39 lines
1.8 KiB
HTML
39 lines
1.8 KiB
HTML
<section id="research">
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<h2>Research</h2>
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<p>My research is in geometric group theory, with interests in right-angled Coxeter groups and rewriting systems.</p>
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<h3>Selected Publications</h3>
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<div class="publication-entry">
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<p class="title">Gilman's Conjecture</p>
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<p class="description">Joint with Adam Piggott. We resolve a conjecture made by Robert Gilman in 1984, showing
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that any group presented by a finite, monadic, confluent rewriting system must be a plain group.</p>
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<p class="venue">J. Algebra 517 (2019), 167--185.</p>
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<p class="links">
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<a href="https://arxiv.org/abs/1806.06155">arXiv</a>
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</p>
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</div>
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<div class="publication-entry">
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<p class="title">CAT(0) Extensions of Right-Angled Coxeter Groups</p>
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<p class="description">Joint with Charlie Cunningham, Adam Piggott, and Kim Ruane. We show that any split
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extension of a right-angled Coxeter group by a generating automorphism of finite order acts faithfully and
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geometrically on a CAT(0) metric space.</p>
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<p class="venue">Topol. Proc., 48 (2016), 277-287.</p>
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<p class="links">
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<a href="https://arxiv.org/abs/1508.05403">arXiv</a>
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</p>
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</div>
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<div class="publication-entry">
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<p class="title">Recognizing Right-Angled Coxeter Groups Using Involutions</p>
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<p class="description">Joint with Charlie Cunningham, Adam Piggott, and Kim Ruane. We discuss a new method for
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constructing candidate right-angled Coxeter presentations for a given group, and we apply this method to
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some first examples.</p>
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<p class="venue">Pacific J. Math. 248 (2016), no. 1, 41-77.</p>
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<p class="links">
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<a href="https://arxiv.org/abs/1410.4589">arXiv</a>
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</p>
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</div>
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</section> |