Optimization and sampling are two of the most important mathematical topics at the interface of data science and computation. The two questions are, in fact, connected mathematically through a powerful framework articulated around the geometry of probability distributions. The geometric toolbox that underlies optimization and sampling was initiated in the study of partial differential equations (PDEs) and has evolved into different mathematical disciplines: probability, calculus of variations, analysis and geometry. While connections are slowly beginning to percolate across disciplines, this program is aimed to be a catalyst for new and interdisciplinary ideas using a principled and unified approach to optimization and sampling.
A central goal of this program is to develop and promote a geometric approach to various computational problems in sampling, optimization, and PDEs. For example, the geometry of Optimal Transport has been instrumental to establish fruitful connections between diffusion processes, gradient flows, and diffusive PDEs by eliciting hidden convexity. This success calls for a versatile toolbox to tackle algorithmic questions arising in sampling, optimization, and particle methods for solving PDEs by leveraging the hidden geometric structure of each problem in a systematic way. Moreover, in a large class of problems this geometric structure is supplemented by additional symmetries or other algebraic structures that can be exploited to design better algorithms.
These recent connections between sampling, optimization, and PDEs have placed the fields in a unique position for mutual impact. This program aims at bringing together researchers from various backgrounds to tackle these challenging problems using a unified approach by focusing on the following aspects:
- Sampling as an optimization problem
- Geometry and optimal transport
- The PDE perspective on sampling and optimization
- Eliciting convexity via geometry in sampling and optimization
- The interplay of algebra and geometry in optimization
sympa [at] lists.simons.berkeley.edu (subject: subscribe%20gm2021announcements%40lists.simons.berkeley.edu) (Click here to subscribe to our announcements email list for this program.)
Philippe Rigollet (MIT, co-chair), Martin Wainwright (UC Berkeley, co-chair), Katy Craig (UC Santa Barbara), Simone Di Marino (University of Genova), Nisheeth Vishnoi (Yale), Ashia Wilson (MIT)
List of participants (tentative list, including organizers):
Jose A. Carrillo (University of Oxford), Peter Bartlett (UC Berkeley), Lénaïc Chizat (CNRS), Katy Craig (UCSB), Simone Di Marino (Università di Genova), Jelena Diakonikolas (UW-Madison), Paromita Dubey (Stanford University), Alain Durmus (ENS Paris-Saclay), Murat Erdogdu (University of Toronto), William Franks (MIT), Wilfrid Gangbo (UCLA), Nicolas Garcia Trillos (UW-Madison), Aude Genevay (MIT), Augusto Gerolin (VU Amsterdam), Franca Hoffmann (University of Bonn), Anna Korba (CREST), Thibaut Le Gouic (Ecole Centrale de Marseille), Jianfeng Lu (Duke University), Jan Maas (IST Austria), Andrea Montanari (Stanford University), Eric Moulines (Ecole Polytechnique), Felix Otto (Max Planck Institute for Mathematics in the Sciences), Quentin Paris (HSE University), Vianney Perchet (CREST), Philippe Rigollet (MIT), Andrej Risteski (Carnegie Mellon University), Carola-Bibiane Schönlieb (University of Cambridge), Dejan Slepcev (Carnegie Mellon University), Sui Tang (UCSB), Prasad Tetali (Georgia Institute of Technology), Matthew Thorpe (University of Manchester), Nisheeth Vishnoi (Yale University), Andre Wibisono (Yale University), Ashia Wilson (MIT), Stephen Wright (UW-Madison)
Yongxin Chen (Georgia Institute of Technology), Matt Jacobs (UCLA), Holden Lee (Duke University), Adil Salim (King Abdullah University of Science and Technology), Kevin Tian (Stanford University), Melanie Weber (Princeton University), Yunan Yang (NYU)
Visiting Graduate Students and Postdocs:
Kwangjun Ahn (MIT), Jason Altschuler (MIT), Leon Bungert (University of Bonn), Sinho Chewi (MIT), Majid Farhadi (Georgia Institute of Technology), Rishabh Gvalani (Max-Planck Institute Leipzig), Mufan Li (University of Toronto), Giulia Luise (University College London), Subhadip Mukherjee (University of Cambridge), Chaobing Song (UW-Madison), Austin Stromme (MIT), Urbain Vaes (Ecole Nationale de Ponts et Chausees), Andrew Warren (CMU)
Those interested in participating in this program should send an email to the organizers at this gm2021 [at] lists.simons.berkeley.edu (at this address).