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pro vyhledávání: '"Lam, Thomas"'
Autor:
Lam, Thomas
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 geometry. We develop mathematical formalism to study Cachazo-He-Yuan's scatt
Externí odkaz:
http://arxiv.org/abs/2405.17332
Autor:
Lam, Thomas
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. Our construction is consistent with earlier work of Lukowski, and we
Externí odkaz:
http://arxiv.org/abs/2403.06948
Autor:
Galashin, Pavel, Lam, Thomas
We define monotone links on a torus, obtained as projections of curves in the plane whose coordinates are monotone increasing. Using the work of Morton-Samuelson, to each monotone link we associate elements in the double affine Hecke algebra and the
Externí odkaz:
http://arxiv.org/abs/2307.16794
We show that braid varieties for any complex simple algebraic group $G$ are cluster varieties. This includes open Richardson varieties inside the flag variety $G/B$.
Comment: 29 pages. v2: minor changes
Comment: 29 pages. v2: minor changes
Externí odkaz:
http://arxiv.org/abs/2301.07268
Autor:
Lam, Thomas
The Number Rotation Puzzle (NRP) is a combination puzzle in which the goal is to rearrange a scrambled rectangular grid of numbers back into order via moves that consist of rotating square blocks of numbers of fixed size. Over all possible boards and
Externí odkaz:
http://arxiv.org/abs/2211.16787
Autor:
Lam, Thomas
The second-order singularly-perturbed problem concerns the integral functional $\int_\Omega \varepsilon_n^{-1}W(u) + \varepsilon_n^3\|\nabla^2u\|^2\,dx$ for a bounded open set $\Omega \subseteq \mathbb{R}^N$, a sequence $\varepsilon_n \to 0^+$ of pos
Externí odkaz:
http://arxiv.org/abs/2211.17176
We introduce $3$-dimensional generalizations of Postnikov's plabic graphs and use them to establish cluster structures for type $A$ braid varieties. Our results include known cluster structures on open positroid varieties and double Bruhat cells, and
Externí odkaz:
http://arxiv.org/abs/2210.04778
We study the ring of regular functions on the space of planar electrical networks, which we coin the grove algebra. This algebra is an electrical analogue of the Pl\"ucker ring studied classically in invariant theory. We develop the combinatorics of
Externí odkaz:
http://arxiv.org/abs/2208.12798
Autor:
Lam, Thomas
This short introduction to positive geometries, targeted at a mathematical audience, is based on my talk at OPAC 2022.
Externí odkaz:
http://arxiv.org/abs/2208.05407
Autor:
Galashin, Pavel, Lam, Thomas
We study relations between cluster algebra invariants and link invariants. First, we show that several constructions of positroid links (permutation links, Richardson links, grid diagram links, plabic graph links) give rise to isotopic links. For a s
Externí odkaz:
http://arxiv.org/abs/2208.01175