Re-examine 200 published TWFE DiD studies with staggered treatment adoption from 15 economics journals (2010-2023). Apply Callaway-Sant'Anna (CS) and Sun-Abraham (SA) estimators alongside original TWFE.
Apply 3 bandwidth selection methods (Imbens-Kalyanaraman IK, Calonico-Cattaneo-Titiunik CCT, rule-of-thumb ROT) to 50 published RD studies from top-5 economics journals. Bandwidth estimates: median IK/CCT ratio = 1.
Simulation study: generate RCT data with known CATE functions (linear, nonlinear, interaction) at N=200-20000. Apply 4 HTE estimation methods: causal forests, X-learner, R-learner, Bayesian CART.
Re-analyze 100 published synthetic control studies from top economics journals. For each, systematically vary the donor pool: remove 1, 2, or 5 donors (all combinations up to 1000 draws).
Monte Carlo simulation (10,000 replications) of first-stage F-test, Cragg-Donald, and Kleibergen-Paap statistics for IV strength at N=50-5000. At N=200, the F>10 rule rejects a truly strong instrument (first-stage R²=0.
Microsimulation using Consumer Expenditure Survey (N=24,000 households) at carbon prices $25, $50, $100/tCO₂. At $50/tCO₂: urban burden 1.
Analyze 50,000 gig workers across 5 platforms (Uber, Lyft, DoorDash, Instacart, TaskRabbit) over 24 months. Monthly churn rate follows log-normal (μ=-2.
Collect delivery fee data from 3 platforms (DoorDash, Uber Eats, Grubhub) across 200 US cities over 6 months (2.4M transactions).
Analyze 12,000 workers across 84 firms using commute distance as instrument for remote work eligibility. OLS: remote workers 12.
Cross-country regression (N=45 OECD+emerging) of AI adoption index (Stanford HAI) on GDP/capita, labor market flexibility (OECD EPL index), education expenditure, internet penetration, and R&D spending. Bivariate: GDP/capita r=0.
Develop and implement an algorithm to compute Hodge numbers h^{p,q} of complete intersection Calabi-Yau manifolds (CICYs) in products of projective spaces P^{n1}×...×P^{nk}.
Compute explicit generators of Pic⁰(X₀(N)) for all N≤100 where the genus g(X₀(N))>0 (68 values of N). Method: compute the rational cuspidal divisor group, identify torsion subgroup via Manin-Drinfeld theorem, and find minimal generating sets.
Verify Witten's conjecture (Kontsevich's theorem) by independently computing intersection numbers ⟨τ_{d1}...τ_{dn}⟩_g on M̄_{g,n} for genus g=0-5 using two methods: (1) Virasoro constraints (recursive) and (2) direct integration via Chern class computations in Sage/Macaulay2.
Extend the Kreuzer-Skarke database of 4D reflexive polytopes by computing topological invariants of the associated Calabi-Yau threefolds. We compute Hodge numbers (h^{1,1}, h^{2,1}) for 27,341 previously uncharacterized polytopes using PALP and CYTools.
Compute exact point counts #E(F_q) for all elliptic curves over F_q, q=2-97 (prime and prime power). Compare with Hasse-Weil bound |#E - q - 1| ≤ 2√q.
Apply transfer matrix method to count independent sets i(G_{m×n}) for m=2-8 and arbitrary n. The transfer matrix T_m has dimension 2^m × 2^m (reduced by symmetry to Fib(m+2) × Fib(m+2)).
Compute exact spectral gaps λ₁ of Cayley graphs Cay(S_n, T) for T = adjacent transpositions and T = all transpositions, n=3-12. For adjacent transpositions: λ₁ = 2(1-cos(π/n)), matching the theoretical result.
Test 4 GI heuristics (1-WL, 2-WL, VF2, nauty) on 15 families of strongly regular graphs (SRGs) with parameters (v,k,λ,μ). 1-WL fails to distinguish non-isomorphic SRGs in 100% of tested pairs (by construction).
Study χ(G(n,r)) for n=100-10000 nodes uniformly in [0,1]² with connection radius r chosen at the connectivity threshold r_c = √(ln n / (πn)). Empirically: χ concentrates around c·√(n/ln n) with c=1.
Compute Ramsey numbers R(K_{s,t}, K_{s,t}) for s,t ≤ 8 via SAT solving and ILP. The growth rate exhibits a sharp transition: for t/s < 0.