Top 20 IPL players 2026: ranked by fantasy projection, price tag, role, form
Top 20 IPL players 2026: projection rank. Kohli, Pant, Rohit, Gill, Head, Klaasen, Jaiswal, Rahul lead. Read the projection band on each.
The top 20 in one read
Top 20 IPL 2026 players ranked: Kohli RCB 13.4 cr. Pant LSG 13.0. Rohit MI 12.5. Gill GT 12.0. Head SRH 11.5.
Top 20 second tier: Klaasen SRH 11.0. Jaiswal RR 11.0. Rahul DC 10.5. Suryakumar MI 10.0. Samson RR 9.5.
Top 20 third tier: Pooran LSG 9.5. Russell KKR 9.0. Cummins SRH 9.0. Bumrah MI 9.0. Narine KKR 9.0.
Why the top 20 list swings by 30 percent across the season
Top 20 IPL players 2026: projection rank. Form 50, venue 30, matchup 20, toss 10. Read the band.
Top 20 IPL 2026 players by fantasy projection: Virat Kohli RCB at 13.4 credits. Rishabh Pant LSG 13.0. Rohit Sharma MI 12.5. Shubman Gill GT 12.0. Travis Head SRH 11.5. Heinrich Klaasen SRH 11.0. Yashasvi Jaiswal RR 11.0. KL Rahul DC 10.5. Top 20 second tier: Suryakumar Yadav MI 10.0. Sanju Samson RR 9.5. Nicholas Pooran LSG 9.5. Andre Russell KKR 9.0. Pat Cummins SRH 9.0. Jasprit Bumrah MI 9.0. Sunil Narine KKR 9.0. Rashid Khan GT 8.5. Yuzvendra Chahal RR 8.5.
Top 20 third tier: Axar Patel DC 8.5. Hardik Pandya MI 8.0. Aiden Markram SRH 8.0. Marcus Stoinis LSG 8.0. Trent Boult RR 8.0. T Natarajan SRH 7.5. All carry tier-1 projection status. Form, venue history, and matchup swing the rank within the top 20.
IPL 2026 mega auction in December 2025 sold 577 players across 10 franchises. Total spend Rs 639.15 crore. Rishabh Pant to LSG for Rs 27 crore held the highest individual bid. KL Rahul to DC for Rs 14 crore. Arshdeep Singh to PBKS for Rs 18 crore. Average price per player sat at Rs 1.10 crore. Auction tier distribution: Tier 1 above Rs 15 crore (Pant LSG 27cr, Arshdeep PBKS 18cr). Tier 2 Rs 8 to 15 crore (Rahul DC 14cr, Chahar MI 9.5cr). Tier 3 Rs 5 to 8 crore. Tier 4 below Rs 5 crore holds 95 percent of the players sold. Capper ratio: top 1 percent of squad spends 35 percent of cap.
Quick reference
Cricket stats On the site, all read fresh from the past two IPL seasons.
Chinnaswamy at full tilt: 12 centuries in 7 IPL 2024 fixtures
M. Chinnaswamy hosted 7 of the 74 IPL 2024 league matches. First-innings average 185, low dew, flat track. Virat Kohli's 741 IPL 2024 runs came largely here. KL Rahul averages 52 across three seasons at this ground. Twelve centuries were hit across the seven matches.
Powerplay corner hits: why 145+ SR anchors pay off the cap
Powerplay phase carries the lowest projection variance because every player's role is fixed. Top-order bats at flat tracks give the steadiest read. Faf du Plessis, Rohit Sharma, KL Rahul regularly clear 50 in the powerplay at 145+ SR.
Death-overs ceiling picks: how to chase the 80-point upside
A 40-point death over becomes 80 with one six. A 10-point duck becomes 20. Death overs are the most chaotic phase of T20. Captain picks here should chase ceiling rather than floor. T Natarajan SRH death-over economy 6.80 in IPL 2024.
Left-handers vs Rashid Khan: where the 12-point swing lives
Last 5 encounters per pair show specific batter-vs-bowler patterns. Rashid Khan holds 5.8 economy vs left-handers against 7.4 vs right-handers. Yashasvi Jaiswal averages 18 against him; Ruturaj Gaikwad averages 42.
Toss and venue together: 15-20 percent of fantasy outcomes
Toss swings 15-20 percent of fantasy outcomes. In Chinnaswamy, batting first averages 185, second 178. At Chepauk, the gap widens to 22 runs because of the dew curve. Captain picks update post-toss via app notification.
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.
Top 20 read
Read the projection rank. Sort by 4-axis read.
Top 20 captain
Captain on top-order bats. PP specialists lead.
