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

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.)

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), 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), 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 (Simons Institute, UC Berkeley), Andrew Warren (CMU), Manxi Wu (UC Berkeley), Manxi Wu (UC Berkeley), Yuchen Wu (Stanford University), Elizabeth Yang (UC Berkeley), Angela Zhou (Cornell University)

Workshops

Aug. 30Sep. 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)
Sep. 27Oct. 1, 2021

Organizers:

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

Organizers:

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

Organizers:

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

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

 Subscribe to the program calendar.

Internal Program Activities

Wednesday, December 1st 12:45 pm – 1:45 pm 
Next event (Weekly): Tuesday, December 7th 10:00 am – 11:00 am 
Next event (Weekly): Wednesday, December 8th 10:00 am – 11:00 am 
Wednesday, December 8th 11:00 am – 12:00 pm 
TBD
Wednesday, December 8th 2:30 pm – 3:30 pm 
Felix Otto (Max Planck Institute for Mathematics in the Sciences)
Next event (Weekly): Thursday, December 9th 11:00 am – 12:00 pm 
Next event (Weekly): Friday, December 10th 11:00 am – 12:00 pm 
Friday, December 10th 2:00 pm – 3:00 pm 

Past Internal Program Activities

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