# Séminaire Bourbaki 2019–2023 — Consolidated Candidate List

Deduplicated master list (merged from 3 extractors). Organized by exposé. ~110 unique candidates.
Format: NAME | KIND | DESCRIPTION | DEPENDENCIES | SOURCE

## 1151 (Bost) — Euclidean lattices
- Bost slope formalism for Euclidean lattices | technique | Adaptation of the Arakelov-geometric slope/Harder–Narasimhan filtration formalism to Euclidean lattices (Hermitian bundles over Spec Z), assigning slopes and a canonical filtration. | Euclidean lattices, theta series, HN filtrations, Arakelov geometry | Exp 1151 Bost
- Theta series of a Euclidean lattice | state | The holomorphic function attached to a Euclidean lattice summing q^{|v|^2/2} over lattice vectors, encoding the length distribution of lattice vectors. | Euclidean lattice, Poisson summation, modular forms | Exp 1151 Bost
- Reverse-Minkowski / transference inequalities for lattices | theorem | Quantitative inequalities relating covering radius, smoothing parameter, and theta function of a Euclidean lattice and its dual. | theta series, dual lattice, Banaszczyk bounds | Exp 1151, d'après Banaszczyk, Regev, Stephens-Davidowitz

## 1152 (Dujardin) — equidistribution
- Equidistribution of Fekete points via pluripotential theory | theorem | Energy-minimizing (Fekete) configurations on a compact complex manifold equidistribute toward the equilibrium measure of the associated weighted potential as the number of points grows. | pluripotential theory, Monge–Ampère measures, large deviations | Exp 1152, d'après Berman, Boucksom, Witt Nyström
- Coulomb gas / determinantal pluripotential point process | state | A point process weighting configurations by an exponential of a pairwise logarithmic-energy functional, whose macroscopic limit is an equilibrium pluripotential measure. | Monge–Ampère energy, large deviation principle, equilibrium measure | Exp 1152

## 1153 (Bordenave) — random regular graphs
- Asymptotic normality of eigenvectors of random regular graphs | theorem | The entries of eigenvectors of a uniformly random d-regular graph become jointly Gaussian (delocalized) in the large-vertex limit. | random regular graphs, Benjamini–Schramm limits, local weak convergence | Exp 1153, d'après Backhausz–Szegedy
- Typical processes on the d-regular tree (factor-of-i.i.d. method) | technique | Analyzing eigenvectors of random regular graphs via invariant typical processes (factors of i.i.d.) on the infinite d-regular tree with entropy inequalities. | factor of i.i.d., infinite regular tree, Benjamini–Schramm | Exp 1153

## 1154 (Khukhro) — coarse geometry
- Coarse embeddability of non-exact groups into Hilbert space | theorem | There exist finitely generated groups that are not exact (lack property A) yet admit a coarse embedding into Hilbert space, separating the two coarse-geometric properties. | coarse embedding, property A, exactness, expanders | Exp 1154, d'après Arzhantseva–Guentner–Osajda–Špakula
- Property A (coarse amenability) | axiom | A coarse amenability condition on a metric space requiring uniformly large controlled-boundary finite subsets, equivalent to exactness of the reduced group C*-algebra for groups. | bounded geometry metric spaces, amenability | Exp 1154

## 1155 (Cadoret) — crystalline companions
- Crystalline companions theorem | theorem | For a smooth variety over a finite field, every ℓ-adic lisse sheaf in a compatible system admits ℓ'-adic and crystalline (p-adic, overconvergent F-isocrystal) companions with matching Frobenius characteristic polynomials. | ℓ-adic sheaves, overconvergent F-isocrystals, Langlands for function fields | Exp 1155, d'après Deligne, Drinfeld, L. Lafforgue, Abe
- Abe's p-adic Langlands correspondence for function fields | theorem | A bijection, compatible with L. Lafforgue's ℓ-adic correspondence, between overconvergent F-isocrystals and automorphic forms over a function field, realizing crystalline companions. | overconvergent F-isocrystals, rigid cohomology, Drinfeld correspondence | Exp 1155, d'après T. Abe

## 1156 (Raum) — C*-simplicity
- Furstenberg-boundary criterion for C*-simplicity | theorem | A discrete group has a simple reduced C*-algebra iff its action on its Furstenberg boundary is topologically free, equivalently it has no nontrivial amenable normal subgroup (Kalantar–Kennedy / BKKO). | Furstenberg boundary, boundary actions, reduced group C*-algebra | Exp 1156, d'après Kalantar–Kennedy, Breuillard–Kalantar–Kennedy–Ozawa
- C*-simplicity | axiom | The property of a discrete group that its reduced group C*-algebra is simple (no nontrivial closed two-sided ideals). | reduced group C*-algebra | Exp 1156

