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...
Contact homology is a Floer-type invariant for contact
manifolds, and is a part of Symplectic Field Theory. One of its
first applications was the existence of exotic contact structures
on spheres. Originally, contact homology was defined only
for...
The Zimmer program asks how lattices in higher rank semisimple
Lie groups may act smoothly on compact manifolds. Below a certain
critical dimension, the recent proof of the Zimmer conjecture by
Brown-Fisher-Hurtado asserts that, for SL(n,R) with n...
Statistical mechanics models undergoing a phase transition often
exhibit rich, fractal-like behaviour at their critical points,
which are described in part by critical exponents, the indices
governing the power-law growth or decay of various...
The Loewner energy is a Möbius invariant quantity that measures
the roundness of Jordan curves on the Riemann sphere. It arises
from large deviation deviations of SLE0+ and is also a Kähler
potential on the Weil-Petersson Teichmüller space...