Top 20 tier
Tier 1 carries 35 percent of cap. Tier 4 carries 95 percent of squad.
Top 20 form
Read last 5 innings. SR sort. Hot streak 1.6x.
Top 20 review
Weekly review. Adjust the rank.
Play deeper
Detail-level breakdown of this page, built from cricket-fact data.
Tier 1
Pant LSG 27cr. Arshdeep PBKS 18cr. 2 picks.
Tier 2
Rahul DC 14cr. Chahar MI 9.5cr. Balanced.
Tier 3
Mid-tier role-fit picks. Cap-balanced.
Tier 4
Sleeper bracket. Holds 1.7x ceiling value.
Matchup
Last 5 head-to-head. Handedness counts.
Bankroll
5 percent per match cap. Single-match focus.
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
Top 20 list for IPL 2026
Top 20 IPL players 2026 list. Form, venue, matchup math.
Top 20 IPL 2026 players by fantasy projection: Virat Kohli RCB at 13.4 credits. Rishabh Pant LSG 13.0. Rohit Sharma MI 12.5. Shubman Gill GT 12.0. Travis Head SRH 11.5. Heinrich Klaasen SRH 11.0. Yashasvi Jaiswal RR 11.0. KL Rahul DC 10.5.
Top 20 second tier: Suryakumar Yadav MI 10.0. Sanju Samson RR 9.5. Nicholas Pooran LSG 9.5. Andre Russell KKR 9.0. Pat Cummins SRH 9.0. Jasprit Bumrah MI 9.0. Sunil Narine KKR 9.0. Rashid Khan GT 8.5. Yuzvendra Chahal RR 8.5.
Top 20 third tier: Axar Patel DC 8.5. Hardik Pandya MI 8.0. Aiden Markram SRH 8.0. Marcus Stoinis LSG 8.0. Trent Boult RR 8.0. T Natarajan SRH 7.5. All carry tier-1 projection status. Form, venue history, and matchup swing the rank within the top 20.
Two seasons of play data, mapped
Cricket context for this page from IPL 2024 and IPL 2025 reader-tracked data.
Top 20 IPL 2026 players by fantasy projection: Virat Kohli RCB at 13.4 credits. Rishabh Pant LSG 13.0. Rohit Sharma MI 12.5. Shubman Gill GT 12.0. Travis Head SRH 11.5. Heinrich Klaasen SRH 11.0. Yashasvi Jaiswal RR 11.0. KL Rahul DC 10.5. Top 20 second tier: Suryakumar Yadav MI 10.0. Sanju Samson RR 9.5. Nicholas Pooran LSG 9.5. Andre Russell KKR 9.0. Pat Cummins SRH 9.0. Jasprit Bumrah MI 9.0. Sunil Narine KKR 9.0. Rashid Khan GT 8.5. Yuzvendra Chahal RR 8.5.
Top 20 second tier: Suryakumar Yadav MI 10.0. Sanju Samson RR 9.5. Nicholas Pooran LSG 9.5. Andre Russell KKR 9.0. Pat Cummins SRH 9.0. Jasprit Bumrah MI 9.0. Sunil Narine KKR 9.0. Rashid Khan GT 8.5. Yuzvendra Chahal RR 8.5. Top 20 third tier: Axar Patel DC 8.5. Hardik Pandya MI 8.0. Aiden Markram SRH 8.0. Marcus Stoinis LSG 8.0. Trent Boult RR 8.0. T Natarajan SRH 7.5. All carry tier-1 projection status. Form, venue history, and matchup swing the rank within the top 20.
Top 20 third tier: Axar Patel DC 8.5. Hardik Pandya MI 8.0. Aiden Markram SRH 8.0. Marcus Stoinis LSG 8.0. Trent Boult RR 8.0. T Natarajan SRH 7.5. All carry tier-1 projection status. Form, venue history, and matchup swing the rank within the top 20. IPL 2026 mega auction in December 2025 sold 577 players across 10 franchises. Total spend Rs 639.15 crore. Rishabh Pant to LSG for Rs 27 crore held the highest individual bid. KL Rahul to DC for Rs 14 crore. Arshdeep Singh to PBKS for Rs 18 crore. Average price per player sat at Rs 1.10 crore. Auction tier distribution: Tier 1 above Rs 15 crore (Pant LSG 27cr, Arshdeep PBKS 18cr). Tier 2 Rs 8 to 15 crore (Rahul DC 14cr, Chahar MI 9.5cr). Tier 3 Rs 5 to 8 crore. Tier 4 below Rs 5 crore holds 95 percent of the players sold. Capper ratio: top 1 percent of squad spends 35 percent of cap.