## 1157 (Kebekus) — Fano boundedness
- Boundedness of singular Fano varieties (BAB conjecture) | theorem | For each dimension d and ε>0, the ε-log-canonical Fano varieties of dimension d form a bounded family. | minimal model program, log-canonical singularities, Fano varieties, complements | Exp 1157, d'après Birkar
- Theory of complements (boundedness of complements) | technique | A birational-geometry method bounding the index of n-complements of log Fano pairs to establish boundedness of Fano families. | log canonical pairs, MMP, vanishing theorems | Exp 1157, d'après Birkar

## 1158 (Benoist) — KSBA moduli
- Moduli of stable (KSBA) varieties of general type | theorem | Families of higher-dimensional varieties of general type admit a separated proper moduli space of stable (semi-log-canonical, ample canonical) objects, generalizing Deligne–Mumford stable reduction. | MMP, semi-log-canonical singularities, KSBA stability | Exp 1158, d'après Kollár, Hacon–McKernan–Xu

## 1159 (Pozzetti) — higher Teichmüller
- Higher Teichmüller theory | state | Connected components of the character variety of a surface group into a higher-rank semisimple Lie group consisting entirely of discrete faithful representations, generalizing Teichmüller space. | surface group representations, Hitchin components, positive representations | Exp 1159
- Anosov representation | axiom | A representation of a hyperbolic group into a semisimple Lie group whose flat bundle admits a continuous equivariant transverse limit map with uniform contraction (dominated splitting). | hyperbolic groups, geodesic flow, flag varieties, dominated splittings | Exp 1159

## 1160 (Migliorini) — HOMFLY/Hilbert schemes
- HOMFLY polynomial from Hilbert schemes of a plane curve singularity | theorem | The HOMFLY polynomial of the link of a plane curve singularity equals the generating series of Euler characteristics of Hilbert schemes of points on the curve (Oblomkov–Shende, proved by Maulik). | Hilbert schemes of points, plane curve singularities, link invariants | Exp 1160, d'après Maulik (Oblomkov–Rasmussen–Shende)
- Oblomkov–Shende / Maulik conjecture | state | The identity equating the HOMFLY invariant of a singularity link with a Hilbert-scheme generating function, refined by the perverse filtration. | Hilbert schemes, compactified Jacobians, HOMFLY homology | Exp 1160

## 1161 (Harper) — extreme values of zeta
- Maximum of the Riemann zeta function in short intervals | theorem | The maximum of |ζ(1/2+it)| over a typical short interval of length ~2π near height T is governed to leading order by log-correlated field / branching random walk statistics. | log-correlated Gaussian fields, branching random walks, moments of zeta, RMT | Exp 1161, d'après Najnudel, Arguin et al.
- Log-correlated field / branching random walk heuristic for zeta | technique | Modeling the local behaviour of log|ζ| on the critical line by a logarithmically correlated Gaussian field, transferring extreme-value results from branching random walks. | branching random walk maxima, multiplicative chaos, Fyodorov–Hiary–Keating | Exp 1161

## 1162 (Théret) — sharp phase transition
- Sharpness of the phase transition (Duminil-Copin–Raoufi–Tassion) | theorem | For a broad class of percolation and Ising-type models the phase transition is sharp, with exponential decay of correlations throughout the subcritical regime. | OSSS inequality, randomized algorithms, differential inequalities | Exp 1162, d'après Duminil-Copin–Raoufi–Tassion
- OSSS inequality method for sharp thresholds | technique | Using the O'Donnell–Saks–Schramm–Servedio decision-tree inequality to derive differential inequalities on percolation probabilities yielding sharp phase transitions. | randomized algorithms, revealment, monotone Boolean functions | Exp 1162

## 1163 (Stipsicz) — triangulation conjecture
- Disproof of the Triangulation Conjecture | theorem | For every dimension n ≥ 5 there exist closed topological manifolds admitting no triangulation (not homeomorphic to any simplicial complex). | Pin(2)-Seiberg–Witten Floer homology, Rokhlin invariant, homology cobordism | Exp 1163, d'après Manolescu
- Pin(2)-equivariant Seiberg–Witten Floer homology (Manolescu invariants) | technique | A Pin(2)-equivariant Seiberg–Witten Floer homology of homology 3-spheres producing invariants (α,β,γ) obstructing order-two elements of the homology cobordism group with wrong Rokhlin invariant. | Seiberg–Witten Floer homology, Pin(2) symmetry, homology cobordism Θ³ | Exp 1163

