Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Banica, Teo"'
Autor:
Banica, Teo
This is an introduction to graph theory, from a geometric and analytic viewpoint. A finite graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, which can be thought of as being a kind of discrete Laplacian, and we first discuss the basics
Externí odkaz:
http://arxiv.org/abs/2406.03664
Autor:
Banica, Teo
This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and of the in
Externí odkaz:
http://arxiv.org/abs/2401.00911
Autor:
Banica, Teo
A closed subgroup $G\subset_uU_N^+$ is called easy when its associated Tannakian category $C_{kl}=Hom(u^{\otimes k},u^{\otimes l})$ appears from a category of partitions, $C=span(D)$ with $D=(D_{kl})\subset P$, via the standard implementation of part
Externí odkaz:
http://arxiv.org/abs/2312.12368
Autor:
Banica, Teo
This is a joint introduction to classical and free probability, which are twin sisters. We first review the foundations of classical probability, notably with the main limiting theorems (CLT, CCLT, PLT, CPLT), and with a look into examples coming fro
Externí odkaz:
http://arxiv.org/abs/2208.07515
Autor:
Banica, Teo
This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which are stable u
Externí odkaz:
http://arxiv.org/abs/2208.03600
Autor:
Banica, Teo
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed volume. We dis
Externí odkaz:
http://arxiv.org/abs/2206.09283
Autor:
Banica, Teo
We work out axioms for the duals $G\subset U_N^+$ of the finite quantum permutation groups, $F\subset S_N^+$ with $|F|<\infty$, and we discuss how the basic theory of such quantum permutation groups partly simplifies in the dual setting. We discuss a
Externí odkaz:
http://arxiv.org/abs/2106.11185
Autor:
Banica, Teo, McCarthy, J. P.
A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting the problem is to understand the structure of the compact quantum groups which can appear as quantum automorphism g
Externí odkaz:
http://arxiv.org/abs/2106.04999
Autor:
Banica, Teo
The partial automorphisms of a graph $X$ having $N$ vertices are the bijections $\sigma:I\to J$ with $I,J\subset\{1,\ldots,N\}$ which leave invariant the edges. These bijections form a semigroup $\widetilde{G}(X)$, which contains the automorphism gro
Externí odkaz:
http://arxiv.org/abs/2105.09886
Autor:
Banica, Teo
This is an introduction to noncommutative geometry, from an affine viewpoint, that is, by using coordinates. The spaces $\mathbb R^N,\mathbb C^N$ have no free analogues in the operator algebra sense, but the corresponding unit spheres $S^{N-1}_\mathb
Externí odkaz:
http://arxiv.org/abs/2012.10973