While the vast majority of the light from our galaxy comes from
the Galactic disk, the vast majority of the mass of the Milky Way
(MW) is in its dark matter halo. Because we cannot directly observe
the MW's dark matter halo, we must use luminous...
A cornerstone result in geometry is the Szemerédi–Trotter
theorem, which gives a sharp bound on the maximum number of
incidences between m points and n lines in the real plane. A
natural generalization of this is to consider
point-hyperplane...
Triangulated surfaces are Riemann surfaces formed by gluing
together equilateral triangles. They are also the Riemann surfaces
defined over the algebraic numbers. Brooks, Makover, Mirzakhani and
many others proved results about the geometric...
In this talk, I will discuss lower bounds for a certain
set-multilinear restriction of algebraic branching programs. The
significance of the lower bound and the model is underscored by the
recent work of Bhargav, Dwivedi, and Saxena (2023), which...
In this talk I will discuss holographic duals of topological
operators. At low energy sugra, they can be realized by Page
charge associated to Gauss law constraints. In the UV string
theory, topological operators can be characterized by
various...
Recent observations reveal that cosmic rays (CRs) are more
tightly confined in various astrophysical systems (e.g. radio
bubbles) than current theories predict. I show that microscale
magnetic fluctuations, particularly from the mirror
instability...
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...
Quantum critical points usually separate two distinct phases of
matter. Here I will discuss a class of "unnecessary" quantum
critical points that lie within a single phase of matter (much like
the liquid-gas transition, except that they are...
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...
