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Bloch's conjecture for a surface X over an algebraically closed field k states that every homologically trivial correspondence acts as 0 on the Albanese kernel. When X is a K3 surface, this conjecture...
This is the main paper in a sequence in which, in collaboration with I. Rodnianski and J. Szeftel, we give a complete proof of the conjecture according to which the time of existence of solutions to t...
We find further implications of the BMV conjecture, which states that for hermitian matrices A and B, the function Tr exp(A - t B) is the Laplace transform of a positive measure.
Abstract: A complete construction of the AFLT states is proposed. With this construction and for all the cases we have checked, the AGT conjecture on the equivalence of Nekrasov Instanton Counting (NI...
Abstract: The concept of deformation of Riemannian geometry is reviewed, with applications to gravitation and cosmology. Starting with an analysis of the cosmological constant problem, it is shown tha...
Abstract: Donald Saari conjectured that the $N$-body motion with constant configurational measure is a motion with fixed shape. Here, the configurational measure $\mu$ is a scale invariant product of ...
Abstract: We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time $\tau(G_{N})$ of a planar graph $G_{N}$ o...
Abstract: Conrey, Farmer, Keating, Rubinstein, and Snaith recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjec...
Abstract: In this paper, we show that the derivative of the genus-1 Virasoro conjecture for Gromov-Witten invariants along the direction of quantum volume element holds for all smooth projective varie...
Abstract: It is given a simple proof of the collapse conjecture for a diagonal Bianchi type-IX vacuum space-time. It is shown that the codimension of the infinity stable attractor, restricted to the a...
What if? On the interplay between Serendipity, Intuition and Conjecture
A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the substitution of conformal blocks by the Dotsenko-Fateev beta-ensemble averages and Nekrasov functions by a...
It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from r...
The quantum inequalities, and the closely related quantum interest conjecture, impose restrictions on the distribution of the energy density measured by any time-like observer, potentially preventing ...

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