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people:dobbins:papers_title_only [2021/08/31 15:11]
dobbins
people:dobbins:papers_title_only [2021/09/08 12:17] (current)
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-**
-Publications:​
-**
-
-{{:​people:​dobbins:​realizability_of_polytopes_as_a_low_rank_matrix_completion_problem.pdf| Realizability of polytopes as a low rank matrix completion problem}}
-
-{{:​people:​dobbins:​weight_balancing_on_boundaries_and_skeletons.pdf| Weight balancing on boundaries and skeletons}}
-
-{{:​people:​dobbins:​the_erdos-szekeres_problem_for_non-crossing_convex_sets.pdf| The Erdős-Szekeres
-problem for non-crossing convex sets}}

{{:​people:​dobbins:​a_point_in_a_nd-polytope_is_the_barycenter_of_n_points_in_its_d-faces.pdf| A point in a nd-polytope is the barycenter of n points in its d-faces}} {{:​people:​dobbins:​a_point_in_a_nd-polytope_is_the_barycenter_of_n_points_in_its_d-faces.pdf| A point in a nd-polytope is the barycenter of n points in its d-faces}}

-{{:people:​dobbins:​the_shadows_of_a_cycle_cannot_all_be_paths.pdf| The shadows ​of a cycle cannot all be paths}}+[[https://arxiv.org/pdf/2108.02134A strong equivariant deformation retraction from the homeomorphism group of the projective plane to the special orthogonal group]]

-{{:people:​dobbins:​regular_systems_of_paths_and_families_of_convex_sets_in_convex_position.pdf| Regular systems of +[[https://arxiv.org/pdf/1908.02213|
-paths and families of convex sets in convex position}}+A Universality Theorem for Nested Polytopes.
+]]

{{:​people:​dobbins:​antiprismlessness.pdf| Antiprismlessness,​ or: Reducing combinatorial equivalence to {{:​people:​dobbins:​antiprismlessness.pdf| Antiprismlessness,​ or: Reducing combinatorial equivalence to
projective equivalence in realizability problems for polytopes}} projective equivalence in realizability problems for polytopes}}
+
+[[https://​arxiv.org/​pdf/​1809.01613| Barycenters of points in polytope skeleta]]
+
+[[https://​arxiv.org/​pdf/​2106.08907| Continuous dependence of curvature flow on initial conditions]]
+
+{{:​people:​dobbins:​grassmannians_and_pseudosphere_arrangements.pdf| Grassmannians and pseudosphere arrangements}}
+
+{{:​people:​dobbins:​packing_segments_in_a_convex_3-polytope_is_np-hard.pdf|
+Packing segments in a convex 3-polytope is NP-hard. ​
+}}
+
+{{:​people:​dobbins:​realizability_of_polytopes_as_a_low_rank_matrix_completion_problem.pdf| Realizability of polytopes as a low rank matrix completion problem}}

{{:​people:​dobbins:​realization_spaces_of_arrangements_of_convex_bodies.pdf| Realization spaces of arrangements of convex bodies}} {{:​people:​dobbins:​realization_spaces_of_arrangements_of_convex_bodies.pdf| Realization spaces of arrangements of convex bodies}}

-{{:​people:​dobbins:​the_number_of_holes_in_the_union_of_translates_of_a_convex_set_in_three_dimensions.pdf| The number +{{:​people:​dobbins:​realization_spaces_of_arrangements_of_convex_bodies_socg_.pdf|
-of holes in the union of translates of a convex ​set in three dimensions}}+Realization spaces ​of arrangements ​of convex ​bodies (SoCG)}}

-[[https://arxiv.org/pdf/1712.05142∀∃R-completeness ​and area-universality]]+{{:people:​dobbins:​regular_systems_of_paths_and_families_of_convex_sets_in_convex_position.pdf| Regular systems of
+paths and families of convex sets in convex position}}

-[[https://arxiv.org/pdf/1809.01613Barycenters of points in polytope skeleta]]+{{:people:​dobbins:​the_erdos-szekeres_problem_for_non-crossing_convex_sets.pdf| The Erdős-Szekeres
+problem for non-crossing convex sets}}

{{:​people:​dobbins:​the_inverse_kakeya_problem.pdf| The inverse Kakeya problem}} {{:​people:​dobbins:​the_inverse_kakeya_problem.pdf| The inverse Kakeya problem}}

-{{:​people:​dobbins:​grassmannians_and_pseudosphere_arrangements.pdf| Grassmannians and pseudosphere arrangements}}+{{:​people:​dobbins:​the_number_of_holes_in_the_union_of_translates_of_a_convex_set_in_three_dimensions.pdf| The number
+of holes in the union of translates of a convex set in three dimensions}}

-** +{{:people:​dobbins:​the_number_of_holes_in_the_union_of_translates_of_a_convex_set_in_three_dimensions_socg_.pdf|
-Submitted for publication+The number
-**+of holes in the union of translates of a convex set in three dimensions (SoCG)}}

-[[https://arxiv.org/pdf/2106.08907Continuous dependence ​of curvature flow on initial conditions]]+{{:people:​dobbins:​the_shadows_of_a_cycle_cannot_all_be_paths.pdf| The shadows ​of a cycle cannot all be paths}}

-[[https://arxiv.org/pdf/2108.02134A strong equivariant deformation retraction from the homeomorphism group of the projective plane to the special orthogonal group]]+{{:people:​dobbins:​weight_balancing_on_boundaries_and_skeletons.pdf| Weight balancing on boundaries and skeletons}}

+[[https://​arxiv.org/​pdf/​1712.05142| ∀∃R-completeness and area-universality]]

-**
-Other papers (unreviewed):​
-**

-
-{{:​people:​dobbins:​packing_segments_in_a_convex_3-polytope_is_np-hard.pdf|
-Packing segments in a convex 3-polytope is NP-hard. ​
-}}
-
-[[https://​arxiv.org/​pdf/​1908.02213| ​
-A Universality Theorem for Nested Polytopes.
-]]