Patterns of primes in the Sato–Tate conjecture by Gillman, Nate, Kural, Michael, Pascadi, Alexandru, Peng, Junyao, Sah, Ashwin

“…Abstract Fix a non-CM elliptic curve $$E/\mathbb {Q}$$E/Q, and let $$a_E(p) = p + 1 - \#E(\mathbb {F}_p)$$aE(p)=p+1-#E(Fp) denote the trace of Frobenius at p. The Sato–Tate conjecture gives the limiting distribution $$\mu _{ST}$$μST of $$a_E(p)/(2\sqrt{p})$$aE(p)/(2p) within $$[-1, 1]$$[-1,1]. …”
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Children selectively endorse speculative conjectures by Chu, Junyi, Schulz, Laura E.

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Endoscopic decompositions and the Hausel–Thaddeus conjecture by Maulik, Davesh, Shen, Junliang

“…This provides a complete description of the cohomology of the moduli space of stable <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S205050862100007X_inline3.png" /> <jats:tex-math>$\mathrm {SL}_n$</jats:tex-math> </jats:alternatives> </jats:inline-formula>-Higgs bundles in terms of the tautological classes, and gives a new proof of the Hausel–Thaddeus conjecture, which was also proven recently by Gröchenig, Wyss and Ziegler via <jats:italic>p</jats:italic>-adic integration.…”
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Proof of the satisfiability conjecture for large k by Ding, Jian, Sly, Allan, Sun, Nike

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The p-adic local langlands conjecture by Malon, Christopher D

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A counterexample to a conjecture of Serre by Anick, David Jay

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A solution to the Papadimitriou-Ratajczak conjecture by Moitra, Ankur

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On the multiple unicast network coding conjecture by Langberg, Michael, Medard, Muriel

“…In this paper, we study the multiple unicast network communication problem on undirected graphs. It has been conjectured by Li and Li [CISS 2004] that, for the problem at hand, the use of network coding does not allow any advantage over standard routing. …”
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Observations and conjectures on the U.S. employment miracle by Krueger, Alan B., Pischke, Jrn-Steffen

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How the Upper Bound Conjecture Was Proved by Stanley, Richard P.

“…We give a short history of how the Upper Bound Conjecture for Spheres was proved.…”
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The Kierstead's Conjecture and limitwise monotonic functions by Wu, Guohua, Zubkov, Maxim

“…In this paper, we prove Kierstead's conjecture for linear orders whose order types are ∑q∈QF(q), where F is an extended 0′-limitwise monotonic function, i.e. …”
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Williamson matrices and a conjecture of Ito's by Bernhard, Schmidt.

“…Finally, we verify Ito‘s conjecture for all t\le 46.…”
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A conjecture of Beauville and Catanese revisited by Pink, R, Roessler, D

“…Furthermore, we prove partial analogs of the conjecture of Beauville and Catanese in positive characteristic.…”

On Thurston's Euler class-one conjecture by Yazdi, M

“…In 1976, Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that conversely, any integral second cohomology class with norm equal to one is the Euler class of a taut foliation. …”

Kummer's conjecture for cubic Gauss sums by Heath-Brown, D

“…This improves on the estimate established by Heath-Brown and Patterson in demonstrating the uniform distribution of the cubic Gauss sums around the unit circle. When $l=0$ it is conjectured that the above sum is asymptotically of order $X^{5/6}$, so that the upper bound is essentially best possible. …”

Swampland conjectures and infinite flop chains by Brodie, CR, Constantin, A, Lukas, A, Ruehle, F

“…We investigate swampland conjectures for quantum gravity in the context of M-theory compactified on Calabi-Yau threefolds which admit infinite sequences of flops. …”

Estimating natural resource harvests: Conjectures? by Menton, M, Lawrence, A, Merry, F, Brown, N

The randomized k-server conjecture is false! by Bubeck, S, Coester, C, Rabani, Y

“…We prove a few new lower bounds on the randomized competitive ratio for the k-server problem and other related problems, resolving some long-standing conjectures. In particular, for metrical task systems (MTS) we asympotically settle the competitive ratio and obtain the first improvement to an existential lower bound since the introduction of the model 35 years ago (in 1987). …”

A topological variation of the reconstruction conjecture by Pitz, M, Suabedissen, R

“…This paper investigates topological reconstruction, related to the reconstruction conjecture in graph theory. We ask whether the homeomorphism types of subspaces of a space X which are obtained by deleting singletons determine X uniquely up to homeomorphism. …”

On Hrushovski’s proof of the Manin-Mumford conjecture by Pink, R, Rossler, D

“…The Manin-Mumford conjecture in characteristic zero was first proved by Raynaud. …”