On a conjecture of Andrews by Padmavathamma, T. G. Sudha

“…In this paper, we prove a particular case of a conjecture of Andrews on two partition functions Aλ,k,a(n) and Bλ,k,a(n).…”
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On the asymptotic Bieberbach conjecture by Mauriso Alves, Armando J. P. Cavalcante

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On a conjecture of Vukman by Qing Deng

“…The purpose of this paper is to prove the following conjecture of Vukman.…”
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Reheating after swampland conjecture by Vahid Kamali

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Cosmology, the big bang and the BKL conjecture by Ringström, Hans

“…It starts with a brief description of some of the essential questions: strong cosmic censorship; the relation between the future asymptotics and geometrization in the vacuum setting; the cosmic no-hair conjecture; and the BKL-proposal. It then turns to results, starting with ones obtained in situations with symmetry. …”
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On the generalised André–Pink–Zannier conjecture. by Richard, Rodolphe, Yafaev, Andrei

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On the Probabilistic Proof of the Convergence of the Collatz Conjecture by Kamal Barghout

“…A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by 2 that follows a recurrent pattern of the form x,1,x,1…, where x represents divisions by 2 more than once. …”
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On the reconstraction of the matching polynomial and the reconstruction conjecture by E. J. Farrell, S. A. Wahid

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A new proof of the GGR conjecture by Ash, J. Marshall, Catoiu, Stefan, Fejzić, Hajrudin

“…For each positive integer $n$, function $f$, and point $x$, the 1998 conjecture by Ginchev, Guerragio, and Rocca states that the existence of the $n$th Peano derivative $f_{(n)}(x)$ is equivalent to the existence of all $n(n+1)/2$ generalized Riemann derivatives, \[ D_{k,-j}f(x)=\lim _{h\rightarrow 0}\frac{1}{h^{n}}\sum _{i=0}^k(-1)^i\binom{k}{i}f(x+(k-i-j)h), \] for $j,k$ with $0\le j…”
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A Note on the Primitive Roots and the Golomb Conjecture by Yiwei Hou, Hongyan Wang

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Holonomic modules and 1-generation in the Jacobian Conjecture by Bavula, Volodymyr V.

Subjects: “…The Jacobian Conjecture…”
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Some remarks on the companions conjecture for normal varieties by D’Addezio, Marco

“…Drinfeld in 2010 proved the companions conjecture for smooth varieties over a finite field, generalizing L. …”
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A heterotic Kähler gravity and the distance conjecture by Javier José Murgas Ibarra, Paul-Konstantin Oehlmann, Fabian Ruehle, Eirik Eik Svanes

“…We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. …”
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Transplanckian censorship and the local swampland distance conjecture by Patrick Draper, Szilard Farkas

“…Abstract The swampland distance conjecture (SDC) addresses the ability of effective field theory to describe distant points in moduli space. …”
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Massive spectrum in F-theory and the distance conjecture by Keren Chen, Qinjian Lou, Yi-Nan Wang

“…To exactly match with the results in the distance conjecture, we propose that the definition of 8D Planck mass should receive a large correction. …”
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Calabi–Yau structures on Drinfeld quotients and Amiot’s conjecture by Keller, Bernhard, Liu, Junyang

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Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem by L. Haddad, C. Helou, J. Pihko

“…It is this analogy that we pursue, thus establishing many properties and giving equivalent statements to the well-known Erdös-Turán conjectures in terms of supported series and extending to them a version of Erdös-Fuchs theorem.…”
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Artificial Intelligence in Orthodontics: Concerns, Conjectures, and Ethical Dilemmas by Rosalia Leonardi, Nikhillesh Vaiid

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A cone conjecture for log Calabi-Yau surfaces by Jennifer Li

“…These statements can be viewed as versions of the Morrison cone conjecture for log Calabi–Yau surfaces. In addition, if the number of components of D is no greater than six, we show that the nef cone of $Y_e$ is rational polyhedral and describe it explicitly. …”
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Density of states, black holes and the Emergent String Conjecture by Alek Bedroya, Rashmish K. Mishra, Max Wiesner

“…This provides evidence for the Emergent String Conjecture without explicitly relying on string theory or supersymmetry.…”
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