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Reflection Representations of Coxeter Groups and Homology of Coxeter Graphs
We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These...
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Geometric analysis of the generalized surface quasi-geostrophic equations
We investigate the geometry of a family of equations in two dimensions which interpolate between the Euler equations of ideal hydrodynamics and the...
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Introduction to Geometric Algebra
Geometric algebra was initiated by W.K. Clifford over 140 years ago. It unifies all branches of physics, and has found rich applications in robotics,...
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Deformation of Rigid Conjugate Self-dual Galois Representations
In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a...
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Morphing Triangle Contact Representations of Triangulations
A morph is a continuous transformation between two representations of a graph. We consider the problem of morphing between contact representations of...
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Differential Operator Approach to ıquantum Groups and Their Oscillator Representations
For a quasi-split Satake diagram, we define a modified q -Weyl algebra, and show that there is an algebra homomorphism between it and the...
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Representations of Various Power Sums
We give new representations of various power sums, including the signed/alternating sum of powers of consecutive integers as well as odd numbers. The...
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Birational Maps to Grassmannians, Representations and Poset Polytopes
We study the closure of the graph of the birational map from a projective space to a Grassmannian. We provide explicit description of the graph...
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Discrete Weierstrass-Type Representations
Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We...
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Irreducible Representations of GLn(ℂ) of Minimal Gelfand–Kirillov Dimension
In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of G ...
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Linear periods for unitary representations
Let F be a local non-Archimedean field of characteristic zero with a finite residue field. Based on Tadić’s classification of the unitary dual of
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Variational representations of annealing paths: Bregman information under monotonic embedding
Markov chain Monte Carlo methods for sampling from complex distributions and estimating normalization constants often simulate samples from a...
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Scalable enforcement of geometric non-interference constraints for gradient-based optimization
Many design optimization problems include constraints to prevent intersection of the geometric shape being optimized with other objects or with...
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Geometric variations of local systems and elliptic surfaces
Geometric variations of local systems are families of variations of Hodge structure; they typically correspond to fibrations of Kähler manifolds for...
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Relatively dominated representations from eigenvalue gaps and limit maps
Relatively dominated representations give a common generalization of geometrically finiteness in rank one on the one hand, and the Anosov condition...
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Basic Ideas of Geometric Sampling
Most of the material in Chapter 1 is concerned with integral-geometric formulae for motion-invariant...
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Littlewood-Richardson rule for generalized Schur Q-functions
Littlewood-Richardson rule gives the expansion formula for decomposing a product of two Schur functions as a linear sum of Schur functions, while the...