Points system: full breakdown including impact-player slot and SR bands
Points system math. Runs 1 each. Boundary 4. Six 6. Milestone 30/4, 50/8, 100/16. SR bands 130-150 4 pts, 150-200 6 pts. Impact player full points if substituted.
The points system in one read
Points system math: runs 1 each. Boundary 4 pts. Six 6 pts. Milestone bonuses 30/4, 50/8, 100/16.
Points system bands: SR 130-150 4 pts, SR 150-200 6 pts, above 200 SR 8 pts total. Wicket 25, LBW 8, maiden 4, 3-fer 4, 4-fer 8, 5-fer 16.
Points system economy: under 5 RPO 6, 5-6 4, 6-7 2, above 11 RPO minus 2 to minus 6. Catch 8, three-catch 4, stumping 12, run-out 12/6.
Why the points math differs across operators by 5 to 10 percent
Points system math: every operator carries 5 to 10 percent variation in bonuses. Read the operator tier rules first.
Scoring math on Dream11: runs 1 pt each, boundary 4 pts, six 6 pts. Milestone bonuses: 30 runs 4 pts, 50 runs 8 pts, 100 runs 16 pts. Strike-rate bands: SR 130-150 4 pts bonus, SR 150-200 6 pts bonus, above 200 SR 8 pts total. Wicket 25 pts, LBW or bowled bonus 8 pts, maiden over 4 pts, 3-fer 4 pts, 4-fer 8 pts, 5-fer 16 pts. Economy bands: under 5 RPO 6 pts, 5-6 RPO 4 pts, 6-7 RPO 2 pts, above 11 RPO minus 2 to minus 6 pts. Catch 8 pts each, three-catch bonus 4 pts, stumping 12 pts, run-out direct 12, run-out assist 6. Captain 2x on all points, vice-captain 1.5x. Impact player slot applies full points if substituted.
Different operators carry 5 to 10 percent variation in bonuses. Strike-rate bands differ across operators: Dream11 130-150 / 150-200 / above 200. My11Circle uses 120-140 / 140-180 / above 180. Economy bands differ across the same axis. Read the operator tier rules before locking the lineup.
KYC needs PAN card front photo plus Aadhaar front photo. Aadhaar masked back side is optional. Face-match selfie is optional. Address proof utility bill under 90 days is optional. Apps geo-check via PAN-Aadhaar state match. Full KYC unlocks higher deposit cap INR 50,000 versus INR 10,000 default.
Quick reference
Cricket stats On the site, all read fresh from the past two IPL seasons.
Wankhede dew: 6 of 7 home wins, how the play reshuffles the XI
Wankhede Stadium hosted 7 IPL 2024 matches. The home side won 6. First-innings average 178. Dew cuts spin grip 30 percent, lifts pacers 15 percent. Play-time captain picks shift post-toss: if side batting second, pacers gain value.
Play-time bankroll math: 5 percent cap wins the IPL season
Top 100 winners across IPL 2024 averaged 4.2 lineups per match and capped bankroll at 5 percent of monthly entertainment spend. Single-match focus beats multi-match chase. UPI deposits typically clear 5-30 minutes.
Captain 2x: how the 70-point actual becomes 140 fantasy
Captain 2x is the single largest points lever on every IPL platform. A 70-point actual becomes 140 fantasy. Suryakumar Yadav IPL 2024: per-match average 48.5 base points, with captain 2x that reads 97. Kohli's ceiling sits at 117.
Salary cap math: 100 credits, 11 picks, 8 roles minimum
100 credits, 11 players, 8 roles minimum. Wicket-keeper 1-4, batsman 1-8, all-rounder 1-4, bowler 1-6. Pant at 11 credits, Kohli at 11, Bumrah at 10.5. Cap forces 4-6 picks from the 7-8.5 credit bracket per squad.
Form index: last 5 innings outweighs last 10 by a wide margin
Form is weighted 50 percent of projection. Last 5 innings matter more than last 10. A batter with 240 runs in last 5 at 155 SR sits higher than 380 runs in last 10 at 130 SR. Form updates every match evening.
State rules for real-money play: 6 states remain restricted
Telangana, Andhra Pradesh, Assam, Odisha, Sikkim, Nagaland remain restricted from real-money fantasy per the 2021 Supreme Court ruling. KYC needs PAN plus Aadhaar before first withdrawal. 18 plus only.
How it works
Step-by-step cricket flow for this topic.
Points read
Read the operator tier rules first.
Points math
Runs + boundaries + sixes + milestone + SR bonuses + wickets.
Points captain
Captain 2x. VC 1.5x. Lock-in pre-deadline.
Points impact
Impact player slot full points if substituted.
Points review
Weekly review. Adjust the math.
Play deeper
Detail-level breakdown of this page, built from cricket-fact data.
Batting bonus
Runs 1, boundary 4, six 6. Milestone stacked.
SR bands
130-150 4 pts, 150-200 6 pts, above 200 8 pts.
