エレン・メフメット・クラル Eren Mehmet Kıral

Hello, I am Eren Mehmet Kıral, I am currently a JSPS fellow at Sophia University working with Prof. Nakasuji on Bruhat cell decompositions of various matrix groups with a view towards finding number theoretic applications. I am also a visiting scientist here at ITHEMS. Starting March 2020 I will be an SPDR at RIKEN working at the Mathematical Science team of Advanced Intelligence Project (AIP) with Prof. Bannai.

My research interest is in automorphic forms, and their associated L-functions, including the Riemann zeta function. Automorphic forms can be thought of generalizations of harmonics. Just like sin(nx), cos(nx) are the periodic harmonics on the real line, automorphic forms are the harmonics on more general homogeneous spaces. However unlike the real line, the group of transformations on the space forms a non-commutative Lie group, and hence the harmonic analysis (or equivalently the representation theory) on this group is more involved. It is fascinating that simply the setup of a discrete subgroup sitting inside a homogeneous space, spawns objects that are intrinsically related to number theory. I am looking forward to talking to physicists who work with Lie group representations on a regular basis.