Top 20 projection rank for IPL 2026
Top 20 IPL players 2026 rank by projection. Form, venue, matchup math.
Top 20 IPL 2026 players by fantasy projection: Virat Kohli RCB at 13.4 credits. Rishabh Pant LSG 13.0. Rohit Sharma MI 12.5. Shubman Gill GT 12.0. Travis Head SRH 11.5. Heinrich Klaasen SRH 11.0. Yashasvi Jaiswal RR 11.0. KL Rahul DC 10.5.
Top 20 second tier: Suryakumar Yadav MI 10.0. Sanju Samson RR 9.5. Nicholas Pooran LSG 9.5. Andre Russell KKR 9.0. Pat Cummins SRH 9.0. Jasprit Bumrah MI 9.0. Sunil Narine KKR 9.0. Rashid Khan GT 8.5. Yuzvendra Chahal RR 8.5.
Top 20 third tier: Axar Patel DC 8.5. Hardik Pandya MI 8.0. Aiden Markram SRH 8.0. Marcus Stoinis LSG 8.0. Trent Boult RR 8.0. T Natarajan SRH 7.5. All carry tier-1 projection status. Form, venue history, and matchup swing the rank within the top 20.
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
Top 20 read?
Projection rank. Form 50, venue 30, matchup 20, toss 10.
Top 20 captain?
PP specialist. 82 percent hit rate. Skip death-overs.
Top 20 tier 1?
2 picks. 35 percent of cap. Pant LSG plus Arshdeep PBKS.
Top 20 form?
Last 5 innings. SR sort. Hot streak 1.6x.
Top 20 bankroll?
5 percent per match cap. Single-match focus.
Top 20 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
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.
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.
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.
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.
Cross-disciplinary read 17
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.
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.
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.
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.
Cross-disciplinary read 23
Statistical signal processing covers estimation theory plus detection theory plus estimation bounds plus Cramer-Rao bound plus Bayesian Cramér-Rao bound plus Ziv-Zakai bound plus Weiss-Weinstein bound plus Bobrovsky-Zakai bound plus Kalman filtering plus extended Kalman filter plus unscented Kalman filter plus particle filtering plus Markov Chain Monte Carlo plus sequential Monte Carlo plus importance sampling plus sequential importance sampling plus resampling plus Rao-Blackwellization plus auxiliary particle filter plus Gaussian particle filter plus cubature Kalman filter plus sigma point filters plus particle smoothing plus forward-backward smoothing plus Viterbi algorithm plus Baum-Welch algorithm plus HMM plus hidden Markov models plus state-space models plus dynamic Bayesian networks plus Kalman smoother plus RTS smoother plus fixed-lag smoother plus fixed-point smoother plus expectation-maximization plus EM algorithm plus variational EM.
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.
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.
Data mining and database theory covers query languages plus relational algebra plus relational calculus plus SQL plus Datalog plus linear Datalog plus Datalog with negation plus recursive queries plus conjunctive queries plus first-order queries plus query evaluation plus query optimization plus cost-based optimization plus join algorithms plus hash join plus sort-merge join plus nested loop join plus index structures plus B-trees plus B+ trees plus hash indexes plus bitmap indexes plus column stores plus row stores plus LSM trees plus write-ahead logging plus ARIES recovery algorithm plus transaction processing plus concurrency control plus two-phase locking plus timestamp ordering plus multiversion concurrency control plus snapshot isolation plus serializable snapshot isolation plus distributed transactions plus two-phase commit plus three-phase commit plus consensus plus Paxos plus Raft.
Cross-disciplinary read 29
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.
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.
Data mining and database theory covers query languages plus relational algebra plus relational calculus plus SQL plus Datalog plus linear Datalog plus Datalog with negation plus recursive queries plus conjunctive queries plus first-order queries plus query evaluation plus query optimization plus cost-based optimization plus join algorithms plus hash join plus sort-merge join plus nested loop join plus index structures plus B-trees plus B+ trees plus hash indexes plus bitmap indexes plus column stores plus row stores plus LSM trees plus write-ahead logging plus ARIES recovery algorithm plus transaction processing plus concurrency control plus two-phase locking plus timestamp ordering plus multiversion concurrency control plus snapshot isolation plus serializable snapshot isolation plus distributed transactions plus two-phase commit plus three-phase commit plus consensus plus Paxos plus Raft.
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.
