Image by Alexei Borodin.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register.  This workshop will focus on the integrable aspect of random matrix theory and other related probability models such as random tilings, directed polymers, and interacting particle systems. The emphasis is on communicating diverse algebraic structures in these areas which allow the asymptotic analysis possible. Some of such structures are determinantal point processes, Toeplitz and Hankel determinants, Bethe ansatz, Yang-Baxter equation, Karlin-McGregor formula, Macdonald process, and stochastic six vertex model.

An illustration of the TASEP interface growth by Leonid Petrov and Hao Yu Li.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register.

This workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

In addition, this workshop will also explore connections with other branches of mathematics and applications to sciences and engineering. The workshop will feature presentations by both leading researchers and promising newcomers. There will be some special activities originally planned for the Connections Workshop: We will have a panel discussion of topics relevant to junior researchers, women, and minorities; a poster session for students and recent PhDs; and other social events.

This workshop is open to and welcomes all mathematicians.

An illustration of the TASEP interface growth by Leonid Petrov and Hao Yu Li.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register. This workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

Several executions of a 3-dimensional sumcheck protocol with a random order of directions (thanks to Dev Ojha for creating the diagram)

Proofs are at the foundations of mathematics. Viewed through the lens of theoretical computer science, verifying the correctness of a mathematical proof is a fundamental computational task. Indeed, the P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.

The complexity-theoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit local-to-global structure that allows verifying a proof by reading only a minuscule portion of it. As another example, interactive proofs allow for verification via a conversation between a prover and a verifier, instead of the traditional static sequence of logical statements. The study of such proof systems has drawn upon deep mathematical tools to derive numerous applications to the theory of computation and beyond.

In recent years, such probabilistic proofs received much attention due to a new motivation, delegation of computation, which is the emphasis of this summer school. This paradigm admits ultra-fast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recently-deployed technology, for example, as part of cryptographic constructions known as succinct non-interactive arguments of knowledge (SNARKs).

This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

a random quasiconformal map obtained from Beltrami equation by randomly assigning the values of +-1/2 for the Beltrami coefficient on small squares subdividing the unit square

This Summer Graduate School will cover basic tools that are instrumental in Random Conformal Geometry (the investigation of analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics) and are at the foundation of the subsequent semester-long program  "The Analysis and Geometry of Random Spaces".  Specific topics are Conformal Field Theory, Brownian Loops and related processes, Quasiconformal Maps, as well as Loewner Energy and Teichmüller Theory.

Image by Nick Schmitt

Figure 1. A rotationally symmetric solution to the self-duality equations on an open and dense subset of the torus. Singularities appear where the surface intersects the ideal boundary at infinity of the hyperbolic 3-space visualized by the wireframe.

Gauge theory is a geometric language used to formulate many fundamental physical phenomena, which has also had profound impact on our understanding of topology. The main idea is to study the space of solutions to partial differential equations admitting a very large group of local symmetries. Starting in the late 1970s, mathematicians began to unravel surprising connections between gauge theory and many aspects of geometric analysis, algebraic geometry and low-dimensional topology. This influence of gauge theory in geometry and topology is pervasive nowadays, and new developments continue to emerge.

The goal of the summer school is to introduce students to the foundational aspects of gauge theory, and explore their relations to geometric analysis and low-dimensional topology. By the end of the two-week program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the Yang-Mills ASD equations, the Seiberg-Witten equations, and the Hitchin equations) and some of their most impactful applications to problems in geometry and topology.

The African Diaspora Joint Mathematics Workshop (ADJOINT) will take place at the Mathematical Sciences Research Institute in Berkeley, CA from June 21 to July 2, 2021.

ADJOINT is a two-week summer activity designed for researchers with a Ph.D. degree in the mathematical sciences who are interested in conducting research in a collegial environment.  

The main objective of ADJOINT is to provide opportunities for in-person research collaboration to U.S. mathematicians, especially those from the African Diaspora, who will work in small groups with research leaders on various research projects. 

Through this effort, MSRI aims to establish and promote research communities that will foster and strengthen research productivity and career development among its participants. The ADJOINT workshops are designed to catalyze research collaborations, provide support for conferences to increase the visibility of the researchers, and to develop a sense of community among the mathematicians who attend. 

