IPL 2026 injury watch: how an XI shifts by 18 to 30 percent in a single week
Injury watch. 117 injuries IPL 2024. Soft-tissue 52 percent. Impact 22. Bowling-stress 18. Pre-existing 8. Read the swap math before locking.
The injury watch in one read
Injury watch math: 117 squad-listed injuries IPL 2024. 52 percent soft-tissue pulls. 22 percent impact. 18 percent bowling-stress.
Injury swap math: top-7 batter injury forces a restructure of 3 to 5 picks. Death-overs pacer 1 to 3 picks. Keeper swap most expensive.
Injury watch verdict: top of live-update queue. Captain pivot rotates within 30 seconds.
Why injury watch sits at the top of the live-update queue
Injury watch math: a single injury shift can swing 18 to 30 percent of a week's captain math.
IPL 2024 injury tracker: 117 squad-listed injuries across the 10 franchises. 52 percent were soft-tissue pulls. 22 percent were impact injuries. 18 percent were bowling-stress injuries. 8 percent were pre-existing. A single injury shift can swing 18 to 30 percent of a week's captain math.
Replacement math: an injury to a top-7 batter forces a restructure of 3 to 5 picks in the lineup. An injury to a death-overs pacer forces a restructure of 1 to 3 picks, depending on the bowler role. An injury to a wicket-keeper forces a complete keeper swap, which is the most expensive rebuild path.
Captain picks on injured players drop to zero. Captain pivot picks up the next-best option. Injury watch sits at the top of the live-update queue. Captain pivot rotates to the next-best projection within 30 seconds. Pre-toss captain watch refresh every 8 hours. Post-toss watch refreshes the moment the XI locks.
Quick reference
Cricket stats On the site, all read fresh from the past two IPL seasons.
Wankhede dew: 6 of 7 home wins, how the play reshuffles the XI
Wankhede Stadium hosted 7 IPL 2024 matches. The home side won 6. First-innings average 178. Dew cuts spin grip 30 percent, lifts pacers 15 percent. Play-time captain picks shift post-toss: if side batting second, pacers gain value.
Play-time bankroll math: 5 percent cap wins the IPL season
Top 100 winners across IPL 2024 averaged 4.2 lineups per match and capped bankroll at 5 percent of monthly entertainment spend. Single-match focus beats multi-match chase. UPI deposits typically clear 5-30 minutes.
Captain 2x: how the 70-point actual becomes 140 fantasy
Captain 2x is the single largest points lever on every IPL platform. A 70-point actual becomes 140 fantasy. Suryakumar Yadav IPL 2024: per-match average 48.5 base points, with captain 2x that reads 97. Kohli's ceiling sits at 117.
Salary cap math: 100 credits, 11 picks, 8 roles minimum
100 credits, 11 players, 8 roles minimum. Wicket-keeper 1-4, batsman 1-8, all-rounder 1-4, bowler 1-6. Pant at 11 credits, Kohli at 11, Bumrah at 10.5. Cap forces 4-6 picks from the 7-8.5 credit bracket per squad.
Form index: last 5 innings outweighs last 10 by a wide margin
Form is weighted 50 percent of projection. Last 5 innings matter more than last 10. A batter with 240 runs in last 5 at 155 SR sits higher than 380 runs in last 10 at 130 SR. Form updates every match evening.
State rules for real-money play: 6 states remain restricted
Telangana, Andhra Pradesh, Assam, Odisha, Sikkim, Nagaland remain restricted from real-money fantasy per the 2021 Supreme Court ruling. KYC needs PAN plus Aadhaar before first withdrawal. 18 plus only.
How it works
Step-by-step cricket flow for this topic.
Injury read
Check the live injury watch feed. Refresh every 8 hours.
Injury swap
Batter injury 3 to 5 pick swap. Pacer 1 to 3. Keeper full rebuild.
Injury captain
Captain pivot. Next-best within 30 seconds.
Injury bankroll
5 percent per match cap. Hold the line.
Injury review
Weekly review. Adjust.
Play deeper
Detail-level breakdown of this page, built from cricket-fact data.
Soft-tissue 52%
Pulls and strains. 3 to 5 days recovery.
Impact 22%
Direct hits. 7 to 14 days recovery.