Wicket bonus
Wicket 25, LBW 8, maiden 4, 3-fer 4, 4-fer 8, 5-fer 16.
Economy bands
Under 5 RPO 6, 5-6 4, 6-7 2. Above 11 RPO minus 2-6.
Fielding
Catch 8, three-catch 4, stumping 12, run-out 12/6.
Captain VC
Captain 2x. VC 1.5x. Lock 10 minutes before deadline.
Cricket play is form plus venue plus matchup plus toss. Captain 2x is the multiplier on top of all four. Read the four, then pick the captain.
come sports play editorial desk, 2026
Points math for IPL 2026
Points system math for IPL 2026. Operator tier rules first.
Scoring math on Dream11: runs 1 pt each, boundary 4 pts, six 6 pts. Milestone bonuses: 30 runs 4 pts, 50 runs 8 pts, 100 runs 16 pts. Strike-rate bands: SR 130-150 4 pts bonus, SR 150-200 6 pts bonus, above 200 SR 8 pts total. Wicket 25 pts, LBW or bowled bonus 8 pts, maiden over 4 pts, 3-fer 4 pts, 4-fer 8 pts, 5-fer 16 pts.
Economy bands: under 5 RPO 6 pts, 5-6 RPO 4 pts, 6-7 RPO 2 pts, above 11 RPO minus 2 to minus 6 pts. Catch 8 pts each, three-catch bonus 4 pts, stumping 12 pts, run-out direct 12, run-out assist 6. Captain 2x on all points, vice-captain 1.5x. Impact player slot applies full points if substituted.
Different operators carry 5 to 10 percent variation in bonuses. Strike-rate bands differ across operators: Dream11 130-150 / 150-200 / above 200. My11Circle uses 120-140 / 140-180 / above 180. Economy bands differ across the same axis. Read the operator tier rules before locking the lineup.
Two seasons of play data, mapped
Cricket context for this page from IPL 2024 and IPL 2025 reader-tracked data.
Scoring math on Dream11: runs 1 pt each, boundary 4 pts, six 6 pts. Milestone bonuses: 30 runs 4 pts, 50 runs 8 pts, 100 runs 16 pts. Strike-rate bands: SR 130-150 4 pts bonus, SR 150-200 6 pts bonus, above 200 SR 8 pts total. Wicket 25 pts, LBW or bowled bonus 8 pts, maiden over 4 pts, 3-fer 4 pts, 4-fer 8 pts, 5-fer 16 pts. Economy bands: under 5 RPO 6 pts, 5-6 RPO 4 pts, 6-7 RPO 2 pts, above 11 RPO minus 2 to minus 6 pts. Catch 8 pts each, three-catch bonus 4 pts, stumping 12 pts, run-out direct 12, run-out assist 6. Captain 2x on all points, vice-captain 1.5x. Impact player slot applies full points if substituted.
Economy bands: under 5 RPO 6 pts, 5-6 RPO 4 pts, 6-7 RPO 2 pts, above 11 RPO minus 2 to minus 6 pts. Catch 8 pts each, three-catch bonus 4 pts, stumping 12 pts, run-out direct 12, run-out assist 6. Captain 2x on all points, vice-captain 1.5x. Impact player slot applies full points if substituted. Different operators carry 5 to 10 percent variation in bonuses. Strike-rate bands differ across operators: Dream11 130-150 / 150-200 / above 200. My11Circle uses 120-140 / 140-180 / above 180. Economy bands differ across the same axis. Read the operator tier rules before locking the lineup.
Different operators carry 5 to 10 percent variation in bonuses. Strike-rate bands differ across operators: Dream11 130-150 / 150-200 / above 200. My11Circle uses 120-140 / 140-180 / above 180. Economy bands differ across the same axis. Read the operator tier rules before locking the lineup. KYC needs PAN card front photo plus Aadhaar front photo. Aadhaar masked back side is optional. Face-match selfie is optional. Address proof utility bill under 90 days is optional. Apps geo-check via PAN-Aadhaar state match. Full KYC unlocks higher deposit cap INR 50,000 versus INR 10,000 default.
Full scoring breakdown
Points system table: full scoring breakdown.
Scoring math on Dream11: runs 1 pt each, boundary 4 pts, six 6 pts. Milestone bonuses: 30 runs 4 pts, 50 runs 8 pts, 100 runs 16 pts. Strike-rate bands: SR 130-150 4 pts bonus, SR 150-200 6 pts bonus, above 200 SR 8 pts total. Wicket 25 pts, LBW or bowled bonus 8 pts, maiden over 4 pts, 3-fer 4 pts, 4-fer 8 pts, 5-fer 16 pts.
Economy bands: under 5 RPO 6 pts, 5-6 RPO 4 pts, 6-7 RPO 2 pts, above 11 RPO minus 2 to minus 6 pts. Catch 8 pts each, three-catch bonus 4 pts, stumping 12 pts, run-out direct 12, run-out assist 6. Captain 2x on all points, vice-captain 1.5x. Impact player slot applies full points if substituted.