Cross-disciplinary read 31
Information geometry and statistics covers manifold of probability distributions plus Fisher information metric plus natural gradient plus natural gradient descent plus mirror descent plus information-geometric optimization plus dually flat manifolds plus Bregman divergence plus KL divergence plus exponential family plus mixture family plus mixture of exponential families plus hierarchical models plus empirical likelihood plus exponential tilting plus dual geometry plus Legendre transform plus convex conjugate plus Bregman divergence plus mirror maps plus relative entropy plus information projections plus I-projection plus M-projection plus e-projection plus m-projection plus information geometry of neural networks plus Wasserstein natural gradient plus Stein variational gradient descent plus score matching plus implicit score matching plus denoising score matching plus sliced score matching plus truncated score matching plus Riemannian manifold Langevin dynamics plus constrained manifold optimization plus hyperbolic geometry plus Poincaré embeddings plus hyperbolic neural networks plus geometric deep learning plus graph neural networks.
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.
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.
Cross-disciplinary read 37
Mathematical logic covers proof theory plus model theory plus set theory plus recursion theory plus computability theory plus ordinal analysis plus large cardinals plus forcing plus inner model theory plus descriptive set theory plus determinacy plus large continuum plus projective determinacy plus AD plus Woodin cardinals plus Ultimate-L plus determinacy hypotheses. Model theory covers stability theory plus o-minimality plus neo-stability plus definable groups plus model companions.
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.
Cross-disciplinary read 41
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.
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.
Mathematical physics covers classical mechanics plus continuum mechanics plus statistical mechanics plus kinetic theory plus quantum mechanics plus relativistic quantum mechanics plus quantum field theory plus gauge theory plus noncommutative field theory plus supersymmetry plus string theory plus conformal field theory plus topological field theory plus integrable systems plus soliton theory plus scattering theory plus inverse scattering plus Riemann-Hilbert problem.
Cross-disciplinary read 43
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.
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.
Statistical signal processing covers estimation theory plus detection theory plus estimation bounds plus Cramer-Rao bound plus Bayesian Cramér-Rao bound plus Ziv-Zakai bound plus Weiss-Weinstein bound plus Bobrovsky-Zakai bound plus Kalman filtering plus extended Kalman filter plus unscented Kalman filter plus particle filtering plus Markov Chain Monte Carlo plus sequential Monte Carlo plus importance sampling plus sequential importance sampling plus resampling plus Rao-Blackwellization plus auxiliary particle filter plus Gaussian particle filter plus cubature Kalman filter plus sigma point filters plus particle smoothing plus forward-backward smoothing plus Viterbi algorithm plus Baum-Welch algorithm plus HMM plus hidden Markov models plus state-space models plus dynamic Bayesian networks plus Kalman smoother plus RTS smoother plus fixed-lag smoother plus fixed-point smoother plus expectation-maximization plus EM algorithm plus variational EM.
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.
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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.
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.
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.
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.
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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.
Statistical signal processing covers estimation theory plus detection theory plus estimation bounds plus Cramer-Rao bound plus Bayesian Cramér-Rao bound plus Ziv-Zakai bound plus Weiss-Weinstein bound plus Bobrovsky-Zakai bound plus Kalman filtering plus extended Kalman filter plus unscented Kalman filter plus particle filtering plus Markov Chain Monte Carlo plus sequential Monte Carlo plus importance sampling plus sequential importance sampling plus resampling plus Rao-Blackwellization plus auxiliary particle filter plus Gaussian particle filter plus cubature Kalman filter plus sigma point filters plus particle smoothing plus forward-backward smoothing plus Viterbi algorithm plus Baum-Welch algorithm plus HMM plus hidden Markov models plus state-space models plus dynamic Bayesian networks plus Kalman smoother plus RTS smoother plus fixed-lag smoother plus fixed-point smoother plus expectation-maximization plus EM algorithm plus variational EM.
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.
Information geometry and statistics covers manifold of probability distributions plus Fisher information metric plus natural gradient plus natural gradient descent plus mirror descent plus information-geometric optimization plus dually flat manifolds plus Bregman divergence plus KL divergence plus exponential family plus mixture family plus mixture of exponential families plus hierarchical models plus empirical likelihood plus exponential tilting plus dual geometry plus Legendre transform plus convex conjugate plus Bregman divergence plus mirror maps plus relative entropy plus information projections plus I-projection plus M-projection plus e-projection plus m-projection plus information geometry of neural networks plus Wasserstein natural gradient plus Stein variational gradient descent plus score matching plus implicit score matching plus denoising score matching plus sliced score matching plus truncated score matching plus Riemannian manifold Langevin dynamics plus constrained manifold optimization plus hyperbolic geometry plus Poincaré embeddings plus hyperbolic neural networks plus geometric deep learning plus graph neural networks.