Previous Conferences & Workshops

The recent breakthrough of Limaye, Srinivasan and Tavenas (LST) gave the first super-polynomial lower bounds against low-depth algebraic circuits, for any field of zero (or sufficiently large) characteristic. It was an open question to extend this...

Abstract: I will survey new results on several enumerative problems related to the geometry, topology, and arithmetic of moduli spaces of smooth and stable curves. The enumerative problems include counting isomorphism classes of curves of genus $g$...

Sponsored by Dr. John P. Hempel and the Simons Foundation

Organizers: Paolo Aluffi, Dave Anderson, June Huh, and Leonardo Mihalcea

This workshop was dedicated to the exploration of the combinatorial dimensions of intersection theory and enumerative...

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...

Expressing combinatorial invariants of matroids as intersection numbers on algebraic varieties has become a popular tool in algebraic combinatorics. Several conjectured inequalities among combinatorial data can be traced back to positivity results...

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...

A common heuristic in Diophantine approximation asserts that different arithmetic expansions (such as digit and continued-fraction expansions) should be independent of one another. In some cases, these elementary heuristics have led to surprisingly...

Suppose f is a function with Fourier transform supported on the unit sphere in $R^d$. Elias Stein conjectured in the 1960s that the $L^p$ norm of f is bounded by the $L^p$ norm of its Fourier transform, for any $p> 2d/(d-1)$.  We propose to study...