Mohammad Reza Rahmati

About me

I attended my Bachelor studies in Sharif University of technology in pure mathematics. Both at high school and university was a distinguished student for olympiad of mathematics. My general interests lie in algebra and geometry. Specifically, I am interested in the interface between complex and algebraic geometry with commutative and homological algebra.

I did the Ph.D studies in CIMAT, Centro de Investigacion en Mathematicas, in Mexico, in algebraic geometry and Hodge theory. My Ph.D dissertation is on the asymptotic behaviour of variation of mixed Hodge structures. I made several contributions about the extension of admissible polarized variation of mixed Hodge structure over the degenerate locus. The theory of VMHS, their asymptotic behavior and their motives play a crucial role in Hodge theory. Hodge theory is closely related to other parts of mathematics such as K-theory, representation theory, Shimura varieties, arithmetic groups, modular forms and mirror symmetry, and has been mixed with these theories very much.

I have almost attended in more than 50 local and international conferences in algebraic geometry and Hodge theory and presented in some of them as invited speaker. I also presented several lectures in my institute CIMAT on Intersection theory, D-modules and Hodge theory. At the end of my Ph.D I attended in a school of Clay institute on Motives in ICMAT, and participated on many lectures Motivic cohomology, Motivic fundamental group, l-adic representations, etale fundamental groups and theory of multiple zeta values. I also had a visit of Yau institute in Beijing on Sep. 2014, and provided a short course in Hodge theory there in 3 lectures.

Many parts of Hodge theory including algebraic cycles, asymptotic behavior of Hodge structures, Hodge theoretic motivations in K-theory, and number theoretic applications related to representation theory are of my interest. A vast of different questions from the simplest to the Key words and phrases. Hodge theory, Motive, Arithmetic groups, K- theory, l-adic representation.