7 papers · 1 filter
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…
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…
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…
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…
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.…