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On the distribution of Alexander polynomials in certain families of closed braids
We study the distribution of arithmetic invariants associated to Alexander polynomials for certain infinite families of links. The families of links...
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Twisted Alexander modules of hyperplane arrangement complements
We study torsion properties of the twisted Alexander modules of the affine complement M of a complex essential hyperplane arrangement, as well as...
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Time Rescaling of a Primal-Dual Dynamical System with Asymptotically Vanishing Dam**
In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by a second-order...
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Dual optimization approach to set invariance conditions for discrete-time dynamic systems
Positively invariant set is a key concept in dynamic systems. Positive invariance condition of convex set for discrete-time dynamic systems is...
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Decentralized Strongly-Convex Optimization with Affine Constraints: Primal and Dual Approaches
Decentralized optimization is a common paradigm used in distributed signal processing and sensing as well as privacy-preserving and large-scale...
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Constructions of Quandles over Groups and Rings
We present the following constructions: extension of a trivial quandle by a group with a nontrivial abelian subgroup, a quandle over a noncommutative...
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Control Problems for Hamilton-Jacobi Equations Co-authored by Alexander Keimer
In this chapter, we introduce Hamilton-Jacobi PDEs. These PDEs are related to conservation laws and their solutions are the anti-derivative (in...
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Twisted Neumann–Zagier matrices
The Neumann–Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra...
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Duality in Toric Topology
We characterise integral Poincaré duality moment-angle complexes...
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Homology Groups and Ideal Class Groups III: Asymptotic Formulas
As we discussed in Chap. 10 , there is a group-theoretic analogy between the knot module associated to the...
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Philosophical and mathematical duality in Albert Lautman’s work
The terms “duality” and “dual” appear repeatedly in the writings of the mathematical philosopher and World War II French Resistance fighter Albert...
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Ringel Duality for Extended ZigZag Schur Algebra
Extended zigzag Schur algebras are quasi-hereditary algebras which are conjecturally Morita equivalent to RoCK blocks of classical Schur algebras. We...
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On Decentralized Nonsmooth Optimization
In decentralized optimization, several nodes connected by a network collaboratively minimize some objective function. For minimization of Lipschitz...
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Edge Chromatic Number of a Graph
We can assign a color to each edge of a graph instead of its vertices. This gives birth to the following notion:
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Goeritz and Seifert Matrices
In this lecture, we present two classical concepts introduced in the 1930s: the Goeritz matrix and the Seifert matrix. The first is constructed using...