# GEAR

The GEAR Network is funded by a $5M grant from the U.S. National Science Foundation’s Research Networks in Mathematical Sciences (RNMS) program. The acronym GEAR stands for GEometric structures And Representation varieties and reflects the mathematical focus of the network (described here). The GEAR Network brings together researchers from over 90 nodes at mathematics centers throughout the world (see map). Its goal is to promote research interactions between network members, to facilitate cross-pollination of ideas between different research communities, and to train students and researchers to cross traditional mathematical boundaries.

## GEAR member receives 2020 Breakthrough Prize

Alex Eskin, a GEAR member at the University of Chicago node, received one of the 2020 Breakthrough prizes at a ceremony on November 3, 2019 for revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentials, including the proof of the 'magic wand theorem' with Maryam Mirzakhani." His work has fundamentally changed how mathematicians approach counting problems in geometry and algebra. His earlier achievements included the quantitative version of the 1929 Oppenheim conjecture and the quasi-isometry classification of lattices in Lie groups. We join the rest of the mathematics community in congratulating Professor Eskin on his spectacular achievements.

**GEAR Advisory Board member receives **

2016 Shaw Prize in Mathematics

2016 Shaw Prize in Mathematics

Nigel Hitchin, Savilian Professor of Geometry at Oxford University, UK, and a member of the GEAR Network Advisory Board, is the 2016 Shaw Laureate in Mathematical Sciences. Announced on May 31, 2016, the prize was awarded to Professor Hitchin "for his far reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance."

We join the rest of the mathematics community in congratulating Professor Hitchin on his pioneering work and dazzling mathematical creations.

## GEAR member receives 2016 Breakthrough Prize

**Ian Agol**, a GEAR Network member at the UC Berkeley node, is one of the $3M Breakthrough Prize winners for 2016. Announced on November 9, 2015 the prize was awarded to Professor Agol for "spectacular contributions to low dimensional topology and geometric group theory, including work on the solutions of the tameness, virtual Haken and virtual fibering conjectures." For a lucid explanation of Ian Agol’s work on the virtual Haken conjecture, see the lecture by Nathan Dunfield from the 2012 GEAR Retreat.

We join the rest of the mathematics community in congratulating Professor Agol on his spectacular achievements.

## GEAR member receives 2014 Fields Medal

**Maryam Mirzakhani**, a GEAR member at the Stanford hub of
GEAR, is
one of the 2014 Fields Medal winners. Announced
on August 13, 2014
at the ICM in Seoul, South Korea, the
Fields medal was awarded to Professor Mirzakhani for her
ground breaking work on geometric and dynamical aspects
of moduli spaces of Riemann surfaces.

We join the rest of the mathematics community in congratulating

Professor Mirzakhani on her inspirational achievements.
We note with sadness that Maryam passed away on July 14, 2017.

## Acknowledgements

Any future papers or reports on work done with the aid of support
from

the GEAR Network should please include the following acknowledgement:

"The author(s) acknowledge(s) support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: GEometric structures And Representation varieties" (the GEAR Network)."

## GEAR Logo

For those planning events being funded through GEAR, you can easily put the logo on your event poster and/or website by downloading this high resolution version of the GEAR logo (right click on the image to download).

## Need more information about GEAR?

For more information about GEAR, or for questions about any aspects of this website, contact us at gear@math.uiuc.edu.