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--- meetings_spring_2026 [2026/04/07 13:58] – asjensen
+++ meetings_spring_2026 [2026/06/01 22:09] (current) – asjensen
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 | April 1      | **NO MEETING** |  | | |
 | April 8      | Hamilton-Jacobi Equations on Graphs with Applications to Semi-Supervised Learning and Data Depth  | Andrew Jensen | Kansas State University | [[#april_8_|Abstract]] |
-| April 15     |  |  | | |
+| April 15     | The Combined p-Dirichlet and p-Thomson Principles on Planar Maps | Pietro Poggi-Corradini | Kansas State Univeristy | [[#april_15|Abstract]] |
-| April 22     |  |  | | |
+| April 22     | Safety Verification of AI-Enabled Autonomous Systems: A Formal Approach | Lipsy Gupta | Kansas State Univeristy | [[#april_22|Abstract]] |
-| April 29     |  |  | | |
+| April 29     | Geodesic Trees and bi-Lipschitz Embeddings | Manisha Garg | University of Illinois Urbana-Champaign | [[#april_29|Abstract]] |
-| May 6        |  |  | | |
+| May 6        | The Goldfarb-Idnani Approach for Computing Modulus | Nalen Rangarajan | Kansas State University | [[#may_6|Abstract]] |
 ===== Abstracts =====
@@ Line 43: / Line 43: @@
 **"Hamilton-Jacobi Equations on Graphs with Applications to Semi-Supervised Learning and Data Depth", Andrew Jensen**\\
 We will be reading through a paper by Jeff Calder and Mahmood Ettehad discussing how the p-Eikonal Equation on graphs allows one to recover distances on graphs, and in particular p -> infinity recovers shortest-path graph distance. The authors then apply the finding in machine learning contexts. I will briefly share an overview of the paper's results, then the remaining portion of the meeting will be a group discussion on the paper. You can find the paper at https://arxiv.org/abs/2202.08789.
+==== April 15 ====
+**"The Combined p-Dirichlet and p-Thomson Principles on Planar Maps", Pietro Poggi-Corradini**\\
+I will describe how the $p\neq 2$ case can be handled on planar orthodiagonal maps, by introducing a new "combined" energy that takes contributions from both primal and the dual edges.
+==== April 22 ====
+**"Safety Verification of AI-Enabled Autonomous Systems: A Formal Approach", Lipsy Gupta**\\
+As neural networks are increasingly integrated into safety-critical systems such as autonomous vehicles, robots, and aerospace systems, a fundamental question arises: can we prove that such a system will never enter an unsafe state? This talk introduces formal safety verification for neural network-controlled dynamical systems, with reachability analysis as the core technical challenge. We survey verification approaches and note that scalability remains a central challenge. We then present a reduction technique based on approximate bisimilarity that constructs a provably close smaller network from a large one, making verification more tractable. No background in AI or machine learning is assumed.
+==== April 29 ====
+**"Geodesic Trees and bi-Lipschitz Embeddings", Manisha Garg**\\
+A natural question in the bi-Lipschitz geometry of trees is whether a large class of geodesic trees admits a single universal element, that is, a fixed tree into which every member of the class embeds in a bi-Lipschitz manner. Furthermore, Kinnenberg asked if every quasiconformal tree of Assouad dimension < 2 admits a bi-Lipschitz embedding into R^2. Chrontsios-Garitsis, Ioannidis, and Vellis prove that the class of quasiconformal trees with uniform separation can quasisymmetrically embed into a universal element T, and moreover, this T admits a biLipschitz embedding into R^2. In this talk, we will show that such a universal element cannot be found if one replaces quasisymmetric maps with bi-Lipschitz maps, not even in the case of the geodesic trees. This answers a question of the aforementioned authors. This is joint work with Sylvester Eriksson-Bique.
+==== May 6 ====
+**"The Goldfarb-Idnani Approach for Computing Modulus", Nalen Rangarajan**\\
+The Goldfarb-Idnani algorithm is a dual-based method for solving
+quadratic programs in general. Here, we present an overview of the algorithm in the special case that arises in modulus.