A Lagrangian cobordism between Legendrian knots is an important
notion in symplectic geometry. Many questions, including basic
structural questions about these surfaces are yet unanswered. For
instance, while it is known that these cobordisms form a...
Matrix powering, and more generally iterated matrix
multiplication, is a fundamental linear algebraic primitive with
myriad applications in computer science. Of particular interest is
the problem’s space complexity as it constitutes the main
route...
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...
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...
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,
We prove the existence of subspace designs with any given
parameters, provided that the dimension of the underlying space is
sufficiently large in terms of the other parameters of the design
and satisfies the obvious necessary divisibility...
