While conducting a series of number-theoretic machine learning
experiments, He, Lee, Oliver, and Pozdnyakov noticed a curious
oscillation in the averages of Frobenius traces of elliptic curves
over Q. If one computes the average value of a_p(E)
for...
Suppose that Σ⊂ℂ is compact and symmetric about the real axis
and is a finite union of rectangles and real intervals with
transfinite diameter dΣ greater than 1. Suppose that μ is a H older
arithmetic probability distribution on Σ defined in our...
The conformal bootstrap equations in general dimension are an
infinite set of coupled non-linear equations in infinitely many
variables. According to the lore, the solutions of the full set of
equations correspond to physical CFTs. At the same time...
I will describe the construction of a global Kuranishi chart for
moduli spaces of stable pseudoholomorphic maps of any genus and
explain how this allows for a straightforward definition of GW
invariants. For those not convinced of its usefulness, I...
The formula introduced by Robert Lipshitz for Heegaard Floer
homology is now one of the basic tools for those working with HF
homology. The convenience of the formula is due to its
combinatorial nature. In the talk, we will discuss the
recent...
The question of whether a Symplectic manifold embeds into
another is central in Symplectic topology. Since Gromov
nonsqueezing theorem, it is known that this is a different problem
from volume preserving embeddings. Symplectic capacities are...
In a recent machine learning based study, He, Lee, Oliver, and
Pozdnyakov observed a striking oscillating pattern in the average
value of the P-th Frobenius trace of elliptic curves of prescribed
rank and conductor in an interval range. Sutherland...
Data from ESA’s Gaia mission is already revolutionizing Galactic
astronomy, providing an unprecedented view of the Solar
neighborhood and beyond. However, while it provides us a great
opportunity to transform our understanding of the Milky Way,
it...
In its dynamical formulation, the Furstenberg—Sárközy theorem
states that for any invertible measure-preserving system (X,μ,T),
any set A⊆X with μ(A) greater than 0, and any integer polynomial P
with P(0)=0,
