Positive selector processes are natural stochastic processes
driven by sparse Bernoulli random variables. They play an important
role in the study of suprema of general stochastic processes, and
in particular, Talagrand posed the selector process...
We will outline the proof of an intersection result between
embedded Lagrangian tori and certain 1 parameter families of
product Lagrangian tori in the 4 dimensional symplectic cylinder.
The theorem can be applied to give new computations of the...
Algebraic statistics employs techniques in algebraic geometry,
commutative algebra and combinatorics, to address problems in
statistics and its applications. The philosophy of algebraic
statistics is that statistical models are algebraic
varieties...
The theory of stable polynomials features a key notion called
proper position, which generalizes interlacing of real roots to
higher dimensions. I will show how a Lorentzian analog of proper
position connects the structure of spaces of Lorentzian...
One way to define a matroid is via its base polytope. From
this point of view, some matroid invariants easily have geometric
interpretations: e.g., the number of bases is the number of
vertices of the polytope. It turns out that most
interesting...
We will present recent applications of enumerative algebra to
the study of stationary states in physics. Our point of departure
are classical Newtonian differential equations with nonlinear
potential. It turns out that the study of their stationary...
The Bergelson conjecture from 1996 asserts that the multilinear
polynomial ergodic averages with commuting transformations converge
pointwise almost everywhere in any measure-preserving system. This
problem was recently solved affirmatively for...
We show that skein valued counts of open holomorphic curves in a
symplectic Calabi-Yau 3-fold with Maslov zero Lagrangian boundary
condition are invariant under deformations and discuss applications
(Ooguri-Vafa conjecture and simple recursion...
Hindman’s Theorem states that whenever the natural numbers are
finitely coloured there exists an infinite sequence all of whose
finite sums are the same colour. By considering just powers of 2,
this immediately implies the corresponding result for...
The Prékopa-Leindler inequality (PL) and its strengthening, the
Borell-Brascamp-Lieb inequality, are functional extensions of the
Brunn-Minkowski inequality from convex geometry, which itself
refines the classical isoperimetric inequality. These...
