Suppose you have a set S of integers from {1 , 2 , … , N} that
contains at least N / C elements. Then for large enough N , must S
contain three equally spaced numbers (i.e., a 3-term arithmetic
progression)?
Through the random matrix analogy, Fyodorov, Hiary and Keating
conjectured very precisely the typical values of the Riemann zeta
function in short intervals of the critical line, in particular
their maximum. Their prediction relied on techniques...
In Euclidean geometry, bisectors are perpendicular lines. In
random plane geometry, the situation is more complicated. I will
describe bisectors in the directed landscape, the universal
geometry in the KPZ class. These help answer some open...
For a compact subset K of a closed symplectic manifold,
Entov-Polterovich introduced the notion of (super)heaviness, which
reveals surprising symplectic rigidity. When K
is a Lagrangian submanifold, there is a well-established
criterion for its...
The Mackey-Zimmer representation theorem is a key structural
result from ergodic theory: Every compact extension between ergodic
measure-preserving systems can be written as a skew-product by a
homogeneous space of a compact group. This is used, e.g...
Let X be a smooth projective variety over the field of complex
numbers. The classical Riemann-Hilbert correspondence supplies a
fully faithful embedding from the category of perverse sheaves on X
to the category of algebraic D_X-modules. In this...
Define the Collatz map Col on the natural numbers by setting
Col(n) to equal 3n+1 when n is odd and n/2 when n is even. The
notorious Collatz conjecture asserts that all orbits of this map
eventually attain the value 1. This remains open, even if...
A central goal of physics is to understand the low-energy
solutions of quantum interactions between particles. This talk will
focus on the complexity of describing low-energy solutions; I will
show that we can construct quantum systems for which the...
We will discuss a version of the Green--Tao arithmetic
regularity lemma and counting lemma which works in the generality
of all linear forms. In this talk we will focus on the qualitative
and algebraic aspects of the result.
Liouville conformal field theory is a CFT with central charge
c>25 and continuous spectrum, its correlation functions on
Riemann surfaces with marked points can be expressed using the
bootstrap method in terms of conformal blocks. We will
explain...
