This talk will be a series of vignettes in topological
combinatorics, centering around lower bounds on the chromatic
number of graphs. The Kneser graph KG(n,k) has as vertices the
size-k subsets of {1,...,n}, with an edge placed between any
two...
Fourier series are classically used to construct solutions to
partial differential equations such as the wave and Schrödinger
equations. In Fourier restriction theory, additional conditions are
imposed on the frequencies of these series, giving rise...
The shuffle model is a widely used abstraction for
non-interactive anonymous communication. It allows n parties
holding private inputs x1,…,xn to simultaneously send messages to
an evaluator, so that the messages are received in a random order.
The...
Fourier series are classically used to construct solutions to
partial differential equations such as the wave and Schrödinger
equations. In Fourier restriction theory, additional conditions are
imposed on the frequencies of these series, giving rise...
In Euclidean spaces, star-shaped domains (also known as
Liouville domains) are fundamental objects in modern symplectic
geometry. Several important subclasses have been introduced and
studied, including dynamically convex domains, geometrically...
An important open problem is to classify rational points on all
modular curves, or equivalently to classify the possible adelic
Galois images of elliptic curves over Q, as envisioned in Mazur’s
Program B. However, this problem is inherently infinite...
I will discuss the bulk mechanism of the stringy exclusion
principle in the AdS3/CFT2 case. Consider the duality between
string theory on AdS3 × S3 × M4 and Sym^N(M4). At finite N, both
the chiral-chiral spectrum and the number of the polar terms...
A G-function, in the sense of Siegel, is a power series with
rational coefficients that on the one hand has nice arithmetic
properties (the LCM of the denominators of the first \(n\)
coefficients grows at most exponentially) and on the other
hand...
The nature of mathematical thought has been a central concern in
the development of artificial intelligence since the creation of
the computer in the 1940s. The expansion of AI in the past decade
appears to have sharply reduced the distinction...
Let A be a simple abelian variety, and X and Y be two
subvarieties. We say X and Y are in the Bezout range if \dim X +
\dim Y >= \dim A, and outside of the Bezout range otherwise. It
is known that two varieties in the Bezout range in A always...