Different operators carry 5 to 10 percent variation in bonuses. Strike-rate bands differ across operators: Dream11 130-150 / 150-200 / above 200. My11Circle uses 120-140 / 140-180 / above 180. Economy bands differ across the same axis. Read the operator tier rules before locking the lineup.
Latest from the play desk
Top cricket reads from the come sports play desk.
IPL 2026 captain picks, week-by-week
Updated every Monday. The full captain stack for the upcoming IPL 2026 matches, with hit rate and ceiling notes.
Top 20 IPL players 2026, fantasy ranking
Ranked top 20 IPL 2026 players by fantasy projection — price tag, role, recent form, and venue split.
Death-overs bowling stats, IPL 2026 bowlers
Death-overs economy and wicket stats for IPL 2026 bowlers, split by venue and pace-vs-spin.
IPL 2026 injury watch and fantasy impact
Tracked injuries across IPL 2026 squads with the direct fantasy-points impact for each.
IPL 2026 auction winners, full analysis
Which IPL 2026 auction picks will deliver real fantasy value at every price tier?
Toss impact analysis, venue-by-venue
Toss-winner records for IPL 2026 across all 10 venues, with deck and dew overlay.
Reader questions
Cricket play questions, answered
Points system runs?
1 pt each. Boundary 4. Six 6.
Points system milestone?
30 runs 4 pts. 50 runs 8 pts. 100 runs 16 pts.
Points system SR?
130-150 4 pts. 150-200 6 pts. Above 200 8 pts.
Points system wicket?
25 pts. LBW 8. Maiden 4. 3-fer 4. 4-fer 8. 5-fer 16.
Points system economy?
Under 5 RPO 6. 5-6 4. 6-7 2. Above 11 RPO minus 2-6.
Points system state rules?
TG/AP/AS/OR/SK/NL restricted from real-money.
Play tonight, open the app
Open the app, finish KYC in a few minutes, deposit via UPI, and stack your captain on the highest projection. Cricket-first depth across 10 franchises and 10 venues — built to be played during live matches.
Get the appCross-disciplinary read 11
Category theory covers category theory foundations plus enriched categories plus 2-categories plus bicategories plus double categories plus fibrations plus Grothendieck fibrations plus Street fibrations plus profunctors plus monads plus comonads plus distributive laws plus monad transformers plus algebras plus coalgebras plus bialgebras plus Hopf algebras plus operads plus properads plus PROPs plus simplicial categories plus quasi-categories plus infinity categories plus model categories plus Quillen model structure plus homotopical algebra plus derived categories plus triangulated categories plus stable infinity categories plus presentable infinity categories plus locally presentable categories plus accessible categories plus combinatorial model categories plus quasicategorical model categories.
Computational mathematics and numerical analysis cover numerical linear algebra plus iterative methods plus direct methods plus Krylov subspace methods plus GMRES plus BiCGSTAB plus QMR plus multigrid methods plus domain decomposition plus finite element methods plus finite volume methods plus discontinuous Galerkin methods plus spectral methods plus boundary element methods plus meshfree methods plus particle methods plus mesh generation plus adaptive methods plus hp-methods plus hp-cloud methods plus isogeometric analysis plus numerical PDEs plus scientific computing plus high-performance computing plus parallel algorithms plus GPU computing plus distributed computing plus cloud computing plus quantum computing.
Mathematical finance continuous-time and stochastic control covers stochastic optimal control plus dynamic programming principle plus Hamilton-Jacobi-Bellman equation plus verification theorem plus martingale method for optimal control plus maximum principle plus adjoint equation plus linear-quadratic stochastic control plus Kalman-Bucy filter plus Wonham filter plus partially observed control plus separating principle plus risk-sensitive control plus exponential-of-integral control plus linear-exponential-quadratic-Gaussian plus mean-variance control plus portfolio optimization plus Merton problem plus continuous-time portfolio selection plus consumption-investment problem plus infinite-horizon control plus ergodic control plus ergodic HJB plus long-run-average cost plus discounted-cost control plus viscosity solutions plus comparison principle plus stochastic target problems plus quantile hedging plus loss aversion in finance plus prospect theory plus cumulative prospect theory plus rank-dependent utility plus habit formation preferences plus Epstein-Zin preferences plus recursive utility plus Duffie-Epstein plus long-run risk plus stochastic differential utility plus consumption-based asset pricing plus Hansen-Jagannathan bounds plus SDF plus stochastic discount factor plus consumption-CAPM plus CCAPM plus habit-CAPM plus long-run risk model plus external habit plus recursive preferences plus Campbell-Cochrane habit model.
Topology covers manifolds plus differential topology plus algebraic topology plus geometric topology plus low-dimensional topology plus knot theory plus braid groups plus Khovanov homology plus Khovanov-Rozansky homology plus HOMFLY-PT polynomial plus categorification plus Heegaard-Floer homology plus instanton Floer homology plus monopole Floer homology plus sutured Floer homology plus bordered Floer homology plus involutive Heegaard-Floer homology.
