An online session of the Algebra and Logic Seminar will be held on January 21, 2022 (Friday) at 1:00 pm (UTC+2). A talk on On the distribution of αp modulo one for primes p=aq^2+1 with prime q will be delivered by Tatyana Todorova (FMI, Sofia University, Bulgaria). Abstract. It is a long-standing conjecture that there are infinitely many primes of the form n^2+1. Several approximations to this problem have been made. Baier and Zhao showed that for any ε > 0, there are infinitely many primes of the form p = aq^2 + 1, where a ≤ p^(5/9+ε). The best known result, due to Matomäki is that there are infinitely many primes of the form p = aq^2 + 1, where a ≤ p^(1/2+ε) and [...]