Mathematician Hel Braun, Member (1947–1948) in the School of
Mathematics, left a remarkable legacy, despite facing formidable
challenges. While Braun's mathematical contributions remain
important, her story has been mostly forgotten. In this talk...
Tropical geometry is a modern degeneration technique in
algebraic geometry. Think of it as a very drastic degeneration in
which one associates a limiting object to a family of algebraic
varieties that is entirely combinatorial. I will
introduce...
Matroids are combinatorial structures that model independence,
such as that of edges in a graph and vectors in a linear space. I
will introduce the theory of matroids along with their surprising
connection to a class of multivariate polynomials that...
We show that certain colored-matching numbers fit into a
Lorentzian polynomial. We achieve this via methods arising
from the two featured topics of the workshop: the
tropical geometry of compactifications and the convex geometry of
degrees of...
Tropical geometry is a modern degeneration technique in
algebraic geometry. Think of it as a very drastic degeneration in
which one associates a limiting object to a family of algebraic
varieties that is entirely combinatorial. I will
introduce...
Matroids are combinatorial structures that model independence,
such as that of edges in a graph and vectors in a linear space. I
will introduce the theory of matroids along with their surprising
connection to a class of multivariate polynomials that...
One can associate an HDHF (symmetric) wrapped Fukaya category to
a Liouville domain by counting higher genus curves, which are
required to be branched covers. For the cotangent bundle of an
orientable surface with genus at least one Honda, Tian, and...
We propose and study a new arithmetic invariant of
non-hyperelliptic genus-4 curves: a canonical “quadratic” point on
the Jacobian, defined by the two natural degree-2 maps to
projective lines. Building on Xue’s result, that this point
is...
The Khovanskii-Teissier inequality provides the fundamental
log-concavity property of intersection numbers of divisors of
algebraic varieties, extending the Alexandrov-Fenchel inequality of
convex geometry. In this talk I will explain, and attempt...
For a complex elliptic curve E and a point p of order n on it,
the images of the points pk=kp under the Weierstrass embedding of E
into CP2 are collinear if and only if the sum of indices is
divisible by n. We prove that for n at least 10 a...
