# Poster Session

The following posters will be presented at the poster session on Saturday, April 30th at noon.

## Aaron Kennon (University of California, Santa Barbara), Spin(7)-Manifolds and Multisymplectic Geometry

We utilize Spin(7) identities to prove that the Cayley four-form associated with a torsion-free Spin(7)-structure is non-degenerate in the sense of multisymplectic geometry. Therefore, Spin(7) geometry may be treated as a special case of multisymplectic geometry. We then capitalize on this relationship to make statements about Hamiltonian multivector fields and differential forms associated with torsion-free Spin(7)-structures.

Slides 1.6 MB

## Javier Vega (Universidad Autónoma de Nuevo León), Quantization in 4 minutes

This video has the intention of shortly show the problems with Canonical Quantization and how Geometric Quantization fixes them.

## Abir Bounaama (University of 20 August 1955-Skikda), On the local existence for a quasilinear hyperbolic equation with nonlinear source terms

In this work, we prove by using Faedo Galerkin method the local existence of weak solutions for a quasilinear hyperbolic equation with nonlinear source terms.

## Tahmineh Azizi (Florida State University), Using fractal geometry to classify different data

For the first time in 1983 Mandelbrot introduced ”Fractal” to the world. Fractals are known objects with self-similarity in different scales, i.e., if we look closer at the fractal set, we see a similar geometrical pattern which repeats infinite times to build a fractal object. Mandelbrot fractal geometry could successfully extract mathematical frameworks to model self-similar patterns in nature. Even though a fractal is, by definition, an infinite pattern and cannot be measured, the Koch snowflake lets us see that even though the perimeter of a fractal is infinite, the area is not. The fractal dimension (FD) is a quantitative parameter that has been extensively used to analyze the complexity of structural and functional patterns and it describes a natural object in a better way than Euclidean dimension does. In this study, we will employ the fractal theory to quantify the complexity of different surfaces.

## Xiaobin Li (Southwest Jiaotong University), When Nekrasov partition function meets orientifold 5-plane in the thermodynamic limit

In this talk, I will discuss new dualities appearing in 5d N = 1 Sp(N) gauge theory with N_f (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, I will introduce Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, I will briefly explain the computations about the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, the corresponding Seiberg-Witten curve and boundary conditions are derived and the relations with the prepotential in terms of the cycle integrals are discussed. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities. This is joint work with Futoshi Yagi.