Program
s
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

Organizers:

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), 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), Tarun Kathuria (UC Berkeley), Bill Li (University of Toronto), Giulia Luise (University College London), Theodor Misiakiewicz (Stanford University), Subhadip Mukherjee (Cambridge university), Lorenzo Portinale (University of Bonn), Meyer Scetbon (ENSAE, CREST), Mark Sellke (Stanford), Ruoqi Shen (University of Washington), Chaobing Song (University of Wisconsin-Madison), Austin Stromme (MIT), Yixin Wang (UC Berkeley), Andrew Warren (CMU), Manxi Wu (UC Berkeley), Yuchen Wu (Stanford University), Elizabeth Yang (UC Berkeley), Angela Zhou (Cornell University)

Workshops

Monday, Aug. 30Friday, Sep. 3, 2021

Organizers:

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)
Monday, Sep. 27Friday, Oct. 1, 2021

Organizers:

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

Organizers:

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

Organizers:

Nisheeth Vishnoi (Yale University; chair), Michael Walter (University of Amsterdam and QuSoft), Ashia Wilson (MIT)
Tuesday, Jan. 10Thursday, Jan. 12, 2023

Organizers:

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 University), Ashia Wilson (MIT)

If you are interested in joining this program, please see the Participate page.

 Subscribe to the program calendar.

Past Internal Program Activities

Friday, December 17th, 11:00 am12:00 pm
Friday, December 17th, 9:45 am11:00 am
Thursday, December 16th, 11:00 am12:00 pm
Wednesday, December 15th, 10:00 am11:00 am
Tuesday, December 14th, 10:00 am11:00 am
Friday, December 10th, 11:00 am12:00 pm
Thursday, December 9th, 11:00 am12:00 pm
Wednesday, December 8th, 2:30 pm3:30 pm
Felix Otto (Max Planck Institute for Mathematics in the Sciences)
Wednesday, December 8th, 11:00 am12:00 pm
Jonathan Niles-Weed (New York University)
Wednesday, December 8th, 10:00 am11:00 am
Tuesday, December 7th, 10:00 am11:00 am
Wednesday, December 1st, 12:45 pm1:45 pm
Wednesday, November 24th, 11:00 am12:00 pm
Wednesday, November 24th, 10:00 am11:00 am
Tuesday, November 23rd, 10:00 am11:00 am
Friday, November 19th, 2:00 pm3:00 pm
Friday, November 19th, 11:00 am12:00 pm
Thursday, November 18th, 11:00 am12:00 pm
Wednesday, November 17th, 11:00 am12:00 pm
Aram-Alexandre Pooladian (New York University)
Wednesday, November 17th, 10:00 am11:00 am
Tuesday, November 16th, 10:00 am11:00 am
Friday, November 12th, 11:00 am12:00 pm
Thursday, November 11th, 11:00 am12:00 pm
Thursday, November 11th, 10:00 am11:00 am
Wednesday, November 10th, 11:00 am12:00 pm
Simone Di Marino (University of Genova)
Wednesday, November 10th, 10:00 am11:00 am
Tuesday, November 9th, 10:00 am11:00 am
Friday, November 5th, 2:00 pm3:00 pm
Friday, November 5th, 11:00 am12:00 pm
Thursday, November 4th, 11:00 am12:00 pm
Thursday, November 4th, 10:00 am11:00 am
Wednesday, November 3rd, 10:00 am11:00 am
Tuesday, November 2nd, 10:00 am11:00 am
Friday, October 22nd, 2:00 pm3:00 pm
Friday, October 22nd, 12:00 pm1:00 pm
Friday, October 22nd, 11:00 am12:00 pm
Thursday, October 21st, 11:00 am12:00 pm
Thursday, October 21st, 10:00 am11:00 am
Wednesday, October 20th, 10:00 am11:00 am
Tuesday, October 19th, 10:00 am11:00 am
Friday, October 15th, 12:00 pm1:00 pm
Friday, October 15th, 11:00 am12:00 pm
Thursday, October 14th, 11:00 am12:00 pm
Thursday, October 14th, 10:00 am11:00 am
Wednesday, October 13th, 11:00 am12:00 pm
Paromita Dubey (University of Southern California)
Wednesday, October 13th, 10:00 am11:00 am
Tuesday, October 12th, 10:00 am11:00 am
Friday, October 8th, 2:00 pm3:00 pm
Friday, October 8th, 12:00 pm1:00 pm
Friday, October 8th, 11:00 am12:00 pm
Thursday, October 7th, 11:00 am12:00 pm
Thursday, October 7th, 10:00 am11:00 am
Thursday, October 7th, 9:00 am10:00 am
Wednesday, October 6th, 11:00 am12:00 pm
Sui Tang (UC Santa Barbara)
Tuesday, October 5th, 10:00 am11:00 am
Monday, September 27th, 1:00 pm2:00 pm
Friday, September 24th, 2:00 pm3:00 pm
Friday, September 24th, 12:00 pm1:00 pm
Friday, September 24th, 11:00 am12:00 pm
Thursday, September 23rd, 11:00 am12:00 pm
Thursday, September 23rd, 10:00 am11:00 am
Wednesday, September 22nd, 11:00 am12:00 pm
Leon Bungert (University of Bonn)
Wednesday, September 22nd, 10:00 am11:00 am
Tuesday, September 21st, 10:00 am11:00 am
Monday, September 20th, 11:00 am12:00 pm
Friday, September 17th, 12:00 pm1:00 pm
Friday, September 17th, 11:00 am12:00 pm
Friday, September 17th, 10:00 am11:00 am
Thursday, September 16th, 11:00 am12:00 pm
Thursday, September 16th, 10:00 am11:00 am
Wednesday, September 15th, 11:00 am12:00 pm
Ruoqi Shen (University of Washington)
Wednesday, September 15th, 10:00 am11:00 am
Tuesday, September 14th, 10:00 am11:00 am
Friday, September 10th, 2:00 pm3:00 pm
Friday, September 10th, 1:30 pm2:30 pm
Friday, September 10th, 10:00 am11:00 am
Thursday, September 9th, 10:00 am4:30 pm
Wednesday, September 8th, 10:00 am5:30 pm
Wednesday, September 8thThursday, September 9th
Tuesday, September 7th, 4:00 pm5:30 pm
Friday, August 27th, 12:00 pm1:00 pm
Friday, August 20th, 1:00 pm3:00 pm