Cayley graphs provide interesting bridges between graph theory,
additive combinatorics and group theory. Fixing an ambient finite
group, random Cayley graphs are constructed by choosing a
generating set at random. These graphs reflect interesting...
To any unital, associative ring R one may associate a family of
invariants known as its algebraic K-groups. Although they are
essentially constructed out of simple linear algebra data over the
ring, they see an extraordinary range of information...
I will discuss an adaptation of Gromov's ideal-valued measures
to symplectic topology. It leads to a unified viewpoint at three
"big fiber theorems": the Centerpoint Theorem in combinatorial
geometry, the Maximal Fiber Inequality in topology, and...
Subsets A of an abelian group with a small doubling |A+A|/|A|
have been extensively studied, and results of Freiman, Ruzsa and
Green give fundamental structural descriptions of such sets. These
have important applications across combinatorics and...
We consider an energy model for N ordered elastic membranes
subject to forcing and boundary conditions. The heights of the
membranes are described by real functions u_1, u_2,...,u_N, which
minimize an energy functional involving the Dirichlet...
We study multiply warped product geometries
MN:=Bn×Fn1×···×FnA
g = g_B + \sum_{a=1}^A v_a^2 g_{F^{n_a}} and show that for an
open set of initial data within multiply warped product geometries
the Ricci flow starting at any of those develops...
An old question of Poincaré concerns creating periodic orbits
via perturbations of a flow/diffeomorphism. While pseudoholomorphic
methods have successfully addressed this question in dimensions
2-3, the higher-dimensional case remains less...
We will describe emerging understanding of the structures
related to the arithmetic of Zeta and Multizeta values for function
fields through various results and conjectures.
In a 3-𝖷𝖮𝖱 game , the verifier samples a challenge (x,y,z)∼μ
where μ is a probability distribution over Σ×Γ×Φ, and a map
t:Σ×Γ×Φ→ for a finite Abelian group defining a constraint.
The verifier sends the questions x, y and z to the
players...
A sparsification of a structure, with respect to a class of
queries, produces a compressed representation of the structure
while answering every query in the class approximately correctly.
The seminal example of sparsification is "graph...