Freedman CMSA Seminar *Note: via Zoom only* 2:00-3:30 pm ET Speaker: Matt Hastings, Microsoft Quantum Program Title: Invertible Phases of Matter and Quantum Cellular Automata: Dimensions One to Three Abstract: A Quantum Cellular Automaton (QCA) is a *-automorphism of the algebra of local operators. While local quantum circuits provide one example of QCA, we are […]
Freedman CMSA Seminar *Note: via Zoom only* 2:00-3:30 pm ET Speaker: Michael Freedman, Harvard CMSA Title: Some questions and theorems about closed 3 manifolds embedded in S^4 Abstract: Much is unknown about smooth embeddings of 3-manifolds in S^4; the Schoenflies problem (Is there only one smoothly embedded 3-sphere in S^4 up to isotopy?) is […]
Freedman CMSA Seminar Speaker: Michael Freedman Title: A simple model for universal quantum computation Abstract: I’ll present joint (unpublished) work with Charlie Marcus on a surprisingly simple – and potentially practical (?)– model for universal quantum computation whose only quantum primitive is the ability to measure a pair of adjacent electrons into either singlet (spin=0) […]
Freedman CMSA Seminar *via Zoom* Speaker: Sergey Melikhov, Steklov Math Institute Title: Is every knot isotopic to the unknot? Abstract: The following problem was stated by D. Rolfsen in his 1974 paper; according to R. Daverman it was being discussed since the mid-60s. Is every knot in $S^3$ isotopic (=homotopic through embeddings) to a PL knot --- […]
Freedman CMSA Seminar Speaker: Michael Freedman, Harvard CMSA (3:00–4:00 pm ET) Title: How many links can you fit in a box? Abstract: I’ll discuss a “made up” problem on the interface of topology and packing, which may well be classified as “recreational math”. Here is the first question suppose you have a unit box, how many unlinked […]
Freedman CMSA Seminar Speaker: Slava Dzhenzher, MIPT Title: Adversarial KA Abstract: Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or «expressing» functions, we test its robustness by analyzing its ability to withstand adversarial attacks. We find KA to be robust to countable collections of continuous adversaries, but unearth a […]
The Geometry of Machine Learning Dates: September 15–18, 2025 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138 Despite the extraordinary progress in large language models, mathematicians suspect that other dimensions of intelligence must be defined and simulated to complete the picture. Geometric and symbolic reasoning are among these. In fact, there seems […]
Freedman Seminar Speaker: Michael Freedman, Harvard CMSA Title: Sullivan's work on Lipschitz structures Abstract: I'll begin with an elementary, but now little known, piece of PL topology: engulfing. John Stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I'll explain Dennis Sullivan's enhancement of Kirby's torus trick (which relies […]
Freedman Seminar Speaker: Michael Freedman, Harvard CMSA Title: Sullivan’s work on Lipschitz structures Part II (but self-contained) Speaker: Bowen Yang, CMSA Title: Deligne and Sullivan's work on complex bundles with discrete structure group
Freedman Seminar Speakers: Michael Freedman, CMSA and Slava Krushkal, University of Virginia (2-3 pm and 3:15-4:15 pm) Title: Formulating 4D surgery for AI agents Abstract: The topological category surgery exact sequence is still open for free groups (and most groups of exponential growth). The lack of knowledge is about both surgery and s-cobordism; and the […]
Freedman Seminar Speakers: Mattie Ji (Penn) and Jeongwan Haah (Stanford) Mattie Ji Title: Quantum Cellular Automata via Algebraic K-Theory Abstract: Algebraic K-theory, on a very high level, is the study of how to break apart and assemble objects linearly, which makes the field amenable to classification questions. In this work, we apply this methodology to study […]
Freedman Seminar Speaker: Robert Gompf, UT Austin Title: Exotic R^4's are unclassifiable Abstract: We will use descriptive set theory to show that there is a precise sense in which exotic R^4's are unclassifiable. For other open manifolds, we can reach a much higher level of unclassifiability. This is work in progress with Aristotelis Panagiotopoulos.