Conference on Geometric Analysis and Stochastic Methods in Geometry

 In Workshop reports

The University of Queensland, 21–25 July 2014

Bringing together prominent international and Australian geometric analysis experts, this conference highlighted the application of probabilistic methods in differential geometry problems and partial differential equations. Much of the discussion focussed on the high profile areas of heat kernels, Ricci curvature equations and the Willmore functional.

A modern and vibrant area of mathematics, geometric analysis has been broadly applied to achieve remarkable results, many of which were explored by conference participants using traditional and probabilistic techniques. In particular, Professors Elton Hsu, Anton Thalmaier, and Bruce Driver contributed presentations tailor-made as “User Guides” to probabilistic methods in geometric analysis, detailing for example the connection between Hamilton’s classical gradient estimate and Brownian motion. This alternative point of view enables the observation that Hamilton’s gradient estimate is the limiting case of an entire family of gradient estimates.

The conference enjoyed contributions from established experts in the area as well as new stars. Professor Rick Schoen opened the conference with a fundamental new contribution on the application of localisation in cones to the analysis of the rigidity of asymptotically flat space-times. A vast survey was contributed by Professor Karl-Theodor Sturm, Hausdorff Centre and Professor Gerard Besson, Fourier Institute, presented startling facts on how weird and wonderful 3-manifolds may be.

Leading Australian mathematicians were well represented, with a deep application of interior ball curvature presented by Professor Ben Andrews (Australian National University) and Laureate Professor Xu-Jia Wang (Australian National University) detailing recent developments on the p-Minkowski problem.

Distinguished presentations from young mathematicians included that of Dr Yann Bernard (ETH Zurich), speaking on energy quantisation for the Willmore functional, work that recently appeared in the Annals of Mathematics, and Dr Richard Bamler (University California, Berkeley) who found new insights in Perelman’s work on the Ricci flow, enabling him to drastically improve on previous results. Given the level of activity in Ricci flow and in particular the level of interest in Perelman’s work, this is an astonishing achievement.

This conference provided many benefits to the Australian scientific community.

MathSciNet Classification
35J60, 30C40, 60D05

Web Links
https://www.smp.uq.edu.au/GASMG-2014

Other Sponsors
Australian National University, The University of Queensland, University of Wollongong, AustMS

Contact
Dr Artem Pulemotov, The University of Queensland
a.pulemotov@uq.edu.au

Organisers

Professor Thierry Coulhon, Australian National University
Dr Huy The Nguyen, The University of Queensland
Dr Artem Pulemotov, The University of Queensland
Dr Glen Wheeler, University of Wollongong
Dr Valentina-Mira Wheeler, University of Wollongong

Special presenters

Distinguished Professor Rick Schoen, University California, Irvine
Research interests: geometric analysis, general relativity, compact manifolds
Professor Bruce Driver, University California, San Diego
Research interests: probability theory, the analysis of partial differential equations, mathematical physics, geometric group theory and stochastic analysis

Participant Summary

Attendees

NUMBER OF ATTENDEES

40

  • Academic

    50%

  • Early Career Researcher

    13%

  • PhD

    10%

  • Other Students

    15%

  • Industry

    0%

Gender

Gender Breakdown

State Breakdown
Victoria
5%
Australian Capital Territory
12%
New South Wales
20%
Queensland
25%
South Australia
0%
Western Australia
0%
Tasmania
0%
Northern Territory
0%
International
38%
Citizenship Status
Domestic - 60%
50%
International - 40%
50%
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