Talk Abstract: In a joint work with Abdelrazek Dieb, we revisit the literature concerning the fractional Hardy inequality on general domains. In particular, we derive necessary and sufficient condition for which the best constant is achieved. Moreover, when the

fractional order is sufficiently close to 1/2, we obtain that the best constant is never achieved, independent of the domain, hence, behaves differently from that in the local case.

Bio: Remi Yvant Temgoua earned his PhD from Goethe University Frankfurt am Main in 2022. He then had a one-year postdoctoral position at Carleton University in Canada. In 2024, he was awarded the Abbas Bahri Excellence Fellowship for Graduate and Postdoctoral Research in Mathematics Award from Rutgers University. He joined the University of Bertoua in Cameroon as an Assistant Professor in 2025. Currently, he is a Fields-AIMS-Perimeter Postdoctoral Fellow at The Fields Institute, where he works on PDEs, Nonlinear Analysis, and Optimal Transport.