This will be a survey talk about recent progress on pointwise
convergence problems for multiple ergodic averages along polynomial
orbits and their relations with the Furstenberg-Bergelson-Leibman
conjecture.
Expander graphs are fundamental objects in theoretical computer
science and mathematics. They have numerous applications in diverse
fields such as algorithm design, complexity theory, coding theory,
pseudorandomness, group theory, etc.
The notion of Schmidt rank/strength for a collection of m
polynomials plays an important role in additive combinatorics,
number theory and commutative algebra; high rank collections of
polynomials are “psuedorandom”. An arbitrary collection
of...
First-passage percolation studies the geometry obtained from a
random perturbation of Euclidean geometry. In the discrete planar
setting, one assigns random, independent and identically
distributed, lengths to the edges of the lattice Z^2 and...
