Present Challenging Problems

Home Centers & Programs Mathematical Challenges Present Challenging Problems

Present HCMC's Challenging Problems

· Profinite rigidity of free groups (Remeslennikov's Conjecture)

· Conway-Soifer Conjecture, Toth's Angle Sum Problem, Mahler's Conjecture

· Group actions and rigidity - Around the Zimmer Program, the Katok-Spatzier conjecture, and the Centralizer Rigidity Program

· Geometric generalization of the Stanley-Stembridge and Haiman conjectures beyond type A

· Geometric Characterization of the Boundary of Chaos in the Hénon Family

· Endoscopic classification of automorphic representations

· Schoen's Conjecture

· Yau–Tian–Donaldson theorem / K-stability of Fano varieties

· Equidistribution of Periodic Torus Orbits

· Generalized Serre weight conjectures

· Joyce conjecture

· Rigorous proof of localization in stochastic PDEs