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...
Donaldson-Thomas (DT) invariants of a quiver with potential can
be expressed in terms of simpler attractor DT invariants by a
universal formula. The coefficients in this formula are calculated
combinatorially using attractor flow trees. In joint...
This lecture is devoted to a survey on explicit stability
results in Gagliardo-Nirenberg-Sobolev and logarithmic Sobolev
inequalities. Generalized entropy methods based on carré du champ
computations and nonlinear diffusion flows can be used for...
In 1996 Manjul Barghava introduced a notion of P-orderings for
arbitrary sets S of a Dedekind domain, with respect to a prime
ideal P, which defined associated invariants called P-sequences. He
combined these invariants to define generalized...
