Logistics

Dates: August 4 to 8, 2025.

Location: Hill Center for Mathematical Sciences. Rutgers University, New Brunswick. Room: Hill 705.

Organizers: Alex Elchesen, Facundo Mémoli, Aziz Gülen and Amit Patel.

Description: This workshop aims to explore and strengthen the connections between algebraic combinatorics, combinatorial topology, and applied algebraic topology. Topics include, but are not limited to, poset topology, cellular sheaves, Möbius inversion, and related categorifications. The goal is to bring together researchers from both the pure and applied sides of these areas to foster cross-disciplinary collaboration, exchange new ideas, and highlight recent advances in the field.

Speakers

• Hideto Asashiba, Shizuoka U.
• Saugata Basu, Purdue.
• Nate Clause, Ohio State.
• Nir Gadish, UPenn.
• Rob Ghrist, UPenn.
• Woojin Kim, KAIST.
• Alex McCleary, Montana State.
• Amit Patel, Colorado State
• Tatum Rask, Colorado State.
• Zhengchao Wan, Missouri.
• Qingsong Wan, UCSD.
• Ling Zhou, Duke.

Schedule and Abstracts

Abstracts are here.

• Monday August 4th
  • Morning (Background, origins, connections)
    • 9:00 – 10:00: Amit Patel - From Classical Persistence to Möbius Inversion: An Introduction (I)
    • 10:00 – 10:30: Break
    • 10:30 – 11:30: Amit Patel - From Classical Persistence to Möbius Inversion: An Introduction (II)
  • Afternoon
    • 2:00 – 3:30: Woojin Kim — Complexity and Estimation of the Generalized Rank Invariant and Beyond
    • 3:30 – 4:00: Break
    • 4:00 – 5:30: Hideto Asashiba — Interval replacements of persistence modules
• Tuesday August 5th
  • Morning
    • 9:00 – 10:00: Rob Ghrist — Network Sheaves & Torsors
    • 10:00 – 10:30: Break
    • 10:30 – 11:30: Amit Patel — From Möbius Inversion to Möbius Homology
  • Afternoon
    • 2:00 – 3:30: Qingsong Wang — Tight Spans as a Lens on Vietoris–Rips Topology
    • 3:30 – 4:00: Break
    • 4:00 – 5:30: Ling Zhou — Beyond Persistent Homology: Persistent Cup Products and More Discriminative Persistent Invariants
• Wednesday August 6th
  • Discussions, hike, etc.
• Thursday August 7th
  • Morning
    • 9:00 – 10:30: Zhengchao Wan — Grassmannian Persistence Diagrams
    • 10:30 – 11:00: Break
    • 11:00 – 12:00: Tatum Rask — Persistent Laplacians & Möbius Homology
  • Afternoon
    • 2:00 – 3:00: Saugata Basu — New quantitative results in semi-algebraic geometry/topology with applications
    • 3:00 – 3:30: Break
    • 3:30 – 4:30: Nir Gadish — Hömotopical foundations of Möbius inversion
• Friday August 8th
  • Morning
    • 9:00 – 10:00: Alex McCleary — Filtered Moore Spaces
    • 10:00 – 10:30: Break
    • 10:30 – 12:00: Nate Clause — The Generalized Rank Invariant: Möbius invertibility, Discriminating Power, and Connections to Other Invariants
  • Afternoon
    • 2:00 – 3:00: DIMACS-REU group (Belova, Goldberg, Xie) — Discrimination of dynamic data via curvature sets
    • 3:00 – 3:30: Break
    • 3:30 – 5:30: Open Problems session