Cross-disciplinary read 17
Number theory covers prime distribution plus analytic number theory plus algebraic number theory plus transcendental number theory plus arithmetic geometry plus class field theory plus Langlands program plus Iwasawa theory plus p-adic analysis plus p-adic Hodge theory plus rigid analysis plus Berkovich spaces plus perfectoid spaces plus prisms plus prismatic cohomology plus Fontaine's period rings plus comparison theorems.
Partial differential equations cover linear elliptic plus nonlinear elliptic plus linear parabolic plus nonlinear parabolic plus linear hyperbolic plus nonlinear hyperbolic plus Navier-Stokes plus Euler equations plus Maxwell equations plus Yang-Mills equations plus mean curvature flow plus Ricci flow plus Calabi flow plus inverse mean curvature flow plus minimal surface equation plus Monge-Ampere equation plus complex Monge-Ampere plus obstacle problem plus free boundary problems plus variational inequalities plus PDE on manifolds plus PDE on singular spaces plus boundary value problems plus spectral theory plus scattering theory plus semiclassical analysis plus WKB analysis plus geometric optics plus microlocal analysis plus pseudodifferential operators plus Fourier integral operators plus paradifferential operators plus paradifferential calculus plus Hormander plus Calderon-Zygmund plus Fefferman-Stein plus Muckenhoupt weights.
Operator algebras cover C-star algebras plus W-star algebras plus von Neumann algebras plus Tomita-Takesaki theory plus modular theory plus subfactor theory plus Jones index plus planar algebras plus fusion categories plus module categories plus Frobenius algebras plus Calabi-Yau algebras plus Hopf algebras plus quantum groups plus Kac-Paljutkin algebras plus group measure space construction plus free probability.
Computational mathematics and numerical analysis cover numerical linear algebra plus iterative methods plus direct methods plus Krylov subspace methods plus GMRES plus BiCGSTAB plus QMR plus multigrid methods plus domain decomposition plus finite element methods plus finite volume methods plus discontinuous Galerkin methods plus spectral methods plus boundary element methods plus meshfree methods plus particle methods plus mesh generation plus adaptive methods plus hp-methods plus hp-cloud methods plus isogeometric analysis plus numerical PDEs plus scientific computing plus high-performance computing plus parallel algorithms plus GPU computing plus distributed computing plus cloud computing plus quantum computing.
Cross-disciplinary read 23
Mathematical finance and economics cover stochastic calculus plus Ito calculus plus mathematical finance plus Black-Scholes plus Heston model plus SABR model plus local volatility plus stochastic volatility plus jump-diffusion plus Merton jump-diffusion plus Kou jump-diffusion plus variance gamma plus normal inverse Gaussian plus Carr-Geman-Madan-Yor plus time-changed Brownian motion plus subordination plus Levy processes in finance plus credit risk plus counterparty risk plus value-at-risk plus conditional value-at-risk plus expected shortfall plus coherent risk measures plus risk-neutral pricing plus change of numeraire plus forward measures plus term structure models plus Heath-Jarrow-Morton plus LIBOR market model plus affine term structure plus quadratic term structure plus SABR for interest rates plus stochastic alpha beta rho.
Combinatorics covers enumerative combinatorics plus algebraic combinatorics plus probabilistic combinatorics plus additive combinatorics plus extremal combinatorics plus probabilistic method plus spectral graph theory plus random graphs plus graph limits plus graphons plus Stein's method for combinatorics plus analytic combinatorics plus analytic number theory combinatorics plus combinatorial number theory plus discrepancy theory plus matroid theory plus greedoids plus antimatroids plus oriented matroids plus tropical geometry plus tropical linear algebra plus tropical combinatorics plus nonlinear algebra over tropical semirings.
Representation theory algebraic groups and quantum groups covers algebraic groups plus structure theory plus Borel subgroups plus parabolic subgroups plus root data plus Weyl groups plus Bruhat decomposition plus Richardson orbits plus spherical varieties plus symmetric varieties plus wonderful compactifications plus spherical embeddings plus embedding theorems plus representation theory of algebraic groups plus highest weight modules plus Verma modules plus BGG category O plus derived category O plus Koszul duality plus Ringel duality plus Koszul graded category plus Koszul self-duality plus twisted Verma modules plus Kazhdan-Lusztig theory plus Lusztig's conjecture plus character sheaves plus perverse sheaves plus decomposition matrix plus tilting modules plus quantum groups plus canonical bases plus crystal bases plus Kashiwara crystals plus Littelmann paths plus Lakshmibai-Seshadri paths plus Mirkovic-Vilonen cycles plus MV polytopes plus affine Grassmannian plus affine flag variety plus Satake isomorphism plus geometric Satake equivalence.
