Title: Homotopy and Homology of Metric Spaces at Scale: A Framework for Quantitative Topology
Abstract:
Traditional algebraic topology captures the global shape of spaces, but it often ignores how topology behaves when viewed through a quantitative or geometric lens. In this talk, I will discuss a framework for studying homotopy and homology “at scale” in metric and uniform spaces — an approach that unifies ideas from discrete homotopy theory, the homotopy critical spectrum, and homology. The central idea is to replace ordinary continuity with continuity at scale, allowing us to define \epsilon-homotopy and \epsilon-homology groups that encode how topological features appear and disappear as one changes resolution.
Fall 2025
September 8 Dominic Bair First Passage Percolation on Hyperbolic Graphs: Bi-infinite Geodesics, Radial Maps, and Infinitely Many Thick Triangles
September 12(Friday) Yulan Qing Boundary of infinite groups
September 22 Alex Squires One-endedness in Curve graphs
October 13 Sunrose ShresthaCylinders on the Mucube
October 20 Ivy DeyHomotopy and Homology of Metric Spaces at Scale: A Framework for Quantitative Topology
October 27 Vicky Wen
November 10 Roberta Shapiro
November 17 George Shaji
Spring 2025
Feb 10 Spendcer Dowdall Geometric finiteness in mapping class groups: examples and perspectives
March 3 Xiangdong Xie Rigidity of pattern-preserving quasiisometries of nilpotent Lie groups
March 24 Koichi Oyakawa Geometry and dynamics of the extension graph of graph product of groups
April 21 Manisha Garg Units and zero-divisors of group rings over CAT(0) groups
April 28 Behrang Forghani Poisson boundary Identification Problem
Fall 2024
August 23, Friday Sagnik Jana Sublinearly Morse boundary
September 9 Rachel Skipper Braiding groups of homeomorphisms of the Cantor set
October 21 Meenakshy Jyothis Towards Ivanov’s meta-conjecture for geodesic currents
November 4 Alex Margolis Coarse homological invariants of metric spaces
November 11 Petr Kosenko Random walks on Fuchsian groups and Hardy spaces: an unexpected connection
November 25 Ekaterina Rybak Frattini subgroups of hyperbolic-like groups
December 2 Dimitrios Nikolakopoulos Log-Concavity of Characteristic Polynomial Coefficients in Representable Matroids
Spring 2024
Feb 26 Thomas Ng Quotients of free products
March 4 Mark Pengitore Residual finiteness growth functions of surface groups with respect to characteristic quotients
March 18 Sahana Balasubramanya The semi simple theory of acylindricity in higher rank
