Lars Kindler#

AFFILIATION: Freie Universität Berlin, currently Harvard University FIELD OF SCHOLARSHIP: Mathematics

BIOGRAPHICAL NOTE:

• Began studying Mathematics in 2003, at the Georg-August-University Göttingen
• One year abroad at University of California, Berkeley
• Finished Diplom in 2009 under the supervision of Prof. Dr. Yuri Tschinkel
• Began Ph.D. studies in 2009 at University of Duisburg-Essen under the supervision of Prof. Dr. Dr. mult. Hélène Esnault
• Extended stay at University of Chicago, 2012
• Defended thesis in 2013, title: “Regular singular stratified bundles in positive characteristic”, grade: “summa cum laude”
• From 2013: Research Assistant (Wissenschaftlicher Mitarbeiter) at Freie Universität Berlin
• Fall 2016 - Summer 2017: Visiting Scholar at Harvard University

DETAILS OF RESEARCH:

The field of my research is Algebraic Geometry. It is part of what is called “pure” mathematics. Its content is the interplay between algebraic and geometric ideas; more precisely it encompasses the study of geometric problems by algebraic (as opposed to analytic) methods and conversely, the study of algebraic problems with geometric methods. The formalism of Algebraic Geometry as it mainstream today, was initiated by Alexander Grothendieck (1928-2014) in the 1950s. One great achievement of this formalism is that it allows one to transpose purely geometric settings into contexts in which there is no clear geometric intuition; one of these contexts is what is called “positive characteristic Algebraic Geometry”.

My work is concerned with one instance of such a transposition: I study differential equations in positive characteristic. Parallel to the classical singularity theory of algebraic differential equations, I was able to define and study a notion of regular singularity for differential equations in positive characteristic. My work shows that this theory is closely related to the notion of “tame ramification” which occurs in a neighboring part of algebraic geometry.

TWO KEY PUBLICATION REFERENCES:

Regular singular stratified bundles and tame ramification (Trans. Amer. Math. Soc. 367 (2015), 6461-6485)

Local-to-global extensions of D-modules in positive characteristic (International Mathematics Research Notices, 2014, doi: 10.1093/imrn/rnu227)