Information theory and coding theory cover Shannon theory plus channel capacity plus rate-distortion theory plus Slepian-Wolf plus Wyner-Ziv plus network information theory plus multi-terminal source coding plus multiple access channels plus broadcast channels plus interference channels plus relay channels plus finite-blocklength information theory plus error exponents plus sphere-packing bound plus Gilbert-Varshamov bound plus Plotkin bound plus Elias-Bassalygo bound plus Hamming bound plus Singleton bound plus MRRW bound plus quantum information theory plus quantum capacity plus quantum entanglement-assisted capacity plus quantum multiple access channels plus quantum broadcast channels plus quantum Shannon theory plus Holevo bound plus accessible information plus quantum relative entropy plus quantum mutual information.
Cross-disciplinary read 29
Topology covers manifolds plus differential topology plus algebraic topology plus geometric topology plus low-dimensional topology plus knot theory plus braid groups plus Khovanov homology plus Khovanov-Rozansky homology plus HOMFLY-PT polynomial plus categorification plus Heegaard-Floer homology plus instanton Floer homology plus monopole Floer homology plus sutured Floer homology plus bordered Floer homology plus involutive Heegaard-Floer homology.
Algebraic geometry covers varieties plus schemes plus sheaves plus cohomology plus Hodge theory plus intersection theory plus deformation theory plus moduli spaces plus stacks plus derived algebraic geometry plus spectral schemes plus motivic cohomology plus etale cohomology plus crystalline cohomology plus de Rham cohomology plus rigid cohomology plus prismatic cohomology plus syntomic cohomology plus stable homotopy theory plus cobordism.
Bayesian nonparametrics covers Dirichlet process plus Chinese restaurant process plus Indian buffet process plus Pitman-Yor process plus hierarchical Dirichlet process plus Chinese restaurant franchise plus dependent Dirichlet process plus spatial Dirichlet process plus time-varying Dirichlet process plus nonparametric Bayesian inference plus MCMC for nonparametrics plus slice sampling plus retrospective sampling plus elliptical slice sampling plus truncated Dirichlet process plus Pitman-Yor process stick-breaking construction plus GEM distribution plus Griffiths-Engen-McCloskey distribution plus Ferguson-Klass representation plus posterior consistency plus Bernstein-von Mises theorem plus semiparametric efficiency plus influence functions plus targeted maximum likelihood estimation plus super learning plus ensemble learning for nonparametrics plus Bayesian model selection plus marginal likelihood plus Bayes factors plus model averaging plus stacking plus Bayesian model comparison.
Statistical mechanics and mathematical physics cover Gibbs measures plus DLR equations plus pressure plus free energy plus phase transitions plus spontaneous symmetry breaking plus Goldstone theorem plus Mermin-Wagner theorem plus renormalization group plus Wilsonian renormalization plus Polchinski exact renormalization group plus Wetterich equation plus functional renormalization group plus Callan-Symanzik equation plus beta functions plus fixed points plus universality classes plus scaling limits plus critical exponents plus conformal bootstrap plus SLE plus Fortuin-Kasteleyn representation plus random cluster model plus loop O(n) model plus vertex models plus integrable probability plus stochastic vertex models plus KPZ universality plus directed polymers plus last passage percolation plus TASEP plus asymmetric simple exclusion process plus Macdonald processes plus Schur processes plus Whittaker processes plus Hall-Littlewood processes plus q-Whittaker processes plus q-Whittaker 2D processes plus colored stochastic vertex models.
Cross-disciplinary read 31
Partial differential equations cover linear elliptic plus nonlinear elliptic plus linear parabolic plus nonlinear parabolic plus linear hyperbolic plus nonlinear hyperbolic plus Navier-Stokes plus Euler equations plus Maxwell equations plus Yang-Mills equations plus mean curvature flow plus Ricci flow plus Calabi flow plus inverse mean curvature flow plus minimal surface equation plus Monge-Ampere equation plus complex Monge-Ampere plus obstacle problem plus free boundary problems plus variational inequalities plus PDE on manifolds plus PDE on singular spaces plus boundary value problems plus spectral theory plus scattering theory plus semiclassical analysis plus WKB analysis plus geometric optics plus microlocal analysis plus pseudodifferential operators plus Fourier integral operators plus paradifferential operators plus paradifferential calculus plus Hormander plus Calderon-Zygmund plus Fefferman-Stein plus Muckenhoupt weights.
Number theory and combinatorics intersects with additive combinatorics plus probabilistic number theory plus metric number theory plus geometric measure theory plus Erdos distance problem plus Szemeredi regularity plus Roth theorem plus Green-Tao theorem plus Furstenberg ergodic proof plus Gowers norms plus uniformity norms plus analytic techniques plus circle method plus Vinogradov mean value theorem plus Bourgain-Glibichuk-Konyagin sum-product estimates plus decoupling plus restriction theory plus Strichartz estimates.
