Toss impact IPL: 60 percent won by toss winner, 70 percent on high-dew venues
Toss impact math. 60 percent won by toss winner overall. 70 percent high-dew venues. 52 percent low-dew. Captain flip within 30 seconds of toss.
The toss impact in one read
Toss impact math: 47 of 78 IPL 2024 matches won by toss winner. 60 percent overall.
Toss impact venues: 70 percent high dew. 52 percent low dew. Toss-winner bias grows season-over-season.
Toss impact verdict: pre-toss captain lock. Post-toss flip within 30 seconds of toss-confirm.
Why the toss overlay fits in the last 30 seconds
Toss impact math: 60 percent. 70 percent high dew. 52 percent low dew. Read the overlay math.
Toss swings 15 to 20 percent of fantasy outcomes, mostly through venue overlay. 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 within 30 seconds of toss-confirm. Toss-winner records across IPL 2024: 47 of 78 matches won by the team that won the toss. 60 percent overall. High dew venues tip the toss advantage to 70 percent. Low dew venues sit at 52 percent. Toss-winner bias grows with each passing season.
Captain picks that flip post-toss win more contests. Play-time captain pick: pre-toss lock Suryakumar Yadav if MI batting first; post-toss flip to Rohit Sharma if MI batting second. The delta across the season sits at 9 to 14 percent on the contest leaderboard.
Venue distribution by dew factor: high dew Wankhede, Chepauk, Eden Gardens, Mohali. Medium dew Bengaluru, Lucknow, Jaipur. Low dew Hyderabad, Ahmedabad, Delhi. Venue history matters more in T20 cricket than across any other format. The past 5 seasons form the deepest read.
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.
Toss read
Note venue. Dew factor first.
Toss captain
Pre-toss captain lock.
Toss flip
Wait for toss. Flip captain within 30 seconds.
Toss XI
Lock XI 10 minutes before deadline.
Toss review
Weekly review. Adjust the math.
Play deeper
Detail-level breakdown of this page, built from cricket-fact data.
Toss winner
60 percent won. Bias grows season-over-season.
Dew overlay
High dew 70 percent. Low dew 52 percent.
Captain flip
Within 30 seconds. Pre-toss lock first.
Matchup
Last 5 head-to-head. Handedness counts.
Venue read
Wankhede, Chepauk high dew. Hyderabad low dew.
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
Toss overlay for IPL 2026
Toss impact math for IPL 2026. 60 percent overall. Dew overlay.
Toss swings 15 to 20 percent of fantasy outcomes, mostly through venue overlay. 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 within 30 seconds of toss-confirm.
Toss-winner records across IPL 2024: 47 of 78 matches won by the team that won the toss. 60 percent overall. High dew venues tip the toss advantage to 70 percent. Low dew venues sit at 52 percent. Toss-winner bias grows with each passing season.
Captain picks that flip post-toss win more contests. Play-time captain pick: pre-toss lock Suryakumar Yadav if MI batting first; post-toss flip to Rohit Sharma if MI batting second. The delta across the season sits at 9 to 14 percent on the contest leaderboard.
Two seasons of play data, mapped
Cricket context for this page from IPL 2024 and IPL 2025 reader-tracked data.
Toss swings 15 to 20 percent of fantasy outcomes, mostly through venue overlay. 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 within 30 seconds of toss-confirm. Toss-winner records across IPL 2024: 47 of 78 matches won by the team that won the toss. 60 percent overall. High dew venues tip the toss advantage to 70 percent. Low dew venues sit at 52 percent. Toss-winner bias grows with each passing season.
Toss-winner records across IPL 2024: 47 of 78 matches won by the team that won the toss. 60 percent overall. High dew venues tip the toss advantage to 70 percent. Low dew venues sit at 52 percent. Toss-winner bias grows with each passing season. Captain picks that flip post-toss win more contests. Play-time captain pick: pre-toss lock Suryakumar Yadav if MI batting first; post-toss flip to Rohit Sharma if MI batting second. The delta across the season sits at 9 to 14 percent on the contest leaderboard.
Captain picks that flip post-toss win more contests. Play-time captain pick: pre-toss lock Suryakumar Yadav if MI batting first; post-toss flip to Rohit Sharma if MI batting second. The delta across the season sits at 9 to 14 percent on the contest leaderboard. Venue distribution by dew factor: high dew Wankhede, Chepauk, Eden Gardens, Mohali. Medium dew Bengaluru, Lucknow, Jaipur. Low dew Hyderabad, Ahmedabad, Delhi. Venue history matters more in T20 cricket than across any other format. The past 5 seasons form the deepest read.
Toss overlay math, applied
Toss impact math applied: pre-toss lock, post-toss flip, dew overlay.
Toss swings 15 to 20 percent of fantasy outcomes, mostly through venue overlay. 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 within 30 seconds of toss-confirm.
Toss-winner records across IPL 2024: 47 of 78 matches won by the team that won the toss. 60 percent overall. High dew venues tip the toss advantage to 70 percent. Low dew venues sit at 52 percent. Toss-winner bias grows with each passing season.
Captain picks that flip post-toss win more contests. Play-time captain pick: pre-toss lock Suryakumar Yadav if MI batting first; post-toss flip to Rohit Sharma if MI batting second. The delta across the season sits at 9 to 14 percent on the contest leaderboard.
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
Toss impact math?
60 percent won by toss winner overall. 70 percent high dew.
Toss impact flip?
Within 30 seconds of toss-confirm. Pre-toss lock first.
Toss impact venue?
Wankhede, Chepauk, Eden Gardens, Mohali high dew.
Toss impact bias?
Grows season-over-season. Read the deck.
Toss impact state rules?
TG/AP/AS/OR/SK/NL restricted from real-money.
Toss impact age?
18 plus only. KYC required.
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
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.
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.
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.
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 17
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.
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.
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.
Cross-disciplinary read 23
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.
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.
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.
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.
Cross-disciplinary read 29
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.
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.
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.
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 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
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.
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.
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.
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 41
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.
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.
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.
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.
Cross-disciplinary read 43
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.
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.
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.
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.
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
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.
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.
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 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.