Smale@95: A Conference in Honor of Steve Smale
2025-07-21..2025-07-22
Berkeley, United States
who it's for
dynamical systems researchers, applied mathematicians, theoretical computer scientists, AI researchers, mathematical biologists, control engineers, computational neuroscientists, philosophers of mind
topics
asymptotic stability theory; h-cobordism and topology; Kuramoto synchronization model; Hodgkin-Huxley memristor modeling; Cucker-Smale flocking models; Monge-Kantorovich optimal transport; compositional sparsity in deep nets; Conscious Turing Machine architecture; metacommunity host-microbe exchange; linear representations of concepts in AI models
| title | author | length |
|---|---|---|
| Opening Remarks | Steven Kahn, Martin Olsson | 12m |
Conference opening gives concrete details: the Simons Institute, founded 2012 with ongoing Simons Foundation support, runs semester-long programs that convene… | ||
| Oscillating networks from a biological point of view | Nancy Kopell | 34m |
Argues that some oscillation results are universal while others require physiological detail, using phase-reduced chain models and a discretization to a… | ||
| Asymptotic Dynamics and Topology | Michael Shub | 30m |
Conjecture: the topological entropy of a diffeomorphism bounds below the log of the maximal modulus of eigenvalues of its action on homology, so growth on… | ||
| Hodgkin-Huxley, Memristors, and Edge of Chaos | Leon Chua | 37m |
Claims that the Hodgkin‑Huxley potassium and sodium “time‑varying resistances” are actually memristors and reclassifies those circuit elements, uses matrix… | ||
| Topological and Algebraic Invariants to Classify Types of Singularities of Maps relevant to... | Fred Leve | 24m |
Classifies kinematic singularities into passable vs impassable types and shows when steering via the null space (SVD / Moore‑Penrose pseudoinverse) can recover… | ||
| Emergent Behavior on Flocks | Felipe Cucker | 28m |
Proves that agents with velocities updated by weighted differences converge to a common velocity and keep bounded spread; weights use aij = const/(const +… | ||
| On Professor Smale's legacy for asymptotic stability theory | Matthew Kvalheim | 27m |
Gives a concrete classification: the space of smooth asymptotically stable vector fields on R^n and the space of proper smooth Lyapunov functions are, for n ≠… | ||
| A Metacommunity Model of Interacting Hosts with Microbe Exchange | Mason Porter | 19m |
Proposes a metacommunity framework that replaces continuous dispersal with discrete exchange parameter gamma and Poisson-like interaction times (lambda_ij) on… | ||
| What is Consciousness and Can Machines have it? Part 1 | Lenore Blum | 47m |
A formal model called the Conscious Turing Machine treats short‑term memory as a single-stage broadcast and long‑term processors as competitors that submit… | ||
| What is Consciousness and Can Machines have it? Part 2 | Manuel Blum | 16m |
Argues that phenomenal consciousness can emerge from deterministic classical physics and sketches a formal model called the Conscious Turing Machine as a… | ||
| Dynamical Systems, Linear Programming and the Monge-Kantorovich Problem | Anthony Bloch | 17m |
Connects the Monge-Kantorovich mass‑transport problem to linear programming and dynamics by proving M = K = D in a finite adjoint‑orbit setting and extending… | ||
| Compositional sparsity and learnability | Tomaso Poggio | 29m |
Claim: functions that are compositionally sparse—built from small-arity constituent maps (example: a binary tree of 2-variable nodes)—avoid the curse of… | ||
| Smale’s 18th Problem and Intelligence Science | Michael Xuan, Brian Athey | 20m |
Smale’s 18th frames a concrete program: compare discrete Turing models with the real number machine (BSS), quantify complexity via polynomial time, and test… | ||
| The Singularity is the Observer | Graciela Chichilnisky | 32m |
Claims that quantum physics is fundamentally topological, arguing quantum observables are self-adjoint operators whose space is noncontractible and in fact the… | ||
| Towards Trustworthy AI: Reflections on Learning and Smale's Legacy | Yuan Yao | 30m |
Two decades of work trace a throughline from the Smale 18 problem to concrete limits and fixes for modern ML: learnability requires condition number and… | ||
| The Enabling of McCarthyism by the University of Michigan | Steve Batterson | 25m |
Argument states that during 1948–56 University of Michigan administrators collaborate with HUAC and the FBI to neutralize leftists on campus, using leaked… | ||
| Measures of Perfection | Gene Meieran | 29m |
Compares mineral collecting and mathematics and argues perfection must be measured, not admired: valuation is quantized into discrete quanta units (example: a… | ||
| Kuramoto Problem and Smale Institute | Steve Smale, Indika Rajapakse, Michael Xuan, Charles Pugh, Gregorio Malajovich | 50m |
Kuramoto with five oscillators reduces to a negative‑gradient flow on a 4‑torus and the low‑energy critical set breaks into finitely many saddles organized by… | ||
| Linear representations of concepts in modern AI models | Mikhail Belkin | 37m |
Claim: many human concepts inside LLMs sit on one-dimensional directions recoverable by linear probes, i.e. single index models, and can be found and used to… | ||
| Family Tribute | Judy Smale | 20m |
Photos and anecdotes show a restrained family life turned vivid: a father who works as a ceramic engineer at AC spark plug, bought a country school for $5,000… | ||
| Smale’s 18th Problem and Intelligence Science 2 | Michael Xuan, Brian Athey | 09m |
Claim: AI reaches near-AGI effects in years not decades, with coding automation able to handle the majority of standard programming tasks within about a year… | ||
| nothing matches | ||