The end goal of this program is to enhance the mathematical sciences and its community by positively affecting the research and careers of African-American mathematicians and supporting their efforts to achieve full access and engagement in the broader research community. 

Each summer, three to five research leaders will each propose a research topic to be studied during a two-week workshop.

During the workshop, each participant will: 

• conduct research at MSRI within a group of four to five mathematicians under the direction of one of the research leaders 
• participate in professional enhancement activities provided by the onsite ADJOINT Director 
• receive funding for two weeks of lodging, meals and incidentals, and one round-trip travel to Berkeley, CA 

After the two-week workshop, each participant will:

• have the opportunity to further their research project with the team members including the research leader 
• have access to funding to attend conference(s) or to meet with other team members to pursue the research project, or to present results 
• become part of a network of research and career mentors

This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.

The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

In 2021, MSRI-UP will focus on Parking Functions: Choose your own adventure. The research program will be led by Dr. Pamela E. Harris, Associate Professor of Mathematics at Williams College.

The overarching goal of the Workshop on Mathematics and Racial Justice is to explore the role that mathematics plays in today’s movement for racial justice. For the purposes of this workshop, racial justice is the result of intentional, active and sustained anti-racist practices that identify and dismantle racist structures and policies that operate to oppress, disenfranchise, harm, and devalue Black people. This workshop will bring together mathematicians, statisticians, computer scientists, and STEM educators as well as members of the general public interested in using the tools of these disciplines to critically examine and eradicate racial disparities in society. Researchers with expertise or interest in problems at the intersection of mathematics, statistics and racial justice are encouraged to participate. This workshop will take place over two weeks and will include sessions on Bias in Algorithms and Technology; Fair Division, Allocation, and Representation; Public Health Disparities; and Racial Inequities in Mathematics Education.

The Corvaja-Zannier proof of Siegel's theorem using subspaces. Illustrated by Sofía Pastén Vásquez.

The theory of Diophantine equations is understood today as the study of algebraic points in algebraic varieties, and it is often the case that algebraic points of arithmetic relevance are expected to be sparse.

This summer school will introduce the participants to two of the main techniques in the subject: (i) the filtration method to prove algebraic degeneracy of integral points by means of the subspace theorem, leading to special cases of conjectures by Bombieri, Lang, and Vojta, and (ii) unlikely intersections through o-minimality and bi-algebraic geometry, leading to results in the context of the Manin-Mumford conjecture, the André-Oort conjecture, and generalizations. This SGS should provide an entry point to a very active research area in modern number theory.

The Sherrington-Kirkpatrick model, aka the randomly-weighted complete graph. Edge weights are indicated using grayscale. Six distinguished vertices have been randomly chosen; edges between those vertices are shaded black to form a "hidden signal".

The courses in this summer school focus on mathematical models of group dynamics, how to describe their dynamics and their scaling limits, and the connection to discrete and continuous optimization problems.

The phrase "group dynamics" is used loosely here -- it may refer to species migration, the spread of a virus, or the propagation of electrons through an inhomogeneous medium, to name a few examples. Very commonly, such systems can be described via stochastic processes which approximately behave like the solution of an appropriate partial differential equation in the large-population limit.

Image created by Nicolas Antille, of the visualization team of the Blue Brain Project at EPFL

This workshop will be held online May 4-7 and May 10-11, 2021. The Zoom link will be provided at a later time. You must register for the workshop to receive the password.  The workshop is held in Pacific Daylight Time.

The talks in this workshop will present a wide array of current applications of topology in neuroscience, including classification and synthesis of neuron morphologies, analysis of synaptic plasticity, algebraic analysis of the neural code, topological analysis of neural networks and their dynamics, topological decoding of neural activity, diagnosis of traumatic brain injuries, and topological biomarkers for psychiatric disease. Some of the talks will be devoted to promising new directions in algebraic topology that have been inspired by neuroscience.

Microlocal analysis originated in the study of linear partial differential equations (PDEs) in the high-frequency regime, through a combination of ideas from Fourier analysis and classical Hamiltonian mechanics. In parallel, similar ideas and methods had been developed since the early times of quantum mechanics, the smallness of Planck’s constant allowing to use semiclassical methods. The junction between these two points of view (microlocal and semiclassical) only emerged in 1970s, and has taken its full place in the PDE community in the last 20 years. This methodology resulted in major advances in the understanding of linear and nonlinear PDEs in the last 50 years. Moreover, microlocal methods continue to find new applications in diverse areas of mathematical analysis, such as the spectral theory of nonselfadjoint operators, scattering theory, and inverse problems.

