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--- meetings_spring_2026 [2026/03/16 04:37] – asjensen
+++ meetings_spring_2026 [2026/06/01 22:09] (current) – asjensen
@@ Line 10: / Line 10: @@
 | March 11     | **NO MEETING** |  |  |  |
 | March 18     | **NO MEETING** | | | |
-| March 25     |  |  | | |
+| March 25     | **NO MEETING** |  | | |
-| April 1      |  |  | | |
+| April 1      | **NO MEETING** |  | | |
-| April 8      |  |  | | |
+| 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 39: / Line 39: @@
 **"Modulus of Families of Lipschitz Chains with Arbitrary Dimension and Codimension", Andrew Jensen**\\
 Recently, Lohvansuu (2023) introduced the p-modulus for families of k-dimensional Lipschitz chains and their dual families of (n-k)-dimensional chains. While he established an upper bound for the duality of these families on Lipschitz cubes, the corresponding lower bound remained an open question. Subsequently, Kangasniemi and Prywes (2025) developed dMod, a related notion of modulus based on differential forms, and successfully established a full duality result. In this talk, I will explore the implications of these developments and discuss related open problems.
+==== April 8 ====
+**"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.