1 citations · 2 across the 8 of their papers we have counts for
9 papers
Dual Lattice Functions of Polytopes
Yibo Gao, Thomas Lam, Lei Xue
We define the dual lattice function of a rational polytope via the discrete Laplace transform of the exponential of its support function. This definition is a discrete analogue…
Combinatorial invariance for the coefficient of in Kazhdan-Lusztig polynomials
Grant T. Barkley, Christian Gaetz, Thomas Lam
We prove the combinatorial invariance of the coefficient of in Kazhdan--Lusztig polynomials for arbitrary Coxeter groups. As a result, we obtain the Combinatorial Invariance Co…
The combinatorial geometry of particle physics
Thomas Lam
Recent breakthroughs in the study of scattering amplitudes have uncovered profound and unexpected connections with combinatorial geometry. These connections range from classical st…
Canonical forms of oriented matroids
Christopher Eur, Thomas Lam
Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full-dimensional projecti…
Matroids and amplitudes
Thomas Lam
In the 1990s, Kita--Yoshida and Cho--Matsumoto introduced intersection forms on the twisted (co)homologies of hyperplane arrangement complements. We give a closed combinatorial for…
Dual Mixed Volume
Yibo Gao, Thomas Lam, Lei Xue
We define and study the dual mixed volume rational function of a sequence of polytopes, a dual version of the mixed volume polynomial. This concept has direct relations to the adjo…
Moduli spaces in positive geometry
Thomas Lam
These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M_{0,n} of n distinct points on P^1 as a positive geometry and a binary geomet…
On the face stratification of the amplituhedron
Thomas Lam
We define and study the face stratification of the m=2 amplituhedron. We show that the face poset is an upper order ideal in the face poset of the totally nonnegative Grassmannian.…
Likelihood Degenerations
Daniele Agostini, Taylor Brysiewicz, Claudia Fevola +3
Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points…