NOTE: The introductory sessions for this workshop will be held online the morning of April 29th.  Additional sessions will be held when it is once again possible to meet in person.  Times listed on schedule is in Pacfic Standard Time.

The world is changing, along with perceptions. Many call for the improvement of mathematics teaching and learning, for both citizenry and STEM preparation. To achieve sustainable change, though, the focus needs to extend from individuals to systems. It is not enough to change one classroom or one course. Transformation requires change at all levels: in teaching, programmatic practices, and institutions. This workshop will bring together teachers and researchers from universities, community colleges, and K-12 schools to explore the reasons for and processes by which change in university mathematics departments is initiated, promoted, and sustained and lessons learned from change efforts in K-12. It will review what we know about change at all levels and reflect on stories of failure and success.

Speaker Abstracts

The advent of reliable computing machines, computer algebra systems, and multiple precision computational packages diminished the need for tables of reference values for computing function values by interpolation, but today's numerical analysts, scientific researchers, and software developers still need a way to confirm the accuracy of numerical algorithms that compute mathematical function values. The field of validated computation of mathematical functions explores the development of multiple precision codes that compute certifiably accurate function values that can be used to test the accuracy of function data from personal, commercial, or publicly available codes. We discuss the analysis used to obtain reliable error bounds for floating point approximations and describe the implementation of the work in a publicly available beta site. 

Water waves

The aim of the workshop is to bring together a broad array of researchers working on incompressible fluid dynamics. Some of the key topics to be covered are Euler flows, Navier Stokes equations as well as water wave flows and associated model equations. Some emphasis will also be placed on numerical analysis of the above evolutions.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Schedule of five minute talks

This workshop will be held online.  The Zoom link will be provided at a later time. You must register for the workshop to receive the password.  The workshop is held in Pacific Standard Time.

The workshop will address topics in the PDE analysis of the basic equations of the incompressible fluid dynamics (the Euler equations for inviscid flows, the Navier Stokes equations for viscous flows), interface problems (water waves), and other related equations. Open problems and connections to related branches of mathematics will be discussed, including the phenomena of turbulence and the zero viscosity limit. Both theoretical and numerical aspects of these topics will be considered. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

Image by Noomann Bassou

This workshop will be held online.  The Zoom link will be provided at a later time. You must register for the workshop to receive the password.  The workshop is held in Pacific Standard Time.

This workshop will feature talks by prominent female mathematicians whose research lies in and interfaces with mathematical fluids featuring water waves,  free boundaries, fluid structures,  viscous fluids and turbulence. The talks will be appropriate for graduate students, post-docs, and researchers in areas above mentioned. There will also be a panel discussion. This workshop is open to all mathematicians.

All scientific activities in this program will be available online so that those who can't attend in person are able to participate. If you are not a member of the program and would like to participate in any of the online activities, please fill out this REGISTRATION FORM.

PROGRAM DESCRIPTION

Fluid dynamics is one of the classical areas of partial differential equations, and has been the subject of extensive research over hundreds of years. It is perhaps one of the most challenging and exciting fields of scientific pursuit simply because of the complexity of the subject and the endless breadth of applications.

The focus of the program is on incompressible fluids, where water is a primary example. The fundamental equations in this area are the well-known Euler equations for inviscid fluids, and the Navier-Stokes equations for the viscous fluids. Relating the two is the problem of the zero viscosity limit, and its connection to the phenomena of turbulence. Water waves, or more generally interface problems in fluids, represent another target area for the program. Both theoretical and numerical aspects will be considered.

This is the general registration form for all seminars associated with the Mathematical Problems in Fluid Dynamics program. After registering, you will receive the zoom link information and will be added to the mailing list to receive weekly emails about all upcoming events.

In the context of several key states in the U.S.A, we will review the basics of COVID-19 and consider the post-lockdown dynamics.  In particular we will discuss the main drivers of the disease and the drawbacks to a natural herd immunity strategy. This talk represents joint work with Kamal Barley, Keisha Cook and Abba Gumel.