The next meeting of the Algebra and Logic Seminar will be held on April 25, 2025 (Friday) at 1:00 pm (UTC+2) in Room 578 of IMI-BAS. A talk on: Hilbert scheme of smooth projective curves and some easy examples will be delivered by Changho Keem (Seoul National University, South Korea). Abstract: Hilbert scheme is a parameter space for a family of projective algebraic varieties sharing a given fixed Hilbert polynomial.  In this talk, we will discuss the following topics concerning the Hilbert scheme of smooth projective algebraic curves. 1. Irreducibility problem of the restricted Hilbert scheme of curves. 2. Some easy examples of reducible Hilbert schemes inside or outside the Brill-Noether range. 3. The existence of more than expected dimensional components whose image under the moduli [...]