## 1164 (Randal-Williams) — Hurwitz spaces
- Homological stability for Hurwitz spaces (Cohen–Lenstra over function fields) | theorem | Hurwitz moduli spaces of branched covers exhibit homological stability, implying Cohen–Lenstra-type predictions for class groups of quadratic function fields over finite fields in the large-q limit. | Hurwitz spaces, homological stability, Cohen–Lenstra heuristics | Exp 1164, d'après Ellenberg–Venkatesh–Westerland
- Homological stability method (scanning / group completion) | technique | A topological method establishing that the homology of a sequence of moduli/configuration spaces stabilizes, via arc complexes and scanning/group-completion arguments. | configuration spaces, braid group homology, scanning | Exp 1164

## 1165 (Rivière) — minimal hypersurfaces
- Infinitely many minimal hypersurfaces (Yau's conjecture, dim 3–7) | theorem | Every closed Riemannian manifold of dimension between 3 and 7 contains infinitely many closed embedded minimal hypersurfaces. | min-max theory, Almgren–Pitts theory, Weyl law for volume spectrum | Exp 1165, d'après Marques–Neves and Song
- Almgren–Pitts min-max theory / volume spectrum Weyl law | technique | A variational min-max scheme producing minimal hypersurfaces as critical points of the area functional over multiparameter sweepouts, with a Weyl-type asymptotic law for the widths. | geometric measure theory, varifolds, min-max widths | Exp 1165

## 1166 (Arnaud) — positive entropy
- Herman's positive metric entropy conjecture | state | The conjecture that arbitrarily close to integrable (or near an elliptic fixed point) there exist smooth area-preserving diffeomorphisms with positive metric (Kolmogorov–Sinai) entropy. | area-preserving diffeomorphisms, metric entropy, elliptic fixed points, KAM | Exp 1166
- Berger–Turaev theorem (positive metric entropy) | theorem | Any area-preserving C^r diffeomorphism of a surface with an elliptic fixed point can be C^r-perturbed to one with a chaotic island of positive metric entropy, proving Herman's conjecture. | elliptic fixed points, KAM, Newhouse phenomena, renormalization | Exp 1166, d'après Berger–Turaev

## 1167 (Gallay) — vortex stability
- Asymptotic stability of the Lamb–Oseen vortex | theorem | The two-dimensional Lamb–Oseen vortex is asymptotically stable for the Navier–Stokes equations uniformly in viscosity, with enhanced (inviscid) damping rates. | 2D Navier–Stokes, vorticity formulation, pseudospectrum, enhanced dissipation | Exp 1167, d'après Li–Wei–Zhang
- Pseudospectral / enhanced-dissipation estimates | technique | Using pseudospectral resolvent bounds on the linearized non-self-adjoint operator with enhanced dissipation to control transient growth and prove stability of vortices. | non-self-adjoint operator, pseudospectrum, enhanced dissipation | Exp 1167

## 1168 (Humilière) — closing lemma
- C^∞ closing lemma (Asaoka–Irie) | theorem | For Hamiltonian/Reeb flows on surfaces and 3-manifolds, periodic orbits are C^∞-dense, proving a smooth closing lemma in these settings. | Hamiltonian diffeomorphisms, Reeb flows, ECH spectral invariants | Exp 1168, d'après Asaoka–Irie
- Embedded contact homology spectral invariants (Weyl law) | technique | Spectral invariants from embedded contact homology whose asymptotics obey a Weyl law recovering contact volume, used to force creation/density of periodic Reeb orbits. | embedded contact homology, Reeb dynamics, contact volume | Exp 1168

## 1169 (Pravda-Starov) — pseudospectrum
- Resolvent estimates for non-self-adjoint semiclassical operators | theorem | Sharp bounds on the resolvent and localization of the pseudospectrum for classes of non-self-adjoint semiclassical pseudodifferential operators, governed by subprincipal-symbol bracket conditions. | semiclassical pseudodifferential calculus, pseudospectrum, condition (Ψ) | Exp 1169, d'après Dencker–Sjöstrand–Zworski

## 1170 (Fresán) — period maps & o-minimality
- O-minimal structure (tame geometry) | axiom | An order-minimal expansion of the real ordered field in which every definable subset of the line is a finite union of points and intervals, yielding strong tameness/finiteness properties. | first-order logic, real ordered field, definable sets, R_an,exp | Exp 1170
- Definability of period maps | theorem | Any period map of an admissible polarized variation of (mixed) Hodge structure is definable in the o-minimal structure R_an,exp. | variations of Hodge structure, period domains, R_an,exp | Exp 1170, d'après Bakker–Brunebarbe–Klingler–Tsimerman
- Definable Chow / o-minimal GAGA (Peterzil–Starchenko) | technique | A transfer principle stating a definable complex analytic subset of an algebraic variety is algebraic, used to deduce algebraicity from definable analytic statements. | o-minimal structures, complex analytic geometry | Exp 1170, d'après Peterzil–Starchenko
- Algebraicity of Hodge loci (via o-minimality) | theorem | The Hodge locus in a family is an algebraic subvariety, reproved using definable Chow / o-minimal GAGA (theorem of Cattani–Deligne–Kaplan). | definability of period maps, normal functions | Exp 1170, d'après Bakker–Klingler–Tsimerman

