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We suggest a new strategy for proving large $N$ duality by interpreting Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function. For the resolved…
We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…
We exhibit the Kontsevich matrix model with arbitrary potential as a BKP tau-function with respect to polynomial deformations of the potential. The result can be equivalently formulated in terms of Cartan-Pl\"ucker relations of certain…
A previous work of A. Conway and the author introduced $L^2$-Burau maps of braids, which are generalizations of the Burau representation whose coefficients live in a more general group ring than the one of Laurent polynomials. This same…
The twisted Alexander polynomial of a knot is defined associated to a linear representation of the knot group. If there exists a surjective homomorphism of a knot group onto a finite group, then we obtain a representation of the knot group…
Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the \emph{rectangular braid diagram (RBD)} method is proposed to compute the braid monodromy of a completely reducible $n$-gonal curve,…
Using Wilson's Haar basis in $\R^n$, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in $\R^n$. We can then extend "trivially" Beznosova's Bellman function proof of the linear…
A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence…
We consider subgroups of the braid groups which are generated by $k$-th powers of the standard generators and prove that any infinite intersection (with even $k$) is trivial. This is motivated by some conjectures of Squier concerning the…
Building on the approach of Bar-Natan and Van der Veen to universal knot invariants using (perturbed) Gaussian functions, we develop a Gaussian model to compute the Alexander polynomial $\Delta_{\mathcal{K}}(T)$ of an oriented knot…
A stochastic representation for the solutions of the Poisson-Vlasov equation, with several charged species, is obtained. The representation involves both an exponential and a branching process and it provides an intuitive characterization…
Bands with non-trivial topological indices have a topological obstruction preventing them from being represented by exponentially localized Wannier states. Here, we propose a procedure to construct exponentially localized Wannier functions…
In this work, we study the computation of reduction coefficients for multi loop Feynman integrals using generating functions constructed within the Baikov representation. Compared with traditional Feynman rules, the Baikov formalism offers…
Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the…
The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…
The recently introduced concept of $\mathcal{D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from Pausinger \& Svane (J. Complexity, 2014)…
We use the notion of Bridgeland stability condition and its associated metric to endow triangulated categories with extriangulated structures and study their extriangulated Grothendieck groups. This study is motivated by Khovanov-Seidel's…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…
We study certain overlap coefficients appearing in representation theory of the quantum algebra $\U_q(\mathfrak{sl}_2(\C))$. The overlap coefficients can be identified as products of Askey-Wilson functions, leading to an algebraic…