Related papers: A Macdonald refined topological vertex
Let $ L((T^{-1}))$ be the space of (inverse) Laurent serieswith coefficients in some field $L$. It has a standard degree map and the induced topology. With its usual addition and a new product on this space which is continuous and preserves…
This paper investigates functions from $\mathbb{R}^d$ to $\mathbb{R} \cup \{\pm \infty\}$ that satisfy axioms of linearity wherever allowed by extended-value arithmetic. They have a nontrivial structure defined inductively on $d$, and…
We compute the motivic Donaldson-Thomas theory of the resolved conifold, in all chambers of the space of stability conditions of the corresponding quiver. The answer is a product formula whose terms depend on the position of the stability…
Motivated by recent results of Tao-Ziegler [Discrete Anal. 2016] and Greenfeld-Tao (2022 preprint) on concatenating affine-linear functions along subgroups of an abelian group, we show three results on recovering affine-linearity of…
We construct the generalized $\beta$ and $(q,t)$-deformed partition functions through $W$ representations, where the expansions are respectively with respect to the generalized Jack and Macdonald polynomials labeled by $N$-tuple of Young…
An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold $\alpha>0$ such that $|\Delta(E)| \gtrsim q$ whenever $|E| \gtrsim q^{\alpha}$, where $E \subset {\Bbb F}_q^d$, the $d$-dimensional vector…
Let V be a plane smooth cubic curve over a finitely generated field k. The Mordell-Weil theorem for V states that there is a finite subset P \subset V(k) such that the whole V(k) can be obtained from P by drawing secants and tangents…
Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q =…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
The extended coset leader weight enumerator of the generalized Reed-Solomon $[q + 1, q - 3, 5]_q$ code is computed. The computation is considered as a question in finite geometry. For this we need the classification of the points, lines and…
We revisit Maxwell theory in 4d with a boundary, with particular attention to the global properties of the boundary conditions, both in the free (topological) and interacting (conformal) cases. We analyze the fate of Wilson-'t Hooft lines,…
Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…
We consider a semi-algebraic function defined on a closed semi-algebraic set X. We give formulas relating the topology of X to the indices of the critical points of the function and to the topological behavior of the function at infinity.…
Topological matter in 3D is characterized by the presence of a topological BF term in its long-distance effective action. We show that, in 3D, there is another marginal term that must be added to the action in order to fully determine the…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic…
In this paper, we study the critical case of the Allard regularity theorem. Combining with Reifenberg's topological disk theorem, we get a critical Allard-Reifenberg type regularity theorem. As a main result, we get the topological…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…