## 1171 (Guihéneuf) — surface homeomorphism dynamics
- Maximal isotopy & transverse singular foliation | state | For a surface homeomorphism isotopic to the identity, a maximal identity isotopy carries a transverse singular foliation whose leaves encode the dynamics. | surface homeomorphisms, isotopies, singular foliations, Brouwer theory | Exp 1171
- Le Calvez–Tal forcing theory | technique | A forcing method using transverse trajectories in a maximal singular foliation to detect periodic orbits and positive topological entropy of surface homeomorphisms. | maximal isotopies, transverse foliations, Brouwer–Le Calvez theory | Exp 1171, d'après Le Calvez–Tal

## 1172 (Ingremeau) — nodal sets
- Nodal-set volume estimates (Yau's nodal conjecture) | theorem | The (n−1)-Hausdorff measure of the nodal set of a Laplace eigenfunction with eigenvalue λ on a compact manifold is bounded above and below by polynomial powers of √λ, settling the analytic case. | Laplace eigenfunctions, nodal sets, doubling index, frequency function | Exp 1172, d'après Logunov–Malinnikova
- Doubling index / frequency-function method | technique | A combinatorial-analytic technique controlling local growth (doubling index) of harmonic/eigenfunctions via almost-monotonicity and cube subdivision to bound nodal-set volume. | frequency function, almost-monotonicity, Cauchy uniqueness | Exp 1172

## 1173 (Tholozan) — Ratner in infinite volume
- Ratner-type rigidity in infinite-volume hyperbolic manifolds | theorem | Classification and equidistribution of orbit closures of unipotent/horospherical flows on geometrically finite infinite-volume hyperbolic manifolds. | unipotent flows, geometrically finite hyperbolic manifolds, Patterson–Sullivan / Burger–Roblin measures | Exp 1173, d'après McMullen, Mohammadi, Oh

## 1174 (Bloom) — Gowers inverse theorem
- Quantitative inverse theorem for the Gowers norms | theorem | A function with non-negligible U^{s+1} Gowers norm correlates with a nilsequence of bounded complexity, with polynomial (effective) bounds. | Gowers uniformity norms, nilsequences, nilmanifolds, higher-order Fourier analysis | Exp 1174, d'après F. Manners
- Higher-order Fourier analysis (inverse-theorem method) | technique | Decomposing functions via degree-s nilsequences and iterating Cauchy–Schwarz / equidistribution on nilmanifolds to invert the Gowers norms. | nilsequences, equidistribution on nilmanifolds, Cauchy–Schwarz–Gowers | Exp 1174

## 1175 (Česnavičius) — topological reconstruction
- Reconstruction of a variety from its Zariski topology | theorem | A normal projective variety of dimension ≥ 2 over an algebraically closed field is determined, as a scheme, by the homeomorphism type of its underlying Zariski topological space. | Zariski topology, normal varieties, intersection theory, ample divisors | Exp 1175, d'après Kollár (Lieblich–Olsson)

## 1176 (Dupont) — Zagier conjecture
- Zagier's polylogarithm conjecture | state | The conjecture that ζ_F(n) of a number field is expressible via a regulator determinant of values of the n-th polylogarithm on F-points. | Dedekind zeta function, polylogarithms, Borel regulator, K-theory | Exp 1176
- Goncharov–Rudenko theorem on ζ_F(4) | theorem | Zagier's conjecture holds in weight 4, expressing ζ_F(4) via the tetralogarithm, proved via the weight-4 polylogarithmic motivic complex and a new functional equation. | motivic complexes, Grassmannian polylogarithm, cluster structure of M_{0,n} | Exp 1176, d'après Goncharov–Rudenko
- Goncharov motivic polylogarithm complexes | state | A family of complexes built from polylogarithmic groups conjecturally computing motivic cohomology and underlying Zagier's conjecture. | polylogarithms, motivic cohomology, regulators, cluster coordinates | Exp 1176
- Motivic correlators / cluster polylogarithm method | technique | Using Goncharov's motivic correlators and the cluster variety structure of M_{0,n} to construct polylogarithm functional equations realizing required cohomology classes. | motivic correlators, cluster varieties, mixed Tate motives | Exp 1176

