Fall 2021

Geometric Methods in Optimization and Sampling

Aug. 18Dec. 17, 2021

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] (subject: (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 (Università di Genova), Nisheeth Vishnoi (Yale University), Ashia Wilson (MIT)

Long-Term Participants (including Organizers):

Krishnakumar Balasubramanian (UC Davis), Jose Antonio Carrillo de la Plata (University of Oxford), Katy Craig (UC Santa Barbara), Jelena Diakonikolas (University of Wisconsin-Madison), Paromita Dubey (Stanford), Alain Durmus (ENS Paris-Saclay), Laurent El Ghaoui (UC Berkeley), Murat Erdogdu (University of Toronto), L. Craig Evans (UC Berkeley), Steven Evans (UC Berkeley), Cole Franks (MIT), Wilfrid Gangbo (UCLA), Shirshendu Ganguly (UC Berkeley), Nicolas Garcia Trillos (University of Wisconsin Madison), Augusto Gerolin (University of Ottawa), Franca Hoffmann (University of Bonn), Anna Korba (ENSAE Paris), Thibaut Le Gouic (Ecole Centrale), Yi Ma (UC Berkeley), Simone Di Marino (Università di Genova), Song Mei (UC Berkeley), Andrea Montanari (Stanford University), Eric Moulines (Ecole Polytechnique), Jelani Nelson (UC Berkeley), Felix Otto (Max Planck Institute for Mathematics in the Sciences), Quentin Paris (HSE University), Vianney Perchet (Université Paris Diderot - Paris 7), Benjamin Recht (UC Berkeley), Philippe Rigollet (MIT; co-chair), Andrej Risteski (Carnegie Mellon University), Carola-Bibiane Schönlieb (University of Cambridge), Dejan Slepcev (Carnegie Mellon University), Nikhil Srivastava (UC Berkeley), Sui Tang (UCSB), Prasad Tetali (CMU), Matthew Thorpe (University of Manchester), Umesh Vazirani (UC Berkeley), Nisheeth Vishnoi (Yale University), Martin Wainwright (UC Berkeley; co-chair), Andre Wibisono (Yale University), Ashia Wilson (MIT), Stephen Wright (University of Wisconsin-Madison), Bin Yu (UC Berkeley), Yuhua Zhu (Stanford University)

Research Fellows:

Yongxin Chen (Georgia Institute of Technology), Matthew Jacobs (UCLA), Holden Lee (Duke University), Adil Salim (KAUST), Kevin Tian (Stanford University), Melanie Weber (Princeton University), Yunan Yang (New York University)

Visiting Graduate Students and Postdocs:

Kwangjun Ahn (MIT), Taejoo Ahn (UC Berkeley), Jason Altschuler (Massachusetts Institute of Technology), Leon Bungert (University of Bonn), Kabir Chandrasekher (Stanford University), Yeshwanth Cherapanamjeri (UC Berkeley), Sinho Chewi (Massachusetts Institute of Technology), Devon Ding (UC Berkeley), Majid Farhadi (Georgia Institute of Technology), Wei Hu (UC Berkeley), Bill Li (University of Toronto), Giulia Luise (University College London), Theodor Misiakiewicz (Stanford University), Subhadip Mukherjee (Cambridge university), Meyer Scetbon (ENSAE, CREST), Mark Sellke (Stanford), Ruoqi Shen (University of Washington), Chaobing Song (University of Wisconsin-Madison), Austin Stromme (MIT), Yixin Wang (Simons Institute, UC Berkeley), Andrew Warren (CMU), Manxi Wu (UC Berkeley), Manxi Wu (UC Berkeley), Yuchen Wu (Stanford University), Angela Zhou (Cornell University)


Aug. 30Sep. 3, 2021


Philippe Rigollet (MIT; chair), Katy Craig (UC Santa Barbara), Simone Di Marino (Università di Genova), Nisheeth Vishnoi (Yale University), Martin Wainwright (UC Berkeley), Ashia Wilson (MIT)
Sep. 27Oct. 1, 2021


Jelena Diakonikolas (University of Wisconsin-Madison), Philippe Rigollet (MIT), Santosh Vempala (Georgia Institute of Technology)
Oct. 25Oct. 29, 2021


Katy Craig (UC Santa Barbara), Simone Di Marino (Università di Genova)
Nov. 29Dec. 3, 2021


Nisheeth Vishnoi (Yale University; chair), Michael Walter (University of Amsterdam and QuSoft)

Those interested in participating in this program should send an email to the organizers at this gm2021 [at] (at this address)

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Internal Program Activities

Monday, September 20 11:00 am12:00 pm
Tuesday, September 14 10:00 am11:00 am
Wednesday, September 15 10:00 am11:00 am
Wednesday, September 22 11:00 am12:00 pm
Leon Bungert (University of Bonn)
Thursday, September 16 11:00 am12:00 pm
Friday, September 17 11:00 am12:00 pm
Friday, September 17 12:00 pm1:00 pm
Friday, September 24 2:00 pm3:00 pm
Monday, September 27 1:00 pm2:00 pm
Tuesday, September 14 10:00 am11:00 am

Past Internal Program Activities

Friday, September 17 12:00 pm1:00 pm
Friday, September 17 11:00 am12:00 pm
Friday, September 17 10:00 am11:00 am
Thursday, September 16 11:00 am12:00 pm
Thursday, September 16 10:00 am11:00 am
Wednesday, September 15 11:00 am12:00 pm
Ruoqi Shen (University of Washington)
Wednesday, September 15 10:00 am11:00 am
Tuesday, September 14 10:00 am11:00 am
Friday, September 10 1:30 pm2:30 pm
Friday, September 10 10:00 am11:00 am
Thursday, September 9 10:00 am4:30 pm
Wednesday, September 8 10:00 am5:30 pm
Wednesday, September 8Thursday, September 9
Tuesday, September 7 4:00 pm5:30 pm
Friday, August 27 12:00 pm1:00 pm
Friday, August 20 1:00 pm3:00 pm