Bowling-stress 18%
Long-term. 14 to 42 days.
Pre-existing 8%
Known. X-icon for weeks.
Batter swap
3 to 5 picks in XI. Most expensive.
Pacer swap
1 to 3 picks. Death-overs math only.
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
Injury watch feed for IPL 2026
Injury watch feed for IPL 2026. Refresh every 8 hours.
IPL 2024 injury tracker: 117 squad-listed injuries across the 10 franchises. 52 percent were soft-tissue pulls. 22 percent were impact injuries. 18 percent were bowling-stress injuries. 8 percent were pre-existing. A single injury shift can swing 18 to 30 percent of a week's captain math.
Replacement math: an injury to a top-7 batter forces a restructure of 3 to 5 picks in the lineup. An injury to a death-overs pacer forces a restructure of 1 to 3 picks, depending on the bowler role. An injury to a wicket-keeper forces a complete keeper swap, which is the most expensive rebuild path.
Captain picks on injured players drop to zero. Captain pivot picks up the next-best option. Injury watch sits at the top of the live-update queue. Captain pivot rotates to the next-best projection within 30 seconds. Pre-toss captain watch refresh every 8 hours. Post-toss watch refreshes the moment the XI locks.
Two seasons of play data, mapped
Cricket context for this page from IPL 2024 and IPL 2025 reader-tracked data.
IPL 2024 injury tracker: 117 squad-listed injuries across the 10 franchises. 52 percent were soft-tissue pulls. 22 percent were impact injuries. 18 percent were bowling-stress injuries. 8 percent were pre-existing. A single injury shift can swing 18 to 30 percent of a week's captain math. Replacement math: an injury to a top-7 batter forces a restructure of 3 to 5 picks in the lineup. An injury to a death-overs pacer forces a restructure of 1 to 3 picks, depending on the bowler role. An injury to a wicket-keeper forces a complete keeper swap, which is the most expensive rebuild path.
Replacement math: an injury to a top-7 batter forces a restructure of 3 to 5 picks in the lineup. An injury to a death-overs pacer forces a restructure of 1 to 3 picks, depending on the bowler role. An injury to a wicket-keeper forces a complete keeper swap, which is the most expensive rebuild path. Captain picks on injured players drop to zero. Captain pivot picks up the next-best option. Injury watch sits at the top of the live-update queue. Captain pivot rotates to the next-best projection within 30 seconds. Pre-toss captain watch refresh every 8 hours. Post-toss watch refreshes the moment the XI locks.
Replacement math: an injury to a top-7 batter forces a restructure of 3 to 5 picks in the lineup. An injury to a death-overs pacer forces a restructure of 1 to 3 picks, depending on the bowler role. An injury to a wicket-keeper forces a complete keeper swap, which is the most expensive rebuild path. Captain picks on injured players drop to zero. Captain pivot picks up the next-best option. Injury watch sits at the top of the live-update queue. Captain pivot rotates to the next-best projection within 30 seconds. Pre-toss captain watch refresh every 8 hours. Post-toss watch refreshes the moment the XI locks.
Live injuries, per squad
Injury watch feed: live injuries, per squad. Refresh every 8 hours.
IPL 2024 injury tracker: 117 squad-listed injuries across the 10 franchises. 52 percent were soft-tissue pulls. 22 percent were impact injuries. 18 percent were bowling-stress injuries. 8 percent were pre-existing. A single injury shift can swing 18 to 30 percent of a week's captain math.
Replacement math: an injury to a top-7 batter forces a restructure of 3 to 5 picks in the lineup. An injury to a death-overs pacer forces a restructure of 1 to 3 picks, depending on the bowler role. An injury to a wicket-keeper forces a complete keeper swap, which is the most expensive rebuild path.
Captain picks on injured players drop to zero. Captain pivot picks up the next-best option. Injury watch sits at the top of the live-update queue. Captain pivot rotates to the next-best projection within 30 seconds. Pre-toss captain watch refresh every 8 hours. Post-toss watch refreshes the moment the XI locks.
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IPL 2026 captain picks, week-by-week
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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
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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
Injury watch feed?
Live injury watch. Refresh every 8 hours.
Injury watch XI swing?
