Related papers: On the Cheltsov--Rubinstein conjecture
We establish isomorphism ranges for the comparison maps between algebraic and topological K-groups, extending classical Quillen-Lichtenbaum conjecture to separated complex schemes of finite type after refinement. Additionally, we…
We study certain kind of polynomials associated with Lissajous curves, called Chebyshev-Lissajous polynomials. We investigate their irreducibilities over the real numbers and complex numbers, thus comfirming two conjectures proposed by…
We propose a non-commutative generalization of Beilinson's Conjecture on the regulator map from algebraic K-theory to Deligne cohomology of algebraic varieties over Q. We also check a baby case of the generalized conjecture, namely, the…
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
We generalise the work of Sarnak-Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik-Selberg Conjecture.
Dass, Qureshi, and Sheel conjecture that the lower bound in the Heisenberg-Robertson uncertainty relation cannot be reached in mixed states. The conjecture is wrong.
In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such generalized Bump-Hoffstein conjecture by proving some special…
According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, sufficient conditions for the Goldbach conjecture, and results…
We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…
We formulate a series of conjectures on the stable tensor product of irreducible representations of symmetric groups, which are closely related to the reduced Kronecker coefficients. These conjectures are certain generalizations of…
We present a general conjecture on the divisibility of a certain expression in terms of Kostka numbers and their close variants. This conjecture is closely related to a variant of the period-index problem of noncommutative algebra, with…
In this paper, we reprove a global converse theorem of Cogdell and Piatetski-Shapiro using purely global methods.
The Shapiro conjecture in the real Schubert calculus fails to hold for flag manifolds, but in a very interesting way. In this extended abstract, we give a refinement of that conjecture for the flag manifold and present massive…
In this paper, we obtain a new generalization of Chebyshev's inequality for random elements taking values in a separate Banach space.
We give an example for the Kuznetsov-Shinder conjecture, with infinitely many non-isomorphic D-equivalent and L-equivalent varieties.
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.
We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…
Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects…
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
We study the conjecture due to V.\,V. Shokurov on characterization of toric varieties. We also consider one generalization of this conjecture. It is shown that none of the characterizations holds true in dimension $\ge 3$. Some weaker…