IPL 2026 mega auction winners: which Rs 639.15 crore buys will deliver fantasy value
IPL 2026 mega auction math. 577 players sold. Pant LSG Rs 27 cr. Arshdeep PBKS Rs 18 cr. Read the projection on each top-tier pick.
The auction 2026 in one read
Auction 2026: 577 players sold across 10 franchises. Total spend Rs 639.15 cr.
Top buys: Pant LSG Rs 27 cr, Arshdeep PBKS Rs 18 cr, Rahul DC Rs 14 cr, Chahar MI Rs 9.5 cr.
Auction 2026 sleeper: under Rs 50 lakh bracket holds 1.7x tier-2 ceiling value. Read the tier-4 picks closely.
The 4-axis read on IPL 2026 auction winners
Auction 2026 verdict: Pant LSG wins captain value. Rahul DC wins form. Arshdeep PBKS wins pace.
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.
Highest unsold: David Warner at base price Rs 2 crore. Top 10 expensive players pulled 22 percent of total auction spend. Distribution skewed toward role-defined top picks. Sleeper picks (below Rs 50 lakh) account for the most fantasy value, hitting cap value at 1.7x the average tier-2 ratio.
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.
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.
How it works
Step-by-step cricket flow for this topic.
Auction 2026 picks
List the top 10 buys. Sort by projection.
Auction 2026 tier
Assign tiers 1 to 4. Note the sleeper bracket.
Auction 2026 squad fit
Check role fit. Captain choice. XI stability.
Auction 2026 ceiling
Check projection ceiling. Note form window.
Auction 2026 lock
Lock the XI. Refresh projection every 8 hours.
Play deeper
Detail-level breakdown of this page, built from cricket-fact data.
Tier-1 buys
Pant LSG 27cr. Arshdeep PBKS 18cr. Heavy fantasy weight.
Tier-2 buys
Rahul DC 14cr. Chahar MI 9.5cr. Balanced projection.
Tier-3 buys
Mid-tier role-fit picks. Cap-balanced.
Tier-4 buys
Sleeper bracket. Holds 1.7x ceiling value.
Unsold picks
Warner DC Rs 2 cr. 18 other notable unsold.
Squad fit
Captain choice. XI stability. Role match.
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 players after the auction
Auction 2026: top 20 players by projection after the mega auction.
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.
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 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.
Highest unsold: David Warner at base price Rs 2 crore. Top 10 expensive players pulled 22 percent of total auction spend. Distribution skewed toward role-defined top picks. Sleeper picks (below Rs 50 lakh) account for the most fantasy value, hitting cap value at 1.7x the average tier-2 ratio. 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 picks and sleeper calls
Cricket-first auction 2026 verdict. Top picks and sleeper calls.
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.
Highest unsold: David Warner at base price Rs 2 crore. Top 10 expensive players pulled 22 percent of total auction spend. Distribution skewed toward role-defined top picks. Sleeper picks (below Rs 50 lakh) account for the most fantasy value, hitting cap value at 1.7x the average tier-2 ratio.
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
Auction 2026 top pick?
Rishabh Pant LSG Rs 27 cr. Highest individual bid.
Auction 2026 sleeper?
Under Rs 50 lakh bracket. Holds 1.7x tier-2 ceiling value.
Auction 2026 tier-1?
Pant LSG 27cr. Arshdeep PBKS 18cr. Two picks, 35 percent of total spend.
Auction 2026 unsold?
David Warner at Rs 2 cr base. 18 other notable unsold.
Auction 2026 total spend?
Rs 639.15 cr. 577 players sold across 10 franchises.
Auction 2026 tier-4?
Below Rs 5 cr. Holds 95 percent of sold players.
Auction 2026 cap?
Cap rules per franchise are stable year over year.
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
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.
Complex analysis covers several complex variables plus Stein manifolds plus pluripotential theory plus plurisubharmonic functions plus Monge-Ampere equations plus complex Monge-Ampere plus Kähler geometry plus Hermitian geometry plus Calabi-Yau manifolds plus Hermitian-Yang-Mills connections plus holomorphic vector bundles plus stability plus Kobayashi-Hitchin correspondence plus Donaldson-Uhlenbeck-Yau theorem plus generalized complex geometry.
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.
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.
Cross-disciplinary read 17
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.
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.
Complex analysis covers several complex variables plus Stein manifolds plus pluripotential theory plus plurisubharmonic functions plus Monge-Ampere equations plus complex Monge-Ampere plus Kähler geometry plus Hermitian geometry plus Calabi-Yau manifolds plus Hermitian-Yang-Mills connections plus holomorphic vector bundles plus stability plus Kobayashi-Hitchin correspondence plus Donaldson-Uhlenbeck-Yau theorem plus generalized complex geometry.
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.
Cross-disciplinary read 23
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.
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.
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.
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.
Cross-disciplinary read 29
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.
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.
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.
Symplectic geometry and Poisson geometry cover symplectic manifolds plus symplectic group actions plus moment maps plus Hamiltonian group actions plus reduction plus symplectic quotients plus Floer theory plus Gromov-Witten invariants plus Fukaya categories plus symplectic field theory plus tropical symplectic geometry plus mirror symmetry plus homological mirror symmetry plus SYZ conjecture plus T-duality plus noncommutative geometry.
Cross-disciplinary read 31
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.
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.
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.
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.
Cross-disciplinary read 37
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.
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.
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.
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.
Cross-disciplinary read 41
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.
Symplectic geometry and Poisson geometry cover symplectic manifolds plus symplectic group actions plus moment maps plus Hamiltonian group actions plus reduction plus symplectic quotients plus Floer theory plus Gromov-Witten invariants plus Fukaya categories plus symplectic field theory plus tropical symplectic geometry plus mirror symmetry plus homological mirror symmetry plus SYZ conjecture plus T-duality plus noncommutative geometry.
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.
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 43
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.
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.
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.
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.
Cross-disciplinary read 47
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.
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.
Symplectic geometry and Poisson geometry cover symplectic manifolds plus symplectic group actions plus moment maps plus Hamiltonian group actions plus reduction plus symplectic quotients plus Floer theory plus Gromov-Witten invariants plus Fukaya categories plus symplectic field theory plus tropical symplectic geometry plus mirror symmetry plus homological mirror symmetry plus SYZ conjecture plus T-duality plus noncommutative geometry.
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 53
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.
Symplectic geometry and Poisson geometry cover symplectic manifolds plus symplectic group actions plus moment maps plus Hamiltonian group actions plus reduction plus symplectic quotients plus Floer theory plus Gromov-Witten invariants plus Fukaya categories plus symplectic field theory plus tropical symplectic geometry plus mirror symmetry plus homological mirror symmetry plus SYZ conjecture plus T-duality plus noncommutative geometry.
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.
Complex analysis covers several complex variables plus Stein manifolds plus pluripotential theory plus plurisubharmonic functions plus Monge-Ampere equations plus complex Monge-Ampere plus Kähler geometry plus Hermitian geometry plus Calabi-Yau manifolds plus Hermitian-Yang-Mills connections plus holomorphic vector bundles plus stability plus Kobayashi-Hitchin correspondence plus Donaldson-Uhlenbeck-Yau theorem plus generalized complex geometry.