Top-7 batter 3 to 5 picks. Pacer 1 to 3. Keeper full.
Injury watch captain pivot?
Next-best within 30 seconds.
Injury watch window?
Soft-tissue 3 to 5 days. Impact 7 to 14. Bowling-stress 14 to 42.
Injury watch feed state rules?
TG/AP/AS/OR/SK/NL restricted from real-money.
Injury watch KYC?
PAN plus Aadhaar. 30 to 90 min full.
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 programming and optimization covers convex optimization plus linear programming plus second-order cone programming plus semidefinite programming plus conic optimization plus disciplined convex programming plus DCP plus disciplined quasiconvex programming plus DQCP plus convex-concave procedure plus DC programming plus difference of convex functions plus majorization-minimization plus MM algorithms plus convex-concave procedure plus sequential convex approximation plus successive convexification plus convex envelope plus convex hull plus linear programming relaxation plus SDP relaxation plus Lagrangian relaxation plus primal-dual interior point methods plus barrier methods plus augmented Lagrangian methods plus alternating direction method of multipliers plus ADMM plus Bregman ADMM plus Douglas-Rachford splitting plus proximal gradient methods plus accelerated proximal gradient plus FISTA plus Bregman proximal methods plus primal-dual hybrid gradient.
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 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.
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 17
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.
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.
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.
Cross-disciplinary read 23
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.
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.
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 29
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.
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.
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.
Cross-disciplinary read 31
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.
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.
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.
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 37
Mathematical statistics covers parametric inference plus nonparametric inference plus semi-parametric inference plus high-dimensional statistics plus shape-constrained inference plus isotonic regression plus convex regression plus sparse estimation plus lasso plus elastic net plus adaptive lasso plus group lasso plus fused lasso plus graphical lasso plus sparse precision matrix estimation plus covariance estimation plus Stein estimation plus shrinkage estimation plus ridge regression plus principal component regression plus partial least squares plus canonical correlation analysis plus independent component analysis plus projection pursuit.
Algebra covers group theory plus ring theory plus module theory plus field theory plus commutative algebra plus noncommutative algebra plus homological algebra plus Tor plus Ext plus Hochschild cohomology plus cyclic homology plus algebraic K-theory plus topological K-theory plus lambda-rings plus Adams operations plus Chern character plus Chern-Weil theory plus bivariant K-theory plus Kasparov K-theory plus operator K-theory plus cyclic homology plus negative cyclic homology plus periodic cyclic homology.
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.
Cross-disciplinary read 41
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.
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.
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.
Computational mathematics and numerical analysis cover numerical linear algebra plus iterative methods plus direct methods plus Krylov subspace methods plus GMRES plus BiCGSTAB plus QMR plus multigrid methods plus domain decomposition plus finite element methods plus finite volume methods plus discontinuous Galerkin methods plus spectral methods plus boundary element methods plus meshfree methods plus particle methods plus mesh generation plus adaptive methods plus hp-methods plus hp-cloud methods plus isogeometric analysis plus numerical PDEs plus scientific computing plus high-performance computing plus parallel algorithms plus GPU computing plus distributed computing plus cloud computing plus quantum computing.
Cross-disciplinary read 43
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.
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 mechanics and mathematical physics cover Gibbs measures plus DLR equations plus pressure plus free energy plus phase transitions plus spontaneous symmetry breaking plus Goldstone theorem plus Mermin-Wagner theorem plus renormalization group plus Wilsonian renormalization plus Polchinski exact renormalization group plus Wetterich equation plus functional renormalization group plus Callan-Symanzik equation plus beta functions plus fixed points plus universality classes plus scaling limits plus critical exponents plus conformal bootstrap plus SLE plus Fortuin-Kasteleyn representation plus random cluster model plus loop O(n) model plus vertex models plus integrable probability plus stochastic vertex models plus KPZ universality plus directed polymers plus last passage percolation plus TASEP plus asymmetric simple exclusion process plus Macdonald processes plus Schur processes plus Whittaker processes plus Hall-Littlewood processes plus q-Whittaker processes plus q-Whittaker 2D processes plus colored stochastic vertex models.
Cross-disciplinary read 47
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.
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.
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.
Cross-disciplinary read 53
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.
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.