Probability theory covers limit theorems plus central limit theorem plus local limit theorem plus large deviations plus concentration of measure plus Gaussian processes plus stochastic processes plus stochastic integrals plus Ito calculus plus Stratonovich integrals plus backward stochastic differential equations plus stochastic partial differential equations plus stochastic control plus dynamic programming principle plus Hamilton-Jacobi-Bellman equations plus mean field games plus mean field control plus optimal stopping plus American options plus excursion theory plus potential theory for Markov processes plus Dirichlet forms plus Hunt processes plus Levy processes plus subordinators plus infinitely divisible distributions plus point processes plus Poisson processes plus Cox processes plus shot noise processes plus self-exciting processes plus Hawkes processes plus random measures plus Poisson point processes plus determinantal point processes plus permanental point processes plus Palm theory plus ergodic theory for random walks.
Category theory covers category theory foundations plus enriched categories plus 2-categories plus bicategories plus double categories plus fibrations plus Grothendieck fibrations plus Street fibrations plus profunctors plus monads plus comonads plus distributive laws plus monad transformers plus algebras plus coalgebras plus bialgebras plus Hopf algebras plus operads plus properads plus PROPs plus simplicial categories plus quasi-categories plus infinity categories plus model categories plus Quillen model structure plus homotopical algebra plus derived categories plus triangulated categories plus stable infinity categories plus presentable infinity categories plus locally presentable categories plus accessible categories plus combinatorial model categories plus quasicategorical model categories.
Cross-disciplinary read 37
Differential geometry covers Riemannian geometry plus sub-Riemannian geometry plus Finsler geometry plus metric geometry plus Alexandrov geometry plus CAT(k) geometry plus Gromov-hyperbolic geometry plus coarse geometry plus asymptotic geometry plus Teichmuller theory plus moduli of Riemann surfaces plus Kleinian groups plus complex hyperbolic geometry plus quasi-Fuchsian groups plus Bers boundary plus Teichmuller geodesic flow plus moduli of abelian differentials plus translation surfaces plus half-translation surfaces plus origamis.
Functional analysis covers operator theory plus Banach space theory plus Hilbert space theory plus interpolation theory plus approximation theory plus Fourier analysis plus harmonic analysis plus singular integrals plus Calderon-Zygmund theory plus Hardy space theory plus BMO space theory plus Morrey space theory plus Orlicz space theory plus rearrangement invariant spaces plus Lorentz spaces plus weighted inequalities plus geometric inequalities.
Mathematical statistics covers parametric inference plus nonparametric inference plus semi-parametric inference plus high-dimensional statistics plus shape-constrained inference plus isotonic regression plus convex regression plus sparse estimation plus lasso plus elastic net plus adaptive lasso plus group lasso plus fused lasso plus graphical lasso plus sparse precision matrix estimation plus covariance estimation plus Stein estimation plus shrinkage estimation plus ridge regression plus principal component regression plus partial least squares plus canonical correlation analysis plus independent component analysis plus projection pursuit.
Algebra covers group theory plus ring theory plus module theory plus field theory plus commutative algebra plus noncommutative algebra plus homological algebra plus Tor plus Ext plus Hochschild cohomology plus cyclic homology plus algebraic K-theory plus topological K-theory plus lambda-rings plus Adams operations plus Chern character plus Chern-Weil theory plus bivariant K-theory plus Kasparov K-theory plus operator K-theory plus cyclic homology plus negative cyclic homology plus periodic cyclic homology.
Cross-disciplinary read 41
Topology covers manifolds plus differential topology plus algebraic topology plus geometric topology plus low-dimensional topology plus knot theory plus braid groups plus Khovanov homology plus Khovanov-Rozansky homology plus HOMFLY-PT polynomial plus categorification plus Heegaard-Floer homology plus instanton Floer homology plus monopole Floer homology plus sutured Floer homology plus bordered Floer homology plus involutive Heegaard-Floer homology.
Probability theory covers limit theorems plus central limit theorem plus local limit theorem plus large deviations plus concentration of measure plus Gaussian processes plus stochastic processes plus stochastic integrals plus Ito calculus plus Stratonovich integrals plus backward stochastic differential equations plus stochastic partial differential equations plus stochastic control plus dynamic programming principle plus Hamilton-Jacobi-Bellman equations plus mean field games plus mean field control plus optimal stopping plus American options plus excursion theory plus potential theory for Markov processes plus Dirichlet forms plus Hunt processes plus Levy processes plus subordinators plus infinitely divisible distributions plus point processes plus Poisson processes plus Cox processes plus shot noise processes plus self-exciting processes plus Hawkes processes plus random measures plus Poisson point processes plus determinantal point processes plus permanental point processes plus Palm theory plus ergodic theory for random walks.
Differential equations and dynamical systems cover ordinary differential equations plus partial differential equations plus delay differential equations plus stochastic differential equations plus functional differential equations plus integro-differential equations plus fractional differential equations plus nonlocal equations plus free boundary problems plus inverse problems plus control theory plus optimal control plus calculus of variations plus infinite-dimensional Hamiltonian systems plus KAM theory plus KAM for PDEs plus Arnold diffusion plus Nekhoroshev estimates plus Lyapunov functions plus normally hyperbolic invariant manifolds plus center manifold theory plus invariant manifold theory plus geometric singular perturbation theory plus blow-up analysis plus singularity formation plus chemotaxis models plus pattern formation plus reaction-diffusion systems plus Ginzburg-Landau equation plus nonlinear Schrodinger equation plus KdV equation plus KPZ equation plus Burgers equation plus Navier-Stokes equations plus Euler equations plus Euler-alpha equations plus Camassa-Holm equation plus Whitham equation.