## 1177 (Dang) — fractal uncertainty
- Fractal uncertainty principle | state | The principle that a function and its Fourier transform cannot both concentrate on a fractal (porous, Ahlfors–David regular) set, quantified by a power-saving operator-norm bound. | Fourier transform, Ahlfors–David regular sets, semiclassical analysis | Exp 1177, d'après Bourgain–Dyatlov, Dyatlov–Jin–Nonnenmacher
- Essential spectral gap via fractal uncertainty | theorem | On convex co-compact hyperbolic surfaces the fractal uncertainty principle yields an essential spectral gap (resonance-free strip) depending only on the limit-set dimension. | fractal uncertainty principle, convex co-compact surfaces, transfer operators, resonances | Exp 1177, d'après Bourgain–Dyatlov, Dyatlov–Zahl

## 1178 (Goujard) — totally geodesic submanifolds
- Finiteness of totally geodesic subvarieties in moduli of curves | theorem | There are only finitely many primitive totally geodesic subvarieties (dimension ≥ 2) in strata of translation surfaces / moduli of Riemann surfaces. | Teichmüller dynamics, SL(2,R) action, affine invariant submanifolds, measure rigidity | Exp 1178, d'après Eskin–McMullen–Mukamel–Wright
- Eskin–Mirzakhani–Mohammadi measure rigidity (magic wand) | technique | Classification of SL(2,R)-invariant ergodic measures and orbit closures on strata of abelian differentials as affine invariant submanifolds. | SL(2,R) action on strata, affine invariant submanifolds, cylinder deformations | Exp 1178

## 1179 (Labourie) — minimal surface counting
- Asymptotic counting of minimal surfaces in hyperbolic 3-manifolds | theorem | The number of closed minimal surfaces (surface subgroups) of bounded genus in a closed hyperbolic 3-manifold grows with an exponential/super-exponential asymptotic analogous to the prime geodesic theorem. | minimal surfaces, surface subgroups, equidistribution, frame-flow mixing | Exp 1179, d'après Calegari–Marques–Neves
- Equidistribution of minimal surfaces (frame-flow mixing) | technique | Proving randomly chosen minimal surfaces equidistribute in the Grassmann bundle via mixing of the frame/geodesic flow to deduce asymptotic counting. | frame flow mixing, Grassmann bundle, exponential mixing | Exp 1179

## 1180 (Le Maître) — property (T) for Polish groups
- Roelcke precompact Polish group | axiom | A topological group precompact for the lower (Roelcke) uniformity; these arise as automorphism groups of ℵ₀-categorical structures. | Polish groups, Roelcke uniformity, ℵ₀-categorical structures | Exp 1180
- Property (T) for Roelcke-precompact Polish groups | theorem | Large classes of Roelcke-precompact Polish groups (e.g. automorphism groups of homogeneous structures) satisfy a continuous-logic version of Kazhdan's property (T). | Kazhdan property (T), unitary representations, continuous model theory | Exp 1180, d'après Ibarlucía

## 1186 (Anscombe) — NIP fields
- Classification of NIP fields (Johnson's theorem) | theorem | Every infinite NIP field is separably closed, real closed, or admits a nontrivial henselian valuation (with finite-or-trivial exceptions), confirming Shelah's conjecture in the dp-finite/henselian case. | model theory of valued fields, NIP, henselian valuations, dp-rank | Exp 1186, d'après W. Johnson
- NIP (dependent theory) | axiom | A first-order theory has the Non-Independence Property if no formula has the independence property, equivalently every formula has finite VC dimension. | first-order logic, VC dimension, stability hierarchy | Exp 1186
- dp-rank / dp-finiteness analysis of valued fields | technique | A method classifying NIP fields by bounding dp-rank and reconstructing a canonical henselian valuation from the model-theoretic structure. | NIP, dp-rank, henselian valuation theory | Exp 1186

## 1187 (Wagner) — high-dimensional expanders
- High-dimensional expanders | state | Higher-dimensional analogues of expander graphs: bounded-degree simplicial complexes exhibiting strong spectral, coboundary, or topological expansion in all dimensions. | simplicial complexes, spectral graph theory, Cheeger inequalities | Exp 1187
- Local spectral expansion / coboundary expansion | technique | A bootstrapping criterion deriving global expansion of a simplicial complex from expansion of all vertex links. | simplicial complexes, links, spectral gaps, cohomology | Exp 1187

