Two days, three worlds: determinacy, graph codes, and proper actions
by Dave · October 18, 2025
Two short days at the University of Tokyo’s NISSAY Lecture Hall brought together three mathematicians who rarely cross orbits:
W. Hugh Woodin, logician of the set-theoretic cosmos;
Noga Alon, combinatorialist of near-infinite graphs;
and Fanny Kassel, geometer of proper actions and symmetry.
Each offered a distinct rhythm of infinity—logical, discrete, geometric.
Schedule Overview
Day 1 – October 18, 2025
・ 13:35–14:35 — W. Hugh Woodin (Harvard)
The AD⁺ Duality Program
・ 15:00–16:00 — Noga Alon (Princeton)
Graph-Codes: Questions, Results and Methods
・ 16:45–17:45 — Fanny Kassel (IHES)
Discrete Subgroups of Lie Groups and Proper Actions
Day 2 – October 19, 2025
・ 10:00–11:00 — W. Hugh Woodin
The HOD Conjecture and the Ultimate-L Conjecture
・ 11:30–12:30 — Noga Alon
Graph-Codes (continued)
・ 14:00–15:00 — Fanny Kassel
Proper Actions and Geometric Structures
・ 15:10–16:10 — Workshop closing with drinks
W. Hugh Woodin — The edges of the set-theoretic universe
Woodin treats foundations as an arena where consistency and truth spar endlessly.
The AD⁺ program explores worlds beyond ZFC’s reach, guided by determinacy axioms.
His Ultimate L project seeks a canonical inner model large enough to host every known large cardinal—Gödel’s constructible universe reinvented.
Recommended reading
・ The HOD Dichotomy (Davis, Rodriguez, Woodin) — arXiv 1605.00613
・ Suitable Extender Models I — PhilPapers
・ Large Cardinals at the Brink — ScienceDirect
・ What a Set Is: the V-View — SpringerLink
・ The Equivalence of Axiom ()⁺ and Axiom ()⁺⁺ — PhilPapers
Noga Alon — The combinatorial imagination
Alon builds mathematics like a universal game of Lego.
His combinatorics fuses algebra, probability, and information theory; randomness becomes a tool for certainty.
In his Graph-Codes talks, graphs are treated as information carriers—structures that encode and decode through spectral behavior.
Recommended reading
・ Alon–Matias–Szegedy, The Space Complexity of Approximating Frequency Moments — PDF
・ High-Girth Near-Ramanujan Graphs with Localized Eigenvectors — arXiv 1908.03694
・ Alon–Krivelevich–Sudakov, Embedding Nearly-Spanning Bounded Degree Trees — arXiv 0706.4100
・ Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits — arXiv 1708.02037
・ Tools from Higher Algebra — PDF
Fanny Kassel — Geometry acts properly
Kassel’s lectures orbit the geometry of discrete symmetry.
She studies when a discrete group acts properly on a homogeneous space—a question where algebra meets dynamics.
Her work ties Lie theory, hyperbolic geometry, and representation theory into a single geometric thread.
Recommended reading
・ Geometric Structures and Representations of Discrete Groups (ICM Rio survey) — PDF
・ Kobayashi–Kassel, Invariant Differential Operators on Spherical Homogeneous Spaces — IHES
・ Kassel–Potrie, Eigenvalue Gaps for Hyperbolic Groups and Semigroups — arXiv 2002.07015
Reading pathways
・ Start with each speaker’s survey paper — they frame the terrain beautifully.
・ Pair the talks with one technical piece:
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Woodin’s HOD Dichotomy,
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Alon’s High-Girth Graphs,
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Kassel’s Eigenvalue Gaps.
・ Look for the bridges: determinacy versus absoluteness, randomness versus structure, discreteness versus continuity.
Closing reflection
Across logic, combinatorics, and geometry, these lectures form a kind of functor network —
each field transforming ideas of regularity, infinity, and structure into its own syntax.
Woodin explores truth at the edge of definability; Alon extracts order from randomness;
Kassel measures the grace of symmetry when discreteness intrudes.
Together, they remind us that mathematics remains a living conversation between different infinities.
Location: University of Tokyo · Graduate School of Mathematical Sciences · NISSAY Lecture Hall
Dates: October 18–19, 2025
Here are some good YouTube (or video) lectures / talks for each of your three mathematicians.
W. Hugh Woodin
・ “Large cardinals and small sets” — W. Hugh Woodin (YouTube)
・ “W. Hugh Woodin — The HOD Dichotomy, weak extender models” (YouTube)
・ “Beyond the infinite: Hugh Woodin” (Rothschild Distinguished Lecture) (YouTube)
These give good insight into his work on inner model theory, determinacy, and large cardinals.
Noga Alon
・ “Graph-Codes: Problems, Results and Methods” — Noga Alon (YouTube)
・ “Topics in Combinatorics lecture 13.0 — Alon’s Combinatorial Nullstellensatz” (YouTube)
・ “Noga Alon: Combinatorial Reasoning in Information Theory” (YouTube)
These nicely illustrate his style: combinatorial methods, coding-theoretic interpretations, and the blending with information theory.
Fanny Kassel
・ “Geometric structures and representations of discrete groups (ICM Rio, 2018)” — Fanny Kassel (YouTube)
・ “Fanny Kassel (IHES) Convex projective structures and Anosov” (YouTube)
・ “Fanny Kassel — Sous-groupes discrets des groupes de Lie” (French talk) (YouTube)
These reflect her interests in discrete group actions, homogeneous spaces, and geometric/dynamical structures.