Welcome to the Good Vibes Corner Office Website!

The Good Vibes Corner Office is a corner of the BARC offices inhabited by Christian Bertram, Théo Borém Fabris, and Mads Vestergaard Jensen. Please consider visiting us in person! We will not ask for "good vibes only"; the name should be interpreted primarily ornithologically.

Guest Book

We love it when guests sign the Good Vibes Corner Office Sofa Guest Book in person. It is located next to the comfortable Good Vibes Corner Office Sofa, which is awaiting your visit. In the meantime, feel free to leave a note in the Good Vibes Corner Office Website Guest Book.

Open problems

Please solve these problems, but leave a few for us to ponder. Some are stated as conjectures.

• Superconstant lower bound for deterministic dictionaries. [1]
• Ω(log^dn) lower bound for d-dimensional range counting. [1, 4, 5]
• Ω(2^klog n) (conditional) lower bound for dynamic treewidth. [6]
• Prove or disprove that VP≠VNP. What about VF≠VP?
• Prove or disprove that P≠PSPACE. What about L≠P?
• Tight bounds for online sorting / online metric TSP with extra space. [7]
• Tight bounds for Personalized PageRank estimation as a function of the damping factor (a.k.a. teleport/termination probability). [8, 9]
• Do three candidates suffice to win a voter majority? [10]

Publications

• Instance-Optimality of Bidirectional Dijkstra on Simple Graphs
  Christian Bertram, Mads Vestergaard Jensen, Mikkel Thorup, Hanzhi Wang, and Shuyi Yan.
  Preprint 2026.
• Derandomized sunflowers and radical lower bounds
  Bruno Pasqualotto Cavalar, Théo Borém Fabris, Partha Mukhopadhyay, Srikanth Srinivasan, and Amir Yehudayoff.
  FOCS 2026.
• Personalized PageRank Estimation in Undirected Graphs
  Christian Bertram and Mads Vestergaard Jensen.
  Preprint 2026.
• Multilinear Algebraic Branching Programs and the Min-Partition Rank Method
  Théo Borém Fabris, Nutan Limaye, Srikanth Srinivasan, and Amir Yehudayoff.
  CCC 2026.
• Negations are powerful even in small depth
  Bruno Pasqualotto Cavalar, Théo Borém Fabris, Partha Mukhopadhyay, Srikanth Srinivasan, and Amir Yehudayoff.
  STOC 2026.
• Dynamic Meta-Kernelization
  Christian Bertram, Deborah Haun, Mads Vestergaard Jensen, Tuukka Korhonen.
  STOC 2026.
• Online Metric TSP (Metric Online Sorting)
  Christian Bertram.
  ESA 2025.
• Estimating Random-Walk Probabilities in Directed Graphs
  Christian Bertram, Mads Vestergaard Jensen, Mikkel Thorup, Hanzhi Wang, and Shuyi Yan.
  Preprint 2025.

Construction in progress