## 1188 (Eskenazis) — metric John theorem
- Metric John theorem (Naor) | theorem | A nonlinear analogue of John's ellipsoid theorem giving average-distortion bounds for embeddings of metric spaces, controlled by nonlinear spectral gaps. | bi-Lipschitz embeddings, nonlinear spectral gaps, average distortion | Exp 1188, d'après A. Naor
- Nonlinear spectral gap | state | A generalization of the spectral gap of a graph to maps into nonlinear metric spaces, quantifying the obstruction to low-distortion embeddings. | graphs, metric spaces, Poincaré inequalities | Exp 1188

## 1189 (Hamenstädt) — length-spectrum rigidity
- Local marked length spectrum rigidity | theorem | On a closed negatively curved (Anosov) manifold the marked length spectrum locally determines the metric up to isometry, in all dimensions. | Anosov geodesic flows, marked length spectrum, X-ray transform, microlocal analysis | Exp 1189, d'après Guillarmou–Lefeuvre
- Microlocal geodesic X-ray transform method | technique | Using the geodesic X-ray transform, its normal operator as an elliptic pseudodifferential operator, and microlocal analysis to prove length-spectrum rigidity. | pseudodifferential operators, Anosov flows, X-ray transform inversion | Exp 1189

## 1190 (Michel) — subconvexity
- Subconvexity bounds for L-functions | theorem | Bounds on automorphic L-functions on the critical line improving on the convexity (Phragmén–Lindelöf) estimate by a power saving. | automorphic forms, L-functions, period formulas, amplification | Exp 1190
- Amplification method | technique | A moment/amplifier technique detecting an individual L-value by weighting it within a family and exploiting averaged second-moment estimates. | spectral theory of automorphic forms, trace formulas, period integrals | Exp 1190

## 1191 (Perelman) — implosion / blow-up
- Finite-time implosion for compressible fluids and NLS | theorem | Construction of smooth solutions of compressible Euler/Navier–Stokes and energy-supercritical NLS developing self-similar implosion singularities in finite time. | self-similar profiles, spectral stability, nonlinear PDE energy methods | Exp 1191, d'après Merle–Raphaël–Rodnianski–Szeftel
- Self-similar imploding profile construction | technique | Building finite-time singularities via smooth self-similar profile solutions and proving their nonlinear stability under perturbation. | self-similar variables, ODE shooting, spectral/energy stability | Exp 1191

## 1192 (Aubrun) — KLS conjecture
- Kannan–Lovász–Simonovits (KLS) conjecture | state | The conjecture that the Cheeger isoperimetric constant of an isotropic log-concave probability measure is bounded below by a universal dimension-independent constant. | log-concave measures, isoperimetry, Cheeger constant, convex geometry | Exp 1192
- Stochastic localization (Eldan) | technique | A measure-valued martingale process gradually localizing a log-concave measure into Gaussians, used to obtain near-optimal bounds toward the KLS conjecture. | log-concave measures, Itô calculus, martingales, covariance control | Exp 1192, d'après Y. Chen

## 1193 (Kowalski) — additive problems over function fields
- Binary additive problems for polynomials over finite fields | theorem | Asymptotic counts (twin-prime and Goldbach-type) for additive problems over F_q[t] in the large-q regime. | function field arithmetic, étale cohomology, equidistribution of Frobenius | Exp 1193, d'après Sawin–Shusterman
- Sheaf-theoretic counting over function fields | technique | Translating additive prime problems over F_q[t] into computations of compactly-supported étale cohomology and bounding Betti numbers. | étale cohomology, Weil bounds, perverse sheaves | Exp 1193

## 1194 (Meyer) — crystalline measures
- Crystalline measure | state | A tempered measure on Euclidean space whose support and the support of whose Fourier transform are both locally finite (discrete), generalizing Poisson summation / quasicrystals. | tempered distributions, Fourier transform, Poisson summation | Exp 1194, d'après Kurasov–Olevskii, Sarnak, Viazovska

## 1195 (Haettel) — K(π,1) for affine Artin groups
- K(π,1) conjecture for affine Artin groups | theorem | The Salvetti complex of an affine Coxeter system is aspherical, so its quotient is a classifying space, proving the K(π,1) conjecture for affine Artin groups. | Coxeter groups, Artin groups, Salvetti complex, hyperplane arrangements | Exp 1195, d'après Paolini–Salvetti
- Dual braid monoid / Garside structure method | technique | Establishing asphericity via Garside-theoretic structures on the dual braid monoid and the associated noncrossing-partition order complex with discrete Morse theory. | Garside theory, noncrossing partitions, discrete Morse theory | Exp 1195

