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18    <title>Research · Michael R. Zeng 曽若凡</title>
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60          <span class="brand__title">Michael R. Zeng 曽若凡</span>
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99  <h2 data-i18n="research.title" id="research">Research</h2>
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101<figure>
102  <img src="/assets/img/spanning%20lines.png" alt="Spanning lines" data-i18n-alt="research.figure.alt" />
103  
104  <figcaption data-i18n="research.figure.caption">A spanning line configuration, made with <a href="https://www.vzome.com/">vZome</a>.
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109<h3 data-i18n="research.interests" id="research-interests">Research Interests</h3>
110
111<p data-i18n="research.intro">I am interested in Schubert calculus, intersection theory on moduli stacks, and enumerative geometry. I am also interested in using machine learning and artificial intelligence to facilitate mathematical discoveries.</p>
112
113<p data-i18n="research.topics">Some of the things I like to think about recently include lines on quartic surfaces, the $K_0$-ring of some moduli stacks, nef divisors on $\overline{\mathscr{M}}_{g,n}$, line bundles of toric varieties, and moduli of stable maps.</p>
114
115<h3 data-i18n="research.publications" id="publications--preprints">Publications &amp; Preprints</h3>
116
117<h4 data-i18n="publications.pure-math">Pure Mathematics</h4>
118<ol reversed="" class="publications">
119  
120  <li>Oriented Cohomology Rings of Some Moduli Spaces via Blowups, with Arkamouli Debnath. 2026. <a href="https://arxiv.org/abs/2604.14536">arXiv:2604.14536</a>.
121</li>
122  
123  <li>The Grothendieck group of the variety of spanning line configurations. 2025. <a href="https://arxiv.org/abs/2512.22769">arXiv:2512.22769</a>.
124</li>
125  
126  <li>$C_p$-Mackey Functors in Macaulay2, with Thomas Brazelton, David Chan, Benjamin Mudrak, Ben Spitz, Chase Vogeli, Chenglu Wang, and Sasha Zotine. 2025. Accepted by <em>Journal of Software for Algebra and Geometry</em>. <a href="https://arxiv.org/abs/2509.05456">arXiv:2509.05456</a>.
127</li>
128  
129  <li>Brackets and Projective Geometry in Macaulay2, with Dalton Bidleman, Timothy Duff, and Jack Kendrick. 2025. <a href="https://arxiv.org/abs/2504.00889">arXiv:2504.00889</a>.
130</li>
131  
132  <li>Appendix in: M. Harada and M. Precup, “Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties.” <em>Osaka Journal of Mathematics</em> <strong>60</strong> (2023), 637–652. <a href="https://arxiv.org/abs/2112.13250">arXiv:2112.13250</a>.
133</li>
134  
135</ol>
136
137<h4 data-i18n="publications.ai-math">AI for Mathematics</h4>
138<ol reversed="" class="publications">
139  
140  <li>Alternating Groups and Embeddings into Groups Invariably Generated by Two Prime-Order Elements, with Ting Gong and Yong Yang. 2026. <a href="https://arxiv.org/abs/2608.00703">arXiv:2608.00703</a>.
141</li>
142  
143  <li>Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration, with Ting Gong and Yong Yang. 2026. <a href="https://arxiv.org/abs/2607.27705">arXiv:2607.27705</a>.
144</li>
145  
146  <li>FactorLibrary: From Polynomials to Circuits via Recursive Subgoals, with Rohan Pandey, Weikun K. Zhang, Kaijie Jin, Na

146omi Morato, Archit Ganapule, Bhaumik Mehta, and Jarod Alper. In <em>3rd AI for Math Workshop (ICML 2026): Toward Self-Evolving Scientific Agents</em>. <a href="https://arxiv.org/abs/2606.25394">arXiv:2606.25394</a> · <a href="https://openreview.net/forum?id=2yIetdPvQh">OpenReview</a>.
147</li>
148  
149  <li>CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning, with Weikun K. Zhang, Rohan Pandey, Bhaumik Mehta, Kaijie Jin, Naomi Morato, Archit Ganapule, and Jarod Alper. In <em>ICLR 2026 Workshop on AI with Recursive Self-Improvement</em>. <a href="https://arxiv.org/abs/2603.17075">arXiv:2603.17075</a>.
150</li>
151  
152</ol>
153
154<h4 data-i18n="publications.ai-languages">AI for Languages</h4>
155<ol reversed="" class="publications">
156  
157  <li>Quantitative Orthographic Analysis of the Ogura Shikishi, with Paul S. Atkins. <em>manuscript cultures</em> <strong>26</strong>.1 (2026), 1–60. <a href="https://doi.org/10.15460/s8e93666">doi:10.15460/s8e93666</a>.
158</li>
159  
160  <li>Jibo-labeled classical hiragana image dataset, with Herman Chau and Paul S. Atkins. Zenodo, 2026. <a href="https://doi.org/10.5281/zenodo.18765466">doi:10.5281/zenodo.18765466</a>.
161</li>
162  
163  <li>Deriving Orthographic Data from Classical Japanese Texts with Machine-Learning Methods, with Herman Chau and Paul Atkins. In <em>Proceedings of IPSJ SIG Computers and the Humanities</em>, 2025. Jinmoncom 2025 Best Paper Award (じんもんこん2025 優秀論文賞) &amp; Student Encouragement Award (学生奨励賞). <a href="https://hdl.handle.net/1773/55355">URI: hdl.handle.net/1773/55355</a>.
164</li>
165  
166</ol>
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