Recent trends in geometric analysis

Organizers: Rod Gover, Pedram Hekmati and Neil Trudinger.

Session speakers:

  • Peter Ebenfelt, University of California, San Diego;
  • Hojoo Lee, Jeonbuk National University;
  • Mariel Saez Trumper, Pontificia Universidad Catlica de Chile;
  • Glenn Wheeler, University of Wollongong, Australia;
  • Yoshihiko Matsumoto, University of Osaka, Japan;
  • Weiping Zhang, Chern Institute of Mathematics, China.

Life sciences – mathematical modelling and analysis

Organizer: Toshiyuki Ogawa.

The life sciences relate to mathematics via the posing of important mathematical problems and as an arena for the development of mathematical tools, This session focusses on contributions to problems in the life sciences from dynamical systems and partial differential equations. The topics include mass conservation in reaction-diffusion systems; bulk-membrane problems; and pattern dynamics in biological problems.

Session speakers:

  • Chiun-Chuan Chen, National Taiwan University, Taiwan;
  • Yong-Jung Kim, KAIST, Korea;
  • Yoichiro Mori, University of Minnesota, USA;
  • Yoshihisa Morita, Ryukoku University, Japan;
  • Michael Ward, University of British Columbia, Canada.

Nonlinear partial differential equations, and fluid dynamics via harmonic analysis

Organizer: Takayoshi Ogawa.

Differential geometry

Organizers: Kazuo Akutagawa, Eric Bahuaud, Rafe Mazzeo and Kaoru Ono.

Session speakers:

  • Ailana Fraser, University of British Columbia;
  • Jesse Gell-Redman, University of Melbourne;
  • Tsuyoshi Kato, Kyoto University;
  • Shinichiroh Matsuo, Nagoya University;
  • Jeff Viaclovsky, University of California, Irvine.

Probability theory

Organizer: Amir Dembo.

Session speakers:

  • Sourav Chatterjee. Stanford University, USA;
  • Amir Dembo, Stanford University;
  • Daniel Remenik, University of Chile;
  • Lisa Sauermann, Stanford University;
  • Insuk Seo, Seoul National University, South Korea.

Number theory

Organizer: Ming-Lun Hsieh.

Session speakers:

  • Wen-Wei Li, Peking University;
  • Yoichi Mieda, University of Tokyo;
  • Cheng-Chiang Tsai, Stanford University;
  •  Shunsuke Yamana, Osaka City University.

Algebraic and complex geometry

Organizers: Yoshinori Namikawa, Yuji Odaka and Song Sun.

Session speakers:

  • Radu Laza, Stony Brook University;
  • Xiaokui Yang, Chinese Academy of Sciences;
  • Mao Sheng, University of Science and Technology of China;
  • Tomoyuki Hisamoto, Nagoya University;
  • Yoshiki Oshima, Osaka University.

Symplectic geometry, dynamical systems and microlocal analysis

Organizer: Alan Hammond, Alvaro Pelayo and Fraydoun Rezakhanlou.

Recently there has been a flurry of activity on problems at the intersection of various interconnected areas from (integrable and non integrable) dynamics and microlocal analysis, in particular problems connecting analytic, topological, and geometric aspects. This session is focused on the interactions between spectral theory, dynamical systems, and finite or infinite dimensional integrable systems, with an emphasis on problems where techniques from microlocal and semiclassical analysis are useful. For example, some topics of particular interest are direct and inverse spectral problems about pseudo differential and Berezin-Toeplitz operators, Fourier integral operators, symplectic and differential geometric aspects of dynamical systems, finite and infinite dimensional integrable systems, and recent advances in microlocal/semiclassical techniques.

Session speakers:

  • Dan Cristofaro-Gardiner, University of California, Santa Cruz;
  • Eleny Ionel, Stanford University.

Classical harmonic analysis and combinatorics

Organizers: Malabika Pramanik and Josh Zahl.

Harmonic analysis studies the mapping properties of operators related to the Fourier transform.  Over the past several decades, deep connections have emerged between harmonic analysis, geometric measure theory, and additive combinatorics. The area has seen a recent resurgence in activity, with advances such as Bourgain and Demeter’s solution to the decoupling conjecture, which has led to progress in areas as diverse as analytic number theory, PDE, and additive combinatorics. Dvir’s 2008 solution to the finite field Kakeya problem and the polynomial methods introduced by Guth and Katz a few years later have led to new progress on a number of longstanding conjectures, including the Kakeya and restriction problems, and Schrodinger maximal estimates. With an abundance of new tools available, now is an important moment for both experts in the field and junior researchers to meet and share their ideas.

Session speakers:

  • Hong Wang, Institute of Advanced Study;
  • Zane Li, Indiana University, Bloomington;
  • Polona Durcik, Caltech;
  • Chun Kit Lai, San Francisco State University.

Representation theory

Organizer: Tony Licata.

Session speakers:

  • Dylan Allegretti, University of British Columbia;
  • Pedram Hekmati, University of Auckland, New Zealand;
  • Ivan Ip, Hong Kong University of Science and Technology;
  • Tony Licata, Australian National University.