The ring of symmetric functions has a linear basis of Schur
functions $s_{\lambda}$ indexed by partitions $\lambda = (\lambda_1
\geq \lambda_2 \geq \ldots \geq 0 )$. Littlewood-Richardson
coefficients $c^{\nu}_{\lambda, \mu}$ are the structure...
A remarkable result of Brändén and Huh tells us that volume
polynomials of projective varieties are Lorentzian polynomials. The
dual notion of covolume polynomials was introduced by Aluffi by
considering the cohomology classes of subvarieties of a...
K-theory arose in the 1950s from Grothendieck’s formulation of
the Riemann-Roch theorem – that is, from attempts to calculate
spaces of sections of vector bundles on a variety X via
intersection theory on X. An equivariant version was
introduced...
K-theory arose in the 1950s from Grothendieck’s formulation of
the Riemann-Roch theorem – that is, from attempts to calculate
spaces of sections of vector bundles on a variety X via
intersection theory on X. An equivariant version was
introduced...
In 1999, Pitman and Stanley introduced the polytope bearing
their name along with a study of its faces, lattice points, and
volume. This polytope is well-studied due to its connections to
parking functions, lattice path matroids, generalized...
I will start by a gentle introduction to operadic structures by
drawing a parallel with classical associative structures. Then we
will see how those structures can be applied to matroid theory via
three examples: Chow rings, Orlik--Solomon algebras...
We consider the space of configurations of n points in the
three-sphere $S^3$, some of which may coincide and some of which
may not, up to the free and transitive action of $SU(2)$ on $S^3$.
We prove that the cohomology ring with rational...
Algebraic statistics employs techniques in algebraic geometry,
commutative algebra and combinatorics, to address problems in
statistics and its applications. The philosophy of algebraic
statistics is that statistical models are algebraic
varieties...
The theory of stable polynomials features a key notion called
proper position, which generalizes interlacing of real roots to
higher dimensions. I will show how a Lorentzian analog of proper
position connects the structure of spaces of Lorentzian...
We will present recent applications of enumerative algebra to
the study of stationary states in physics. Our point of departure
are classical Newtonian differential equations with nonlinear
potential. It turns out that the study of their stationary...