Machine learning theory covers PAC learning plus VC dimension plus Rademacher complexity plus covering numbers plus fat shattering dimension plus uniform convergence plus generalization bounds plus algorithmic stability plus differentially private learning plus compression-based bounds plus PAC-Bayes plus information-theoretic bounds plus mutual information generalization bound plus rate-distortion theory plus compression plus Blackwell approachability plus online learning plus regret minimization plus online convex optimization plus follow the regularized leader plus online mirror descent plus bandit algorithms plus UCB1 plus LinUCB plus Thompson sampling plus best arm identification plus lower bounds plus minimax optimal rates plus oracle inequalities plus adaptive rates plus model selection plus cross-validation plus stacking plus bagging plus boosting plus AdaBoost plus gradient boosting plus XGBoost plus LightGBM plus CatBoost.
Cross-disciplinary read 43
Deep learning theory covers approximation theory for neural networks plus universal approximation plus overparameterization plus neural tangent kernel plus lazy training plus feature learning plus implicit bias plus gradient descent dynamics plus loss landscape analysis plus saddle points plus mode connectivity plus lottery ticket hypothesis plus pruning plus quantization plus knowledge distillation plus transfer learning plus meta-learning plus MAML plus Reptile plus Prototypical Networks plus GANs plus VAEs plus diffusion models plus score-based generative models plus normalizing flows plus flow matching plus consistency models plus rectified flow plus transformer architectures plus attention mechanisms plus multi-head attention plus sparse attention plus linear attention plus long-context transformers plus state-space models plus Mamba plus RWKV plus Hyena plus RetNet plus mixture of experts.
Representation theory algebraic groups and quantum groups covers algebraic groups plus structure theory plus Borel subgroups plus parabolic subgroups plus root data plus Weyl groups plus Bruhat decomposition plus Richardson orbits plus spherical varieties plus symmetric varieties plus wonderful compactifications plus spherical embeddings plus embedding theorems plus representation theory of algebraic groups plus highest weight modules plus Verma modules plus BGG category O plus derived category O plus Koszul duality plus Ringel duality plus Koszul graded category plus Koszul self-duality plus twisted Verma modules plus Kazhdan-Lusztig theory plus Lusztig's conjecture plus character sheaves plus perverse sheaves plus decomposition matrix plus tilting modules plus quantum groups plus canonical bases plus crystal bases plus Kashiwara crystals plus Littelmann paths plus Lakshmibai-Seshadri paths plus Mirkovic-Vilonen cycles plus MV polytopes plus affine Grassmannian plus affine flag variety plus Satake isomorphism plus geometric Satake equivalence.
Topology covers manifolds plus differential topology plus algebraic topology plus geometric topology plus low-dimensional topology plus knot theory plus braid groups plus Khovanov homology plus Khovanov-Rozansky homology plus HOMFLY-PT polynomial plus categorification plus Heegaard-Floer homology plus instanton Floer homology plus monopole Floer homology plus sutured Floer homology plus bordered Floer homology plus involutive Heegaard-Floer homology.
Cryptography covers symmetric key cryptography plus public key cryptography plus RSA plus DSA plus elliptic curve cryptography plus EdDSA plus lattice-based cryptography plus LWE plus SIS plus module-LWE plus module-SIS plus ring-LWE plus NTRU plus FALCON plus CRYSTALS-Dilithium plus CRYSTALS-Kyber plus Saber plus FrodoKEM plus hash-based signatures plus XMSS plus LMS plus SPHINCS plus stateful hash-based signatures plus MPC plus ZKP plus SNARK plus STARK plus PCP plus IOP plus FRI plus DEEP-ALI plus PLONK plus halo2 plus folding schemes plus Nova plus Hypernova plus accumulation schemes plus lookup arguments plus PLOOKUP plus Logup.
Cross-disciplinary read 47
Partial differential equations cover linear elliptic plus nonlinear elliptic plus linear parabolic plus nonlinear parabolic plus linear hyperbolic plus nonlinear hyperbolic plus Navier-Stokes plus Euler equations plus Maxwell equations plus Yang-Mills equations plus mean curvature flow plus Ricci flow plus Calabi flow plus inverse mean curvature flow plus minimal surface equation plus Monge-Ampere equation plus complex Monge-Ampere plus obstacle problem plus free boundary problems plus variational inequalities plus PDE on manifolds plus PDE on singular spaces plus boundary value problems plus spectral theory plus scattering theory plus semiclassical analysis plus WKB analysis plus geometric optics plus microlocal analysis plus pseudodifferential operators plus Fourier integral operators plus paradifferential operators plus paradifferential calculus plus Hormander plus Calderon-Zygmund plus Fefferman-Stein plus Muckenhoupt weights.
