张峻铭 Junming Zhang

张峻铭 Junming Zhang

相声/京剧/古典音乐 爱好者

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portfolio

preprints

Compact Relative $\mathrm{SO}_0(2,q)$-Character Varieties of Punctured Spheres

Preprinted in arxiv:2309.15553, 2023

We prove that there are some relative $\mathrm{SO}_0(2,q)$-character varieties of the punctured sphere which are compact, totally elliptic and contain a dense representation. This work fills a remaining case of the results of N. Tholozan and J. Toulisse. Our approach relies on the utilization of the non-Abelian Hodge correspondence and we study the moduli space of parabolic $\mathrm{SO}_0(2,q)$-Higgs bundles with some fixed weight. Additionally, we provide a construction based on Geometric Invariant Theory (GIT) to demonstrate that such moduli space we find can be viewed as a projective variety over $\mathbb{C}$.

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Non-maximal Anosov Representations from Surface Groups to $\mathrm{SO}_0(2,3)$

Preprinted in arxiv:2406.08118, 2024

We prove the representation given by a stable $\alpha_1$-cyclic parabolic $\mathrm{SO}_0(2,3)$-Higgs bundle through the non-Abelian Hodge correspondence is ${\alpha_2}$-almost dominated. This is a generalization of Filip’s result on weight $3$ variation of Hodge structures and answers a question asked by Collier, Tholozan and Toulisse.

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publications

A Nontrivial Point on the Isogonal Pivotal Cubic with Pivot on the Circumcircle

Published in International Journal of Geometry, 2022

It’s well-known that the nine-point center $X(5)$ and its isogonal conjugate point, Kosnita point $X(54)$, lie on the isogonal pivotal cubic $K316$ with pivot Euler reflection point $X(110)$. In this article we generalize this result to any isopivotal cubic with pivot on the circumcircle to find a nontrivial point on it.

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talks

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

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Teaching experience 2

Workshop, University 1, Department, 2015

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