Sarnak's conjecture

December 10 to December 14, 2018

at the

American Institute of Mathematics, San Jose, California

organized by

Mariusz Lemanczyk and Maksym Radziwill

Original Announcement

This workshop will be devoted to the recent progress on Chowla and Sarnak's conjecture. Chowla's conjecture postulates the lack of correlation of the Liouville function with its shifts and is widely seen as an analogue of the twin prime conjecture. Sarnak's conjecture asserts that the Liouville function is asymptotically orthogonal to any sequence of topological entropy zero. In recent years it has emerged that the two conjectures are deeply related and indeed a large amount of progress has been made on both in tandem. We are at a stage in which it appears that both conjectures are within grasp, perhaps with a few new ideas. The objective of the workshop is to highlight where we stand on those questions and to chart a path for their proofs.

The main topics for the workshop are

• Tao's entropy decrement argument and its place within analytic number theory
• The local Fourier uniformity conjecture for the Liouville function, its relation with additive combinatorics, and Sarnak and Chowla's conjecture
• Recent work of Frantzikinakis-Host on the logarithmic Sarnak conjecture for ergodic weights
• Recent work of Tao-Teravainen on the odd cases of Chowla's conjecture
• Work of Matomaki-Radziwill on multiplicative functions in short intervals and its applications to Sarnak's and Chowla's conjectures
• Recent progress on specific cases of Sarnak's conjecture: for automatic sequences (Mullner), analytic skew products (Wang), etc.
• The classical techniques (Daboussi's criterion, joinings in ergodic theory): the relationship between them and their limitations

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Latinx mathematicians network

December 6 to December 7, 2018

at the

American Institute of Mathematics, San Jose, California

organized by

Jesus A. De Loera and Pamela E. Harris

Original Announcement

This workshop will be devoted to building a Network of Latinx Mathematicians, which will encourage Latinxs to pursue careers in the mathematical sciences, promote the advancement of Latinx currently in the discipline, and showcase the mathematics of Latinxs, especially those within the U.S.

The government predicts that by 2045 non-Hispanic whites will be a minority group within the U.S. population. In light of this fact, the sustainability of the future U.S. economy will require the integration of a new generation of Latinxs to the work force. This means that within 30 years the mathematical community should aim to see a proportional shift in the profession too; from the demand of workers and educators, as well as from the rise in numbers of students of color.

With the fast arrival of such a large demographic change, how can we better facilitate the access and recruitment of Latinxs into the mathematical sciences? What are the optimal strategies to allow for more participation of Latinxs at all levels of the mathematical profession? What are the key obstacles in teaching true representation with in the profession? What are realistic goals and directions in order to address the current underrepresentation of Latinxs in the mathematical sciences?

The purpose of this gathering of latinxs mathematicians and social activists from around the country is to reflect and plan on how to address the above questions.

Material from the workshop

A list of participants.

A report on the workshop activities.

Network of mathematicians of color

December 3 to December 4, 2018

at the

American Institute of Mathematics, San Jose, California

organized by

Michael Young and Shelby Wilson

Original Announcement

This workshop is devoted to building a Network of Mathematicians of Color, which will encourage African Americans to pursue careers in the mathematical sciences, promote the advancement of African Americans currently in the discipline, showcase the mathematics of African Americans, and generally create a space for African American mathematicians to engage with others from different professions/institution types.

African American mathematicians exists in a variety of professions and institution types. However, this group of mathematicians is not integrated across the spectrum. These brings up the following questions. What are the optimal strategies to allow for more participation of African American mathematicians at all levels of the mathematical profession? What are realistic goals and directions that should be thought about to strengthen the connections between African American mathematicians? What kind of events or set of events could be created to support this?

The purpose of this gathering of African American mathematicians from around the country is to reflect and plan on how to address the above questions.

Material from the workshop

A list of participants.

A report on the workshop activities.

Modeling the eye as a window on the body

October 15 to October 19, 2018

at the

American Institute of Mathematics, San Jose, California

organized by

Lucia Carichino, Simone Cassani, Sergey Lapin, and Alice Verticchio Vercellin

Original Announcement

This workshop will be devoted to bringing together experts in mathematical modeling, medical doctors and statisticians to share their perspectives and expertise with the final goal to develop a mathematical model linking the eye to the body. The eye represents a unique organ where first signs of systemic diseases, such as diabetes and hypertension, emerge and may be assessed with non-invasive techniques.

The main topics for the workshop are:

• Identification of the state of the art knowledge on modeling techniques and technologies used to study ocular and systemic diseases.
• Discussion on the main challenges of the mathematical coupling of the eye to other vascular systems and/or organs in the body.
• Implementation of the first steps for the development of the constitutive components of the coupled models.
• Identification of the statistical methods necessary for parameter, estimation and model validation of the coupled models under investigation.
• Development of a list of clinical questions of interest for the coupled mathematical models under investigation.

The central goal of the workshop is to use mathematical modeling, statistical analysis, and clinical data in synergy to help in the early diagnosis, follow up and treatment of ocular and systemic diseases. Since the condition of the eye is indicative of the one of the other organs in the body, coupled mathematical models are suitable tools to investigate correlations and/or to predict the effect of different diseases in different anatomical regions.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop Videos

Papers arising from the workshop: