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Gytis Gytis 1 1 silver badge 7 7 bronze badges. I was losing the hope for an answer : It is very useful and also thank you for the great amount of references!

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Unicorn Meta Zoo 9: How do we handle problem users? Related 7. Hot Network Questions. Question feed. Much of my research involves the study of relationships between the worldsheet geometry of CFT and SCFT and properties of the algebras of correlation functions of the particle interactions.

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For genus-zero holomorphic CFT these algebras are called vertex operator algebras. In addition to being a physical model for particle interactions, vertex operator superalgebras have important and deep links to the theory of finite simple groups, number theory, topology, etc. My research often also touches upon or has applications to such other branches of mathematics.

Selected Publications updated :. Barron and N. Vander Werf, Permutation-twisted modules for even order cycles acting on tensor product vertex operator superalgebras , Internat. Barron, Twisted modules for tensor product vertex operator superalgebras and permutation automorphisms of odd order , in: "Proceedings of the Southeastern Lie Theory Workshop Series ", ed. Misra, D. Nakano and B.

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Parshall, Conf. Series of the AMS, Burdik, O. This shape is shown below. This is shown below. Parabolas have several recognizable features that characterize their shape and placement on the Cartesian plane.

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One important feature of the parabola is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.

In either case, the vertex is a turning point on the graph. Parabolas also have an axis of symmetry, which is parallel to the y-axis. The axis of symmetry is a vertical line drawn through the vertex. The y -intercept is the point at which the parabola crosses the y -axis. There cannot be more than one such point, for the graph of a quadratic function.

Vertex Algebras and Algebraic Curves: Second Edition page 1

The x -intercepts are the points at which the parabola crosses the x -axis. Recall that if the quadratic function is set equal to zero, then the result is a quadratic equation.

The solutions to the equation are called the roots of the function. Describe the solutions to a quadratic equation as the points where the parabola crosses the x-axis. The roots of a quadratic function can also be found graphically by making observations about its graph. These are two different methods that can be used to reach the same values, and we will now see how they are related.