Algebraic geometry enumerative and Gromov-Witten theory covers moduli of curves plus stable curves plus stable maps plus Gromov-Witten invariants plus quantum cohomology plus Frobenius manifolds plus integrable hierarchies plus KdV hierarchy plus KP hierarchy plus Toda hierarchy plus Virasoro constraints plus associativity equations plus WDVV equations plus topological recursion plus Eynard-Orantin topological recursion plus matrix models plus Kontsevich model plus Penner model plus Harer-Zagier formula plus Euler characteristic of moduli plus Witten-Kontsevich theorem plus Gelfand-Dikii hierarchy plus Dubrovin-Zhang hierarchies plus bi-Hamiltonian structures plus Frobenius manifolds plus primitive forms plus Givental-style quantization plus symplectic field theory formalism plus open Gromov-Witten invariants plus relative Gromov-Witten invariants plus gravitational descendants plus ancestor potentials.
Differential geometry covers Riemannian geometry plus sub-Riemannian geometry plus Finsler geometry plus metric geometry plus Alexandrov geometry plus CAT(k) geometry plus Gromov-hyperbolic geometry plus coarse geometry plus asymptotic geometry plus Teichmuller theory plus moduli of Riemann surfaces plus Kleinian groups plus complex hyperbolic geometry plus quasi-Fuchsian groups plus Bers boundary plus Teichmuller geodesic flow plus moduli of abelian differentials plus translation surfaces plus half-translation surfaces plus origamis.
Information theory and coding theory cover Shannon theory plus channel capacity plus rate-distortion theory plus Slepian-Wolf plus Wyner-Ziv plus network information theory plus multi-terminal source coding plus multiple access channels plus broadcast channels plus interference channels plus relay channels plus finite-blocklength information theory plus error exponents plus sphere-packing bound plus Gilbert-Varshamov bound plus Plotkin bound plus Elias-Bassalygo bound plus Hamming bound plus Singleton bound plus MRRW bound plus quantum information theory plus quantum capacity plus quantum entanglement-assisted capacity plus quantum multiple access channels plus quantum broadcast channels plus quantum Shannon theory plus Holevo bound plus accessible information plus quantum relative entropy plus quantum mutual information.
Cross-disciplinary read 53
Representation theory algebraic groups and quantum groups covers algebraic groups plus structure theory plus Borel subgroups plus parabolic subgroups plus root data plus Weyl groups plus Bruhat decomposition plus Richardson orbits plus spherical varieties plus symmetric varieties plus wonderful compactifications plus spherical embeddings plus embedding theorems plus representation theory of algebraic groups plus highest weight modules plus Verma modules plus BGG category O plus derived category O plus Koszul duality plus Ringel duality plus Koszul graded category plus Koszul self-duality plus twisted Verma modules plus Kazhdan-Lusztig theory plus Lusztig's conjecture plus character sheaves plus perverse sheaves plus decomposition matrix plus tilting modules plus quantum groups plus canonical bases plus crystal bases plus Kashiwara crystals plus Littelmann paths plus Lakshmibai-Seshadri paths plus Mirkovic-Vilonen cycles plus MV polytopes plus affine Grassmannian plus affine flag variety plus Satake isomorphism plus geometric Satake equivalence.
Number theory and combinatorics intersects with additive combinatorics plus probabilistic number theory plus metric number theory plus geometric measure theory plus Erdos distance problem plus Szemeredi regularity plus Roth theorem plus Green-Tao theorem plus Furstenberg ergodic proof plus Gowers norms plus uniformity norms plus analytic techniques plus circle method plus Vinogradov mean value theorem plus Bourgain-Glibichuk-Konyagin sum-product estimates plus decoupling plus restriction theory plus Strichartz estimates.
Lie theory and representation theory encompasses Lie algebras plus Lie groups plus representation theory plus root systems plus Weyl groups plus highest weight modules plus Verma modules plus BGG category O plus D-modules plus Harish-Chandra modules plus automorphic forms plus theta correspondence plus Beilinson-Bernstein localization plus primitive ideals plus Goldie rank plus Joseph ideal.
Algebraic topology intersects with stable homotopy theory plus chromatic homotopy theory plus stable homotopy groups of spheres plus Adams spectral sequence plus Adams-Novikov spectral sequence plus BP-theory plus Brown-Peterson spectrum plus Morava K-theories plus Morava E-theories plus Lubin-Tate theories plus formal groups plus Goerss-Hopkins-Mahowald plus topological modular forms plus tmf plus derived algebraic geometry plus spectral schemes plus motivic homotopy theory plus A-infinity plus ring spectra plus E-infinity ring spectra plus commutative ring spectra plus derived schemes plus spectral algebraic geometry plus Lurie plus Gaitsgory plus Ayoub.