A mathematical conjecture associates Martian TARs with sand ripples by Zhang Jinghong, Zheng Xiaojing, Zhu Wei

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A counter-example to Karlin's strong conjecture for fictitious play by Pan, Qinxuan

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The p-parity conjecture for elliptic curves with a p-isogeny by Cesnavicius, Kestutis

“…For an elliptic curve E over a number field K, one consequence of the Birch and Swinnerton-Dyer conjecture is the parity conjecture: the global root number matches the parity of the Mordell-Weil rank. …”
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Refined global Gan–Gross–Prasad conjecture for Bessel periods by Liu, Yifeng

“…We formulate a refined version of the global Gan–Gross–Prasad conjecture for general Bessel models, extending the work of Ichino–Ikeda and R. …”
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Refined global Gan–Gross–Prasad conjecture for Bessel periods by Liu, Yifeng

“…We formulate a refined version of the global Gan-Gross-Prasad conjecture for general Bessel models, extending the work of Ichino-Ikeda and R. …”
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A note on Grothendieck’s standard conjectures of type C⁺ and D by Trigo Neri Tabuada, Goncalo Jorge

“…As an application, we prove that Grothendieck's conjectures are invariant under homological projective duality. …”
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New progress towards three open conjectures in geometric analysis by Gallagher, Paul,Ph.D.Massachusetts Institute of Technology.

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Towards Heim and Neuhauser’s unimodality conjecture on the Nekrasov–Okounkov polynomials by Hong, Letong, Zhang, Shengtong

“…In this paper we partially answer a conjecture of Heim and Neuhauser, which asks if $$Q_n(z)$$ Q n ( z ) is unimodal, or stronger, log-concave for all $$n \ge 1$$ n ≥ 1 . …”
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A counterexample to the Bollobás–Riordan conjectures on sparse graph limits by Sah, Ashwin, Sawhney, Mehtaab, Tidor, Jonathan, Zhao, Yufei

“…Bollobás and Riordan, in their paper 'Metrics for sparse graphs', proposed a number of provocative conjectures extending central results of quasirandom graphs and graph limits to sparse graphs. …”
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A counterexample to the Bollobás–Riordan conjectures on sparse graph limits by Sah, Ashwin, Sawhney, Mehtaab, Tidor, Jonathan, Zhao, Yufei

“…Bollobás and Riordan, in their paper 'Metrics for sparse graphs', proposed a number of provocative conjectures extending central results of quasirandom graphs and graph limits to sparse graphs. …”
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A note on Grothendieck’s standard conjectures of type ����⁺ and ���� in positive characteristic by Tabuada, Gonçalo

“…As a second application, we prove Grothendieck’s (generalized) conjectures in the new cases of “low-dimensional” orbifolds. …”
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A counterexample to the extension space conjecture for realizable oriented matroids by Liu, Gaku

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Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture by Beuzart-Plessis, Raphaël, Liu, Yifeng, Zhang, Wei, Zhu, Xinwen

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Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions by Wang, Danielle

“…The global twisted GGP conjecture is a variant of the Gan-Gross-Prasad conjecture for unitary groups, and considers the restriction of an automorphic representation of GL(V ) to its subgroup U(V ), for a skew-Hermitian space V. …”
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A proof of Tsygan's formality conjecture for an arbitrary smooth manifold by Dolgushev, Vasiliy A

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Invertible sheaves on generic rational surfaces and a conjecture of Hirschowitz's. by Castellacci, Giuseppe

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Validating the conjectural variation method : the sugar industry, 1890-1914 by Genesove, David, Mullin, Wallace P.

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Chromatic number, clique subdivisions, and the conjectures of Hajos and Erdos-Fajtlowicz by Fox, Jacob, Lee, Choongbum, Sudakov, Benny

“…Let H(n) be the maximum of (G)= (G) over all n-vertex graphs G. A famous conjecture of Haj os from 1961 states that (G) (G) for every graph G. …”
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Chromatic number, clique subdivisions, and the conjectures of Hajos and Erdos-Fajtlowicz by Fox, Jacob, Lee, Choongbum, Sudakov, Benny

“…Let H(n) be the maximum of (G)= (G) over all n-vertex graphs G. A famous conjecture of Haj os from 1961 states that (G) (G) for every graph G. …”
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Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture by Garcia-Patron Sanchez, Raul, Navarrete-Benlloch, Carlos, Lloyd, Seth, Shapiro, Jeffrey H., Cerf, Nicolas J.

“…We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory.…”
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