional proof of the André-Oort conjecture for the coarse moduli space 'œ2,1 of principally polarized abelian surfaces, following the strategy outlined by Pila-Zannier. © 2012 The Author(s).…”