Jet schemes and their applications in singularities, toric resolutions and integer partitions
H Mourtada - Handbook of Geometry and Topology of Singularities …, 2023 - Springer
After a brief introduction to jet schemes, this article surveys their applications in singularity
theory (Nash problem, motivic integration, birational geometry, jet components graph …
theory (Nash problem, motivic integration, birational geometry, jet components graph …
Exact Operator Map from Strong Coupling to Free Fields: Beyond Seiberg-Witten Theory
In quantum field theory above two spacetime dimensions, one is usually only able to
construct exact operator maps from UV to IR of strongly coupled renormalization group flows …
construct exact operator maps from UV to IR of strongly coupled renormalization group flows …
Some remarks on associated varieties of vertex operator superalgebras
H Li - European Journal of Mathematics, 2021 - Springer
We study several families of vertex operator superalgebras from a jet (super) scheme point
of view. We provide new examples of vertex algebras which are “chiral-quantizations" of …
of view. We provide new examples of vertex algebras which are “chiral-quantizations" of …
Looking for a new version of Gordon's identities
P Afsharijoo - Annals of Combinatorics, 2021 - Springer
We give a commutative algebra viewpoint on Andrews recursive formula for the partitions
appearing in Gordon's identities, which are a generalization of Rogers–Ramanujan …
appearing in Gordon's identities, which are a generalization of Rogers–Ramanujan …
Multiplicity structure of the arc space of a fat point
R Ait El Manssour, G Pogudin - Algebra & Number Theory, 2024 - msp.org
The equation xm= 0 defines a fat point on a line. The algebra of regular functions on the arc
space of this scheme is the quotient of k [x, x′, x (2),…] by all differential consequences of …
space of this scheme is the quotient of k [x, x′, x (2),…] by all differential consequences of …
Wronskians form the inverse system of the arcs of a double point
RAE Manssour, G Pogudin - arXiv preprint arXiv:2405.08964, 2024 - arxiv.org
The ideal of the arc scheme of a double point or, equivalently, the differential ideal
generated by the ideal of a double point is a primary ideal in an infinite-dimensional …
generated by the ideal of a double point is a primary ideal in an infinite-dimensional …
An Bailey tree and Rogers-Ramanujan-type identities
SO Warnaar - arXiv preprint arXiv:2303.09069, 2023 - arxiv.org
The $\mathrm {A} _2 $ Bailey chain of Andrews, Schilling and the author is extended to a
four-parameter $\mathrm {A} _2 $ Bailey tree. As main application of this tree, we prove the …
four-parameter $\mathrm {A} _2 $ Bailey tree. As main application of this tree, we prove the …
Matrix factorizations and -quantum invariants
A Oblomkov, L Rozansky - arXiv preprint arXiv:2212.02665, 2022 - arxiv.org
arXiv:2212.02665v1 [math.GT] 5 Dec 2022 Page 1 arXiv:2212.02665v1 [math.GT] 5 Dec 2022
MATRIX FACTORIZATIONS AND glpm|kq-QUANTUM INVARIANTS A. OBLOMKOV AND L …
MATRIX FACTORIZATIONS AND glpm|kq-QUANTUM INVARIANTS A. OBLOMKOV AND L …
Graph schemes, graph series, and modularity
K Bringmann, C Jennings-Shaffer, A Milas - Journal of Combinatorial …, 2023 - Elsevier
To a simple graph we associate a so-called graph series, which can be viewed as the
Hilbert–Poincaré series of a certain infinite jet scheme. We study new q-representations and …
Hilbert–Poincaré series of a certain infinite jet scheme. We study new q-representations and …
Cycles and paths in digraphs, monomial ideals and integer partitions
Z Mohsen - 2022 - hal.science
In this thesis, we work in two directions, both concerning problems in combinatorics. The first
direction is related to the study of an important invariant of oriented graphs which is the …
direction is related to the study of an important invariant of oriented graphs which is the …