## 1196 (Peluse) — three-term progressions
- Improved bounds for sets without three-term arithmetic progressions | theorem | Improved upper bounds on subsets of {1,...,N} and of F_q^n with no nontrivial 3-term AP, including the cap-set polynomial-method bound and the Bloom–Sisask logarithmic improvement. | additive combinatorics, Fourier analysis, polynomial method | Exp 1196, d'après Bloom–Sisask, Croot–Lev–Pach, Ellenberg–Gijswijt
- Slice rank / polynomial method (cap sets) | technique | Bounding extremal set sizes by upper-bounding the slice rank of an associated diagonal multilinear tensor via low-degree polynomials. | tensors, slice rank, finite-field polynomial degrees | Exp 1196, d'après Croot–Lev–Pach, Ellenberg–Gijswijt

## 1197 (Fresán) — unbounded denominators
- Unbounded denominators conjecture | theorem | A modular form on a finite-index subgroup of SL₂(Z) whose q-expansion has bounded denominators is a modular form for a congruence subgroup (with vector-valued generalization). | noncongruence modular forms, vector-valued modular forms, congruence subgroup property | Exp 1197, d'après Calegari–Dimitrov–Tang
- Arithmetic holonomicity bound | technique | A potential-theoretic / transcendence inequality bounding the dimension of a space of holonomic power series with arithmetic integrality, combined with Nevanlinna theory. | holonomic functions, capacity/potential theory, Nevanlinna theory | Exp 1197

## 1198 (Golse) — kinetic theory beyond Boltzmann
- Fluctuation theory for the Boltzmann–Grad limit | theorem | Rigorous derivation, in the Boltzmann–Grad limit, of fluctuation and large-deviation corrections to the Boltzmann equation from a hard-sphere system, extending Lanford's theorem. | hard-sphere dynamics, Boltzmann–Grad limit, BBGKY hierarchy | Exp 1198, d'après Bodineau–Gallagher–Saint-Raymond–Simonella
- BBGKY hierarchy / cumulant expansion | technique | Expanding correlations of a hard-sphere system via the BBGKY hierarchy and cluster/cumulant expansions to control fluctuations around the Boltzmann limit. | BBGKY hierarchy, hard-sphere collisions, cumulant expansions | Exp 1198

## 1199 (Krause) — pointwise ergodic theorems
- Pointwise ergodic theorems along polynomial sequences | theorem | Pointwise convergence of ergodic averages along sparse/polynomial sequences, via oscillation and variation estimates (Bourgain's pointwise ergodic theory). | ergodic averages, oscillation/variation inequalities, circle method, harmonic analysis | Exp 1199, d'après J. Bourgain

## 1200 (Rideau-Kikuchi) — twisted Lang–Weil
- Twisted Lang–Weil estimate | theorem | A point-count estimate for definable sets twisted by a Frobenius-type correspondence, quantifying equidistribution, with applications to difference algebra and pseudofinite fields. | Lang–Weil bounds, étale cohomology, correspondences, pseudofinite fields | Exp 1200, d'après Hrushovski–Shuddhodan–Varshavsky

## 1201 (Dospinescu) — direct summand conjecture
- Direct summand conjecture | theorem | For a finite extension of a regular Noetherian ring, the smaller ring is a direct summand as a module, proved in mixed characteristic. | commutative algebra, regular rings, perfectoid spaces, almost mathematics | Exp 1201, d'après André, Bhatt
- Perfectoid / almost-mathematics method | technique | Reducing problems in mixed-characteristic commutative algebra to perfectoid algebras and tilting, controlling errors via Faltings's almost mathematics. | perfectoid spaces, tilting equivalence, almost ring theory | Exp 1201

## 1202 (Maïda) — random permutation matrices
- Strong convergence of spectra of random permutation matrices | theorem | A sum of independent uniformly random permutation matrices, restricted to the orthogonal complement of the trivial representation, has operator norm converging to the spectral radius, giving almost-Ramanujan random regular graphs. | random matrices, free probability, random regular graphs, Ramanujan bound | Exp 1202, d'après Bordenave–Collins
- Strong asymptotic freeness / non-backtracking operator method | technique | Establishing strong (operator-norm) convergence to free limits via the non-backtracking (Ihara–Bass) operator and matched-moment polynomial bounds. | free probability, non-backtracking operator, trace-moment estimates | Exp 1202

## 1203 (de la Salle) — MIP* = RE
- MIP* = RE | theorem | The class of languages decidable by multiprover interactive proofs with entangled (quantum) provers equals the recursively enumerable languages. | interactive proofs, quantum entanglement, quantum correlation sets | Exp 1203, d'après Ji–Natarajan–Vidick–Wright–Yuen
- Refutation of the Connes embedding conjecture | state | The conjecture that every separable II₁ factor embeds into an ultrapower of the hyperfinite II₁ factor, shown false as a consequence of MIP* = RE. | type II₁ factors, ultrapowers, hyperfinite factor, quantum correlations | Exp 1203

