Previous Special Year Seminar

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...

In 2008, looking to bound the face vectors of tropical linear spaces, Speyer introduced the g-invariant of a matroid, defined in terms of exterior powers of tautological bundles on Grassmannians. He proved its coefficients nonnegative for matroids...

Tropical ideals are combinatorial objects that abstract the behavior of the collections of subsets of lattice points that arise as the supports of all polynomials in an ideal. Their structure is governed by a sequence of ‘compatible’ matroids and...

In 2008, looking to bound the face vectors of tropical linear spaces, Speyer introduced the g-invariant of a matroid, defined in terms of exterior powers of tautological bundles on Grassmannians. He proved its coefficients nonnegative for matroids...

Equivariant cohomology was introduced in the 1960s by Borel, and has been studied by many mathematicians since that time.  The talks will be an introduction to some of this work.  We will focus on torus-equivariant cohomology (as well as Borel-Moore...

Equivariant cohomology was introduced in the 1960s by Borel, and has been studied by many mathematicians since that time.  The talks will be an introduction to some of this work.  We will focus on torus-equivariant cohomology (as well as Borel-Moore...