Zobrazeno 1 - 10
of 218
pro vyhledávání: '"WILLIAMSON, GEORDIE"'
We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a classical search algorithm is used to produce many desirable constructions
Externí odkaz:
http://arxiv.org/abs/2411.00566
Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead to interest
Externí odkaz:
http://arxiv.org/abs/2408.00949
We introduce a new algorithm for finding kernel elements in the Burau representation. Our algorithm applies reservoir sampling to a statistic on matrices which is closely correlated with Garside length. Using this we exhibit an explicit kernel elemen
Externí odkaz:
http://arxiv.org/abs/2310.02403
Autor:
Hone, Chris, Williamson, Geordie
We prove that the derived direct image of the constant sheaf with field coefficients under any proper map with smooth source contains a canonical summand. This summand, which we call the geometric extension, only depends on the generic fibre. For res
Externí odkaz:
http://arxiv.org/abs/2309.11780
Autor:
Williamson, Geordie
A personal and informal account of what a pure mathematician might expect when using tools from deep learning in their research.
Comment: 16 pp, v2: clarified some points, final version
Comment: 16 pp, v2: clarified some points, final version
Externí odkaz:
http://arxiv.org/abs/2304.12602
Autor:
Coulembier, Kevin, Williamson, Geordie
We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a bijection wi
Externí odkaz:
http://arxiv.org/abs/2206.05867
We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke category inside
Externí odkaz:
http://arxiv.org/abs/2204.04924
Publikováno v:
Represent. Theory 26 (2022), 1145-1191
Kazhdan-Lusztig polynomials are important and mysterious objects in representation theory. Here we present a new formula for their computation for symmetric groups based on the Bruhat graph. Our approach suggests a solution to the combinatorial invar
Externí odkaz:
http://arxiv.org/abs/2111.15161
Autor:
Romanov, Anna, Williamson, Geordie
These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introduction to the Langlands correspondence from an arithmetical point of vi
Externí odkaz:
http://arxiv.org/abs/2103.02329