## 1204 (Ghys) — non-simplicity of area-preserving Homeo(S²)
- Non-simplicity of the group of area-preserving homeomorphisms of S² | theorem | The group of area- and orientation-preserving homeomorphisms of the 2-sphere is not simple, via unbounded quasimorphisms built from spectral invariants. | area-preserving homeomorphisms, quasimorphisms, Calabi invariant, periodic Floer homology | Exp 1204, d'après Cristofaro-Gardiner–Humilière–Seyfaddini
- Periodic Floer homology spectral invariants | state | Sequences of spectral invariants of area-preserving surface maps defined via periodic Floer homology, assembling into unbounded quasimorphisms and a Calabi homogenization. | periodic Floer homology, mapping tori, quasimorphisms | Exp 1204

## 1205 (Hickman) — Carleson's problem
- Pointwise convergence for the Schrödinger equation (Carleson's problem) | theorem | The free Schrödinger evolution of an H^s(ℝⁿ) datum converges pointwise a.e. to the datum iff s ≥ n/(2(n+1)), resolving Carleson's problem. | Schrödinger maximal operator, restriction/extension estimates, decoupling, fractal measures | Exp 1205, d'après Du–Zhang
- Polynomial partitioning / decoupling for the Schrödinger maximal operator | technique | Bounding the Schrödinger maximal operator via broad–narrow analysis, polynomial partitioning, and ℓ²-decoupling with weighted/fractal restriction estimates. | polynomial partitioning, ℓ² decoupling, fractal Strichartz estimates | Exp 1205

## 1206 (Löh) — growth rates in hyperbolic groups
- Well-ordering of exponential growth rates of hyperbolic groups | theorem | The set of exponential growth rates of finitely generated subgroups of a hyperbolic group is well-ordered, with growth rates achieved and algebraic. | word-hyperbolic groups, growth series, translation lengths, quasi-geodesics | Exp 1206, d'après Fujiwara–Sela

## 1207 (Viale) — forcing axioms
- Asperó–Schindler theorem (MM⁺⁺ implies (∗)) | theorem | Martin's Maximum⁺⁺ implies Woodin's axiom (∗), unifying two strong forcing axioms and settling the continuum at ℵ₂ under them. | forcing axioms, Martin's Maximum, Pmax forcing, stationary tower, large cardinals | Exp 1207, d'après Asperó–Schindler
- Pmax / stationary-tower forcing | technique | Set-theoretic forcing constructions (Pmax, stationary tower) producing canonical models of strong forcing axioms. | Pmax forcing, stationary tower forcing, determinacy, large cardinals | Exp 1207

## 1208 (Dalibard) — Navier–Stokes non-uniqueness
- Non-uniqueness of Leray–Hopf solutions to forced Navier–Stokes | theorem | There exist forcing terms for which the 3D Navier–Stokes equations admit two distinct Leray–Hopf weak solutions, exhibiting non-uniqueness in the energy class. | Navier–Stokes, Leray–Hopf weak solutions, instability of self-similar profiles, spectral analysis | Exp 1208, d'après Albritton–Brué–Colombo
- Unstable self-similar profile / spectral instability method | technique | Constructing two solutions by exhibiting a linearly unstable self-similar background and bifurcating a second trajectory along an unstable eigenmode. | self-similar variables, linearized spectrum, unstable manifold | Exp 1208

## 1209 (Juteau) — symmetric tensor categories
- Classification of symmetric tensor categories in positive characteristic | theorem | Incompressibility/classification results for symmetric tensor categories of moderate growth over a field of characteristic p, with the Verlinde categories as universal fibers. | tensor categories, Frobenius, Verlinde category, fiber functors, Tannakian formalism | Exp 1209, d'après Coulembier–Etingof–Ostrik
- Verlinde category Ver_p | state | The semisimplification of the category of representations of Z/p in characteristic p, the universal incompressible target for symmetric tensor categories of moderate growth. | modular representation theory, semisimplification, symmetric tensor categories | Exp 1209

## 1210 (Tassion) — rotational invariance of percolation
- Rotational invariance of critical planar percolation | theorem | The scaling limit of critical Bernoulli percolation on a class of planar lattices is rotationally invariant, a step toward full conformal invariance. | planar percolation, crossing probabilities, RSW theory | Exp 1210, d'après Duminil-Copin et al.
- RSW / star-triangle (Yang–Baxter) transformation method | technique | Using Russo–Seymour–Welsh box-crossing estimates with star-triangle (Yang–Baxter) transformations to deform lattices and transport crossing events, yielding rotational invariance. | RSW theory, star-triangle transformation, isoradial graphs | Exp 1210
