Коданева Надежда Михайловна
Факультет экономических наук
Профессиональные интересы
Должности
- Преподаватель — Факультет экономических наук, Департамент математики
- Стажер-исследователь — Факультет математики, Международная лаборатория кластерной геометрии
Био
- · Начала работать в НИУ ВШЭ в 2019 году.
Образование
- 2021 · Магистратура: Национальный исследовательский университет "Высшая школа экономики", специальность «Математика», квалификация «Магистр»
- 2019 · Бакалавриат: Национальный исследовательский университет "Высшая школа экономики", специальность «Прикладная математика», квалификация «Бакалавр»
Опыт работы
- · 2019: НИУ ВШЭ (октябрь наст. время)
Публикации (4)
The universal gl-weight system and the chromatic polynomial
2026 · ARTICLE · en
Weight systems associated to the Lie algebras 𝔤𝔩(N) for N = 1,2,... can be unified into auniversal one. The construction is based on an extension of the 𝔤𝔩(N) weight systems to permutations. This universal weight system takes values in the algebra of polynomials C[N;C1,C2,...] in infinitely many variables. We show that under the substitution Cm = xNm−1, m = 1,2,..., the leading term in N of the value of the universal 𝔤𝔩 weight system becomes the chromatic polynomial of the intersection graph of the chord diagram. Moreover, we show that under the substitution Cm = pmNm−1, m = 1,2,..., the leading term in N of the value of the universal 𝔤𝔩-weight system determines a filtered Hopf algebra homomorphism from the rotational Hopf algebra of permutations, which we construct in the present paper, to the Hopf algebra of polynomials C[p1,p2,...].
Polynomial graph invariants induced from the gl-weight system
2025 · ARTICLE · en
Weight systems are functions on chord diagrams satisfying so-called Vassiliev’s 4-term relations. They are closely related to finite type knot invariants, see [31 Certain weight systems can be derived from graph invariants, see a recent account in [19]. Another main source of weight systems are Lie algebras, the construction due to D. Bar-Natan [3] and M. Kontsevich [22]. In recent papers [19,33], the weight systems associated to the Lie algebras gl(N), N = 1, 2, 3,... , were unified in a universal gl-weight system, whi takes values in the ring C[N, C1, C2, C3,...] of polynomials in infinitely many variables. Note that this weight system associated [30] to the HOMFLYPT polynomial, which is an important and powerful knot invariant. The unification has be achieved by extending the gl(N)-weight systems from chord diagrams, which can be considered as involutions without fixed points modulo cyclic shifts, to arbitrary permutations. Similarly to the case of chord diagrams, the extended function on permutations is invariant under their cyclic shifts. The main goal of the extension was to produce an efficient way to compute explicitly the values of the gl(N)-weight systems, and a recurrence relation for such a computation, which works for permutations rather than just for chord diagrams is given in [33]. A natural question then arises, namely, which already known weight systems can be obtained from the universal glweight system. In addition to understanding the internal relationship between weight systems, knowing that a given weight system can be induced from the gl-weight system would immediately lead to extending the former to arbitrary permutations. It is also interesting whether the universal gl-weight system is related to integrable hierarchies of partial differential equations in a way similar to umbral polynomial graph invariants [11,18].
Многочлен переплетений бинарных дельта-матроидов и инварианты зацеплений
2025 · ARTICLE · ru
В этой работе изучен многочлен переплетений как обобщение инварианта графов на дельта-матроиды. Доказано, что многочлен переплетений удовлетворяет четырехчленному соотношению для дельта-матроидов и, следовательно, является инвариантом зацеплений в трехмерной сфере. Также с помощью многочлена переплетений дана нижняя оценка размерности алгебры Хопфа бинарных дельта-матроидов, профакторизованных по четырехчленным соотношениям
The interlace polynomial of binary delta-matroids and link invariants
2019 · PREPRINT · en
In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and determines thus a finite type invariant of links in the 3-sphere.
Курсы (2)
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Дискретная математика · 3 раза
2025/2026, 2024/2025, 2023/2024 · Бакалавриат · рус
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Дискретная математика и теория алгоритмов
2021/2022 · Бакалавриат · рус