Jason P. Miller

Jason P. Miller is an American mathematician who studies stochastics .

Miller studied mathematics, computer science and economics at the University of Michigan in Ann Arbor from 2002 to 2006 , each with a bachelor's degree and then at Stanford University , where he received his doctorate in mathematics with Amir Dembo in 2011 (Limit theorems for Ginzburg-Landau - random surfaces) ${\displaystyle \nabla }$ ${\displaystyle \phi }$ . As a post-doctoral student he was with Microsoft Research and from 2012 to 2015 at the Massachusetts Institute of Technology (Schramm Fellow) with Scott Sheffield . In 2015 he became a Fellow at Trinity College, Cambridge and Reader in the Statistics Laboratory at Cambridge University .

He deals with Schramm-Loewner-Evolution (SLE), random surfaces and random walk, mixing times for Markov chains , interacting particle systems and also with financial mathematics.

With Scott Sheffield he investigated the geometry of Gaussian Free Fields (GFF), which can be understood as analogues of Brownian motion when time is replaced by two spatial dimensions (with values ​​in a flat area D). They studied height functions of the GFF and vector fields (with a constant ) and corresponding flows. They called this imaginary geometry, and they were able to incorporate many SLE into GFF's. Miller and Sheffield also showed that two descriptions of random surfaces, Brownian maps (Brownian Maps, TBM) and Liouville Quantum Gravity (LQG) introduced by Alexander Polyakov , are equivalent. ${\displaystyle h}$ ${\displaystyle e^{iah}}$ ${\displaystyle a}$

In 2015 he received the Rollo Davidson Prize , in 2016 the Whitehead Prize and in 2017 the Clay Research Award . In 2018 the speaker will be at the ICM (Liouville quantum gravity as a metric space and a scaling limit).

Fonts

• Miller, Sheffield: Liouville quantum gravity and the Brownian map, part 1: The QLE (8 / 3,0) metric, 2015, Arxiv , part 2: geodesics and continuity of the embedding, 2016, Arxiv
• Miller, Sheffield: Quantum Loewner Evolution, Duke Math. J., Volume 165, 2016, pp. 3241-3378, Arxiv
• Miller, Sheffield: Imaginary geometry, part 1, 2012, Arxiv , part 2, Arxiv , part 3, Arxiv , part 4, Arxiv

Web links

• Homepage in Cambridge
• Kevin Hartnett, A unified theory of randomness, Quanta Magazine, 2016

Individual evidence

1. ↑ Jason P. Miller in the Mathematics Genealogy Project (English)
2. ↑ In physics also corresponding to Euclidean two-dimensional massless free boson fields.
3. ^ Scott Sheffield, Gaussian free fields for mathematicians , 